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            <title>Geocaching IPhone App Review</title>
            <link>http://geocachinggpstreasurehunt.yolasite.com/index/index/geocaching-iphone-app-review</link>
            <description>by Chiffan from touchmyapps&lt;br&gt;&lt;br&gt;Ever since I read Treasure Island, my mind has been full of dreams of finding buried treasures and going on pirate adventures. Well, that was when I was but a wee little lad – since then I’ve cleared my head of such nonsense, but still, the idea of how great it would be to go on a real treasure hunt haunts me. And then I heard of Geocaching…&lt;br&gt;&lt;br&gt;Ok, to start it off, Geocaching is kind of a game, akin to 150-year-old letterboxing, and appeared shortly after the removal of “Select Availability” from GPS receivers back in 2000. It involves using a GPS receiver to hide and seek containers (“Geocaches”) anywhere in the world. So think of it as extremely advanced treasure hunting. The first cache was laid by Dave Ulmer and as of today, Nov 2 2009, there are over 933 160 active geocaches all over the world. And it was him who formulated the basic rule of the game, used to this day: You’ve got to log your find in the logbook in the cache and if you take something, you must leave something of equal or greater value. And that’s it.&lt;br&gt;&lt;br&gt;Talking about the app, Geocaching, it is actually basically an interface to the site Geocaching.com (the largest and oldest of the geocaching sites) but with a lot of great features thrown in. The app requires a valid Geocaching.com account and the info is synced between the app and website.&lt;br&gt;&lt;br&gt;Talking about features – you can do a full-fledged search using the app, including a quick search for nearby caches, or&amp;nbsp; searching by zip code, address or cache code. You can also view the whole list of results on the map. What is really great is that you can save the results for offline use. This is extremely useful, since you can mark what caches interest you and not waste any time looking them up each time. And it’s also invaluable if you’re abroad. If you want, you can also hide already discovered caches from the search.&lt;br&gt;&lt;br&gt;After you select the cache you’re going to seek out, you can view the route to it on the map. The map is pulled from Microsoft Virtual Earth or OpenStreetMap.org (configurable in settings). Personally I would recommend the Microsoft one. The app can also display the topographic (via OpenCycleMap.org) or satellite view (also from MS Virtual Earth). You can also place waypoints to ease navigation. The downside is that the map is not available in offline mode, which is odd, considering you can save the cache info from offline use. This made it extremely difficult for me to find the cache when I was on my vacation abroad and should definitely be addressed in the next update.&lt;br&gt;&lt;br&gt;Once you find a cache, you’re supposed to post this on the website. You can do this using the app, as well as mark the cache found. If you don’t have Internet access, the post is stored and can be later sent out from the settings tab. Another thing, useful for hardcore geocachers is the ability to follow their trackables (special items, placed in caches to be moved to other ones by friendly geocachers).&lt;br&gt;&lt;br&gt;The settings are quite simple, allowing you to toggle Metric or Imperial units, choose the data sources for the maps and filters. The help section features an extremely simple tutorial, which outlines the process and rules of geocaching in simple statements and comic-style pictures.&lt;br&gt;&lt;br&gt;All in all, if you haven’t yet joined the geocaching community, you should definitely try it out – it is a really fun way to spend the day. It is a real adventure and even my wife loved it (which says more than you can possibly imagine). I would recommend for you to try out the activity using the website or the Geocaching Intro (Access three geocaches near your current location only) in advance though, since it is free and will give you a feel for whether you’re ready to turn out $9.99 for the app. But for any geocacher, this is definitely a must. And the iPhone is perfect for this activity!&lt;br&gt;&lt;br style=&quot;font-family: yui-tmp;&quot;&gt;&lt;a class=&quot;&quot; title=&quot;&quot; href=&quot;http://www.touchmyapps.com/2009/11/02/geocaching-in-review/&quot;&gt;Geocaching GPS Treasure Hunt Review Source&lt;/a&gt;&lt;br&gt;&lt;br&gt;__________________________________________________&lt;br&gt;&lt;br&gt;A great Geocaching IPhone App review from touchmyapps. It is a good deal, good value for the experience. And they're right &quot;the IPhone is perfect for this activity&quot;.&lt;br&gt;</description>
            <pubDate>Fri, 13 Nov 2009 07:18:30 +0100</pubDate>
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            <title>GPS, how about Longitude...</title>
            <link>http://geocachinggpstreasurehunt.yolasite.com/index/index/gps-how-about-longitude-</link>
            <description>&lt;p&gt;&lt;b&gt;Longitude&lt;/b&gt; (pronounced &lt;span title=&quot;Pronunciation in the International Phonetic Alphabet (IPA)&quot; class=&quot;IPA&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Wikipedia:IPA_for_English&quot; title=&quot;Wikipedia:IPA for English&quot;&gt;/ˈlɒndʒɨtjuːd/&lt;/a&gt;&lt;/span&gt; or &lt;span title=&quot;Pronunciation in IPA&quot; class=&quot;IPA&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Wikipedia:IPA_for_English&quot; title=&quot;Wikipedia:IPA for English&quot;&gt;/ˈlɒŋɡɨtjuːd/&lt;/a&gt;&lt;/span&gt;),&lt;sup id=&quot;cite_ref-0&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Longitude#cite_note-0&quot;&gt;&lt;span&gt;[&lt;/span&gt;1&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt; identified by the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Greek_alphabet&quot; title=&quot;Greek alphabet&quot;&gt;Greek letter&lt;/a&gt; &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Lambda&quot; title=&quot;Lambda&quot;&gt;lambda&lt;/a&gt; (λ), is the &lt;a href=&quot;http://en.wikipedia.org/wiki/Geographic_coordinate&quot; title=&quot;Geographic coordinate&quot; class=&quot;mw-redirect&quot;&gt;geographic coordinate&lt;/a&gt; most commonly used in cartography and global navigation for east-west measurement. The line of longitude (&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Meridian_%28geography%29&quot; title=&quot;Meridian (geography)&quot;&gt;meridian&lt;/a&gt;) that passes through the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Royal_Observatory,_Greenwich&quot; title=&quot;Royal Observatory, Greenwich&quot;&gt;Royal Observatory, Greenwich&lt;/a&gt;, in England, establishes the meaning of zero degrees of longitude, or the &lt;a href=&quot;http://en.wikipedia.org/wiki/Prime_meridian&quot; title=&quot;Prime meridian&quot; class=&quot;mw-redirect&quot;&gt;prime meridian&lt;/a&gt;.
Any other longitude is identified by the east-west angle, referenced to
the center of the Earth as vertex, between the intersections with the
equator of the meridian through the location in question and the prime
meridian. A location's position along a meridian is given by its &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Latitude&quot; title=&quot;Latitude&quot;&gt;latitude&lt;/a&gt;, which is identified by the north-south angle between the local vertical and the plane of the equator.&lt;/p&gt;&lt;b&gt;&lt;span class=&quot;editsection&quot;&gt;&lt;/span&gt;&lt;span class=&quot;mw-headline&quot; id=&quot;History&quot;&gt;History&lt;/span&gt;&lt;/b&gt;

&lt;p&gt;&lt;a href=&quot;http://en.wikipedia.org/wiki/Mariner&quot; title=&quot;Mariner&quot; class=&quot;mw-redirect&quot;&gt;Mariners&lt;/a&gt; and &lt;a href=&quot;http://en.wikipedia.org/wiki/Explorer&quot; title=&quot;Explorer&quot; class=&quot;mw-redirect&quot;&gt;explorers&lt;/a&gt; for most of history struggled to determine precise longitude. Latitude was calculated by observing with &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Quadrant&quot; title=&quot;Quadrant&quot;&gt;quadrant&lt;/a&gt; or &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Astrolabe&quot; title=&quot;Astrolabe&quot;&gt;astrolabe&lt;/a&gt; the inclination of the sun or of charted stars, but longitude presented no such manifest means of study. &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Amerigo_Vespucci&quot; title=&quot;Amerigo Vespucci&quot;&gt;Amerigo Vespucci&lt;/a&gt;
was perhaps the first to proffer a solution, after devoting a great
deal of time and energy studying the problem during his sojourns in the
&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/New_World&quot; title=&quot;New World&quot;&gt;New World&lt;/a&gt;:&lt;/p&gt;
&lt;div class=&quot;floatleft&quot;&gt;&lt;a href=&quot;http://en.wikipedia.org/wiki/File:Longitude_Vespucci.png&quot; class=&quot;image&quot;&gt;&lt;img class=&quot;yui-img&quot; alt=&quot;Longitude Vespucci.png&quot; src=&quot;http://upload.wikimedia.org/wikipedia/commons/thumb/a/a6/Longitude_Vespucci.png/200px-Longitude_Vespucci.png&quot; width=&quot;200&quot; height=&quot;209&quot;&gt;&lt;/a&gt;&lt;br&gt;&lt;br&gt;By comparing the relative positions of the moon and Mars with their
anticipated positions, Vespucci was able to crudely deduce his
longitude. But this method had several limitations: First, it required
the occurrence of a specific astronomical event (in this case, Mars
passing through the same &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Right_ascension&quot; title=&quot;Right ascension&quot;&gt;right ascension&lt;/a&gt;
as the moon), and the observer needed to anticipate this event via an
astronomical almanac. One needed also to know the precise time, which
was difficult to ascertain in foreign lands. Finally, it required a
stable viewing platform, rendering the technique useless on the rolling
deck of a ship at sea.&lt;/div&gt;
&lt;p&gt;Unlike latitude, which has the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Equator&quot; title=&quot;Equator&quot;&gt;equator&lt;/a&gt;
as a natural starting position, there is no natural starting position
for longitude. Therefore, a reference meridian had to be chosen. It was
a popular practice to use a nation's capital as the starting point, but
other significant locations were also used. While &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Great_Britain&quot; title=&quot;Great Britain&quot;&gt;British&lt;/a&gt; cartographers had long used the Greenwich meridian in London, other references were used elsewhere, including: &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/El_Hierro&quot; title=&quot;El Hierro&quot;&gt;El Hierro&lt;/a&gt;, &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Rome&quot; title=&quot;Rome&quot;&gt;Rome&lt;/a&gt;, &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Copenhagen&quot; title=&quot;Copenhagen&quot;&gt;Copenhagen&lt;/a&gt;, &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Jerusalem&quot; title=&quot;Jerusalem&quot;&gt;Jerusalem&lt;/a&gt;, &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Saint_Petersburg&quot; title=&quot;Saint Petersburg&quot;&gt;Saint Petersburg&lt;/a&gt;, &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Pisa&quot; title=&quot;Pisa&quot;&gt;Pisa&lt;/a&gt;, &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Paris&quot; title=&quot;Paris&quot;&gt;Paris&lt;/a&gt;, &lt;a href=&quot;http://en.wikipedia.org/wiki/Philadelphia,_Pennsylvania&quot; title=&quot;Philadelphia, Pennsylvania&quot; class=&quot;mw-redirect&quot;&gt;Philadelphia&lt;/a&gt;, and &lt;a href=&quot;http://en.wikipedia.org/wiki/Washington,_DC&quot; title=&quot;Washington, DC&quot; class=&quot;mw-redirect&quot;&gt;Washington&lt;/a&gt;. In 1884, the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/International_Meridian_Conference&quot; title=&quot;International Meridian Conference&quot;&gt;International Meridian Conference&lt;/a&gt; adopted the Greenwich meridian as the &lt;i&gt;universal prime meridian&lt;/i&gt; or &lt;i&gt;zero point of longitude&lt;/i&gt;.&lt;/p&gt;
&lt;h2&gt;&lt;span class=&quot;editsection&quot;&gt;&lt;/span&gt;&lt;span class=&quot;mw-headline&quot; id=&quot;Noting_and_calculating_longitude&quot;&gt;Noting and calculating longitude&lt;/span&gt;&lt;/h2&gt;
&lt;p&gt;Longitude is given as an &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Angle&quot; title=&quot;Angle&quot;&gt;angular measurement&lt;/a&gt; ranging from 0° at the prime meridian to +180° eastward and −180° westward. The Greek letter λ (lambda),&lt;sup id=&quot;cite_ref-2&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Longitude#cite_note-2&quot;&gt;&lt;span&gt;[&lt;/span&gt;3&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt;&lt;sup id=&quot;cite_ref-3&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Longitude#cite_note-3&quot;&gt;&lt;span&gt;[&lt;/span&gt;4&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt; is used to denote the location of a place on Earth east or west of the prime meridian.&lt;/p&gt;
&lt;p&gt;Each degree of longitude is sub-divided into 60 &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Minute_of_arc&quot; title=&quot;Minute of arc&quot;&gt;minutes&lt;/a&gt;, each of which divided into 60 &lt;a href=&quot;http://en.wikipedia.org/wiki/Arcsecond&quot; title=&quot;Arcsecond&quot; class=&quot;mw-redirect&quot;&gt;seconds&lt;/a&gt;. A longitude is thus specified in &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Sexagesimal&quot; title=&quot;Sexagesimal&quot;&gt;sexagesimal&lt;/a&gt; notation as &lt;i&gt;23°&amp;nbsp;27′&amp;nbsp;30&quot;&amp;nbsp;E&lt;/i&gt;. For higher precision, the seconds are specified with a &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Decimal#Decimal_fractions&quot; title=&quot;Decimal&quot;&gt;decimal fraction&lt;/a&gt;.
An alternative representation uses degrees and minutes, where parts of
a minute are expressed in decimal notation with a fraction, thus: &lt;i&gt;23°&amp;nbsp;27.500′&amp;nbsp;E&lt;/i&gt;. Degrees may also be expressed as a decimal fraction: &lt;i&gt;23.45833°&amp;nbsp;E&lt;/i&gt;. For calculations, the angular measure may be converted to &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Radian&quot; title=&quot;Radian&quot;&gt;radians&lt;/a&gt;, so longitude may also be expressed in this manner as a signed fraction of π (&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Pi&quot; title=&quot;Pi&quot;&gt;pi&lt;/a&gt;), or an unsigned fraction of 2π.&lt;/p&gt;
&lt;p&gt;For calculations, the West/East suffix is replaced by a negative sign in the &lt;a href=&quot;http://en.wikipedia.org/wiki/Western_hemisphere&quot; title=&quot;Western hemisphere&quot; class=&quot;mw-redirect&quot;&gt;western hemisphere&lt;/a&gt;.
Confusingly, the convention of negative for East is also sometimes
seen. The preferred convention—that East be positive—is consistent with
a right-handed &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Cartesian_coordinate_system&quot; title=&quot;Cartesian coordinate system&quot;&gt;Cartesian coordinate system&lt;/a&gt; with the North Pole up. A specific longitude may then be combined with a specific latitude (usually positive in the &lt;a href=&quot;http://en.wikipedia.org/wiki/Northern_hemisphere&quot; title=&quot;Northern hemisphere&quot; class=&quot;mw-redirect&quot;&gt;northern hemisphere&lt;/a&gt;) to give a precise position on the Earth's surface.&lt;/p&gt;
&lt;p&gt;Longitude at a point may be determined by calculating the time difference between that at its location and &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Coordinated_Universal_Time&quot; title=&quot;Coordinated Universal Time&quot;&gt;Coordinated Universal Time&lt;/a&gt;
(UTC). Since there are 24 hours in a day and 360 degrees in a circle,
the sun moves across the sky at a rate of 15 degrees per hour (360°/24
hours = 15° per hour). So if the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Time_zone&quot; title=&quot;Time zone&quot;&gt;time zone&lt;/a&gt; a person is in is three hours ahead of UTC then that person is near 45° longitude (3 hours × 15° per hour = 45°). The word &lt;i&gt;near&lt;/i&gt;
was used because the point might not be at the center of the time zone;
also the time zones are defined politically, so their centers and
boundaries often do not lie on meridians at multiples of 15°. In order
to perform this calculation, however, a person needs to have a &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Marine_chronometer&quot; title=&quot;Marine chronometer&quot;&gt;chronometer&lt;/a&gt;
(watch) set to UTC and needs to determine local time by solar
observation or astronomical observation. The details are more complex
than described here: see the articles on &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Universal_Time&quot; title=&quot;Universal Time&quot;&gt;Universal Time&lt;/a&gt; and on the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Equation_of_time&quot; title=&quot;Equation of time&quot;&gt;equation of time&lt;/a&gt; for more details.&lt;/p&gt;
&lt;h2&gt;&lt;span class=&quot;editsection&quot;&gt;&lt;/span&gt;&lt;span class=&quot;mw-headline&quot; id=&quot;Plate_movement_and_longitude&quot;&gt;Plate movement and longitude&lt;/span&gt;&lt;/h2&gt;
&lt;p&gt;The surface layer of the Earth, the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Lithosphere&quot; title=&quot;Lithosphere&quot;&gt;lithosphere&lt;/a&gt;, is broken up into several &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Plate_tectonics&quot; title=&quot;Plate tectonics&quot;&gt;tectonic plates&lt;/a&gt;. Each plate moves in a different direction, at speeds of about 50 to 100&amp;nbsp;mm per year.&lt;sup id=&quot;cite_ref-4&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Longitude#cite_note-4&quot;&gt;&lt;span&gt;[&lt;/span&gt;5&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt; As a result, for example, the longitudinal difference between a point on the equator in Uganda (on the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/African_Plate&quot; title=&quot;African Plate&quot;&gt;African Plate&lt;/a&gt;) and a point on the equator in Ecuador (on the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/South_American_Plate&quot; title=&quot;South American Plate&quot;&gt;South American Plate&lt;/a&gt;) is increasing by about 0.0014 arcseconds per year.&lt;/p&gt;
&lt;p&gt;If a global reference frame such as &lt;a href=&quot;http://en.wikipedia.org/wiki/WGS84&quot; title=&quot;WGS84&quot; class=&quot;mw-redirect&quot;&gt;WGS84&lt;/a&gt;
is used, the longitude of a place on the surface will change from year
to year. To minimize this change, when dealing exclusively with points
on a single plate, a different reference frame can be used, whose
coordinates are fixed to a particular plate, such as &lt;a href=&quot;http://en.wikipedia.org/wiki/NAD83&quot; title=&quot;NAD83&quot; class=&quot;mw-redirect&quot;&gt;NAD83&lt;/a&gt; for North America or &lt;a href=&quot;http://en.wikipedia.org/wiki/ETRS89&quot; title=&quot;ETRS89&quot; class=&quot;mw-redirect&quot;&gt;ETRS89&lt;/a&gt; for Europe.&lt;/p&gt;
&lt;h2&gt;&lt;span class=&quot;editsection&quot;&gt;&lt;/span&gt;&lt;span class=&quot;mw-headline&quot; id=&quot;Elliptic_parameters&quot;&gt;Elliptic parameters&lt;/span&gt;&lt;/h2&gt;
&lt;p&gt;Because most planets (including Earth) are closer to &lt;i&gt;ellipsoids of revolution&lt;/i&gt;, or &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Oblate_spheroid&quot; title=&quot;Oblate spheroid&quot;&gt;spheroids&lt;/a&gt;, rather than to &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Sphere&quot; title=&quot;Sphere&quot;&gt;spheres&lt;/a&gt;,
both the radius and the length of arc varies with latitude. This
variation requires the introduction of elliptic parameters based on an
ellipse's &lt;b&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Angular_eccentricity&quot; title=&quot;Angular eccentricity&quot;&gt;angular eccentricity&lt;/a&gt;&lt;/b&gt;, &lt;img class=&quot;tex yui-img&quot; alt=&quot;o\!\varepsilon\,\!&quot; src=&quot;http://upload.wikimedia.org/math/9/d/a/9da837553648b46588ca5d0ef48cdb03.png&quot;&gt; (which equals &lt;img class=&quot;tex yui-img&quot; alt=&quot;\scriptstyle{\arccos(\frac{b}{a})}\,\!&quot; src=&quot;http://upload.wikimedia.org/math/d/d/6/dd698498d4ba83ed070f6c4f83dc7a9d.png&quot;&gt;, where &lt;img class=&quot;tex yui-img&quot; alt=&quot;a\;\!&quot; src=&quot;http://upload.wikimedia.org/math/1/6/f/16f45a094fa9fac788b8dbcc4a699133.png&quot;&gt; and &lt;img class=&quot;tex yui-img&quot; alt=&quot;b\;\!&quot; src=&quot;http://upload.wikimedia.org/math/7/5/d/75dc17277f9ca3ecc36acf3bc475dc09.png&quot;&gt; are the equatorial and polar radii; &lt;img class=&quot;tex yui-img&quot; alt=&quot;\scriptstyle{\sin(o\!\varepsilon)^2}\;\!&quot; src=&quot;http://upload.wikimedia.org/math/a/4/5/a451fe2e9bc6b9f5d5937f7bacdc6405.png&quot;&gt; is the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Eccentricity_%28mathematics%29&quot; title=&quot;Eccentricity (mathematics)&quot;&gt;first eccentricity&lt;/a&gt; squared, &lt;img class=&quot;tex yui-img&quot; alt=&quot;{e^2}\;\!&quot; src=&quot;http://upload.wikimedia.org/math/8/b/7/8b787522581d795f4903d676b57704b7.png&quot;&gt;; and &lt;img class=&quot;tex yui-img&quot; alt=&quot;\scriptstyle{2\sin(\frac{o\!\varepsilon}{2})^2}\;\!&quot; src=&quot;http://upload.wikimedia.org/math/2/0/7/20750d42d74c0210cb5d34cb0accec14.png&quot;&gt; or &lt;img class=&quot;tex yui-img&quot; alt=&quot;\scriptstyle{1-\cos(o\!\varepsilon)}\;\!&quot; src=&quot;http://upload.wikimedia.org/math/e/c/6/ec6e82dadbe0802b1cd3aeeaa464a4f5.png&quot;&gt; is the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Flattening&quot; title=&quot;Flattening&quot;&gt;flattening&lt;/a&gt;, &lt;img class=&quot;tex yui-img&quot; alt=&quot;{f}\;\!&quot; src=&quot;http://upload.wikimedia.org/math/2/4/8/248254f3cd6aa868ee79b402e6687aa5.png&quot;&gt;). Utilized in creating the &lt;a href=&quot;http://en.wikipedia.org/wiki/Integrand#Terminology_and_notation&quot; title=&quot;Integrand&quot; class=&quot;mw-redirect&quot;&gt;integrands&lt;/a&gt; for &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Curvature&quot; title=&quot;Curvature&quot;&gt;curvature&lt;/a&gt; is the inverse of the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Elliptic_integral#Incomplete_elliptic_integral_of_the_second_kind&quot; title=&quot;Elliptic integral&quot;&gt;principal elliptic integrand&lt;/a&gt;, &lt;img class=&quot;tex yui-img&quot; alt=&quot;E'\;\!&quot; src=&quot;http://upload.wikimedia.org/math/7/8/5/785972d6fd6a1085d02285c3f55df955.png&quot;&gt;:&lt;/p&gt;
&lt;dl&gt;&lt;dd&gt;
&lt;dl&gt;&lt;dd&gt;&lt;img class=&quot;tex yui-img&quot; alt=&quot;n'(\phi)=\frac{1}{E'(\phi)}=\frac{1}{\sqrt{1-\big(\sin(\phi)\sin(o\!\varepsilon)\big)^2}};\,\!&quot; src=&quot;http://upload.wikimedia.org/math/4/8/9/48997c9c05704ece25a952c5be22689a.png&quot;&gt;&lt;/dd&gt;&lt;dd&gt;&lt;img class=&quot;tex yui-img&quot; alt=&quot;\begin{align}M(\phi)&amp;amp;=a\cdot\cos(o\!\varepsilon)^2n'(\phi)^3=\frac{(ab)^2}{\Big((a\cos(\phi))^2+(b\sin(\phi))^2\Big)^{3/2}};\\
N(\phi)&amp;amp;=a{\cdot}n'(\phi)=\frac{a^2}{\sqrt{(a\cos(\phi))^2+(b\sin(\phi))^2}}.\end{align}\,\!&quot; src=&quot;http://upload.wikimedia.org/math/f/5/7/f57f04f35c165a5e3628dbce559a829a.png&quot;&gt;&lt;/dd&gt;&lt;/dl&gt;
&lt;/dd&gt;&lt;/dl&gt;
&lt;h2&gt;&lt;span class=&quot;editsection&quot;&gt;&lt;/span&gt;&lt;span class=&quot;mw-headline&quot; id=&quot;Degree_length&quot;&gt;Degree length&lt;/span&gt;&lt;/h2&gt;
&lt;p&gt;The length of an &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Degree_%28angle%29&quot; title=&quot;Degree (angle)&quot;&gt;arcdegree&lt;/a&gt; of north-south latitude difference, &lt;img class=&quot;tex yui-img&quot; alt=&quot;\scriptstyle{\Delta\phi}\;\!&quot; src=&quot;http://upload.wikimedia.org/math/e/e/e/eee4c5c44fb9232f5f0d46176b3036d2.png&quot;&gt;, is about 60 nautical miles, 111 kilometres or 69 &lt;a href=&quot;http://en.wikipedia.org/wiki/Statute_mile&quot; title=&quot;Statute mile&quot; class=&quot;mw-redirect&quot;&gt;statute miles&lt;/a&gt; at any latitude. The length of an arcdegree of east-west longitude difference, &lt;img class=&quot;tex yui-img&quot; alt=&quot;\scriptstyle{\cos(\phi)\Delta\lambda}\;\!&quot; src=&quot;http://upload.wikimedia.org/math/c/2/3/c23f6c5a490d6384f07140994d9a7460.png&quot;&gt;, is about the same at the equator as the north-south, reducing to zero at the poles.&lt;/p&gt;
&lt;p&gt;In the case of a spheroid, a &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Meridian_%28geography%29&quot; title=&quot;Meridian (geography)&quot;&gt;meridian&lt;/a&gt; and its anti-meridian form an &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Ellipse&quot; title=&quot;Ellipse&quot;&gt;ellipse&lt;/a&gt;, from which an exact expression for the length of an arcdegree of latitude is:&lt;/p&gt;
&lt;dl&gt;&lt;dd&gt;
&lt;dl&gt;&lt;dd&gt;&lt;img class=&quot;tex yui-img&quot; alt=&quot;\frac{\pi}{180^\circ}M(\phi).\;\!&quot; src=&quot;http://upload.wikimedia.org/math/1/5/b/15bf1d90a8265c87d3e7127976a92b15.png&quot;&gt;&lt;/dd&gt;&lt;/dl&gt;
&lt;/dd&gt;&lt;/dl&gt;
&lt;p&gt;This radius of arc (or &quot;arcradius&quot;) is in the plane of a meridian, and is known as the &lt;i&gt;meridional &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Radius_of_curvature_%28applications%29&quot; title=&quot;Radius of curvature (applications)&quot;&gt;radius of curvature&lt;/a&gt;&lt;/i&gt;, &lt;img class=&quot;tex yui-img&quot; alt=&quot;M\;\!&quot; src=&quot;http://upload.wikimedia.org/math/0/1/f/01ff7f895fd77d6be1da38f3e913d8ac.png&quot;&gt;.&lt;sup id=&quot;cite_ref-mathforum_5-0&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Longitude#cite_note-mathforum-5&quot;&gt;&lt;span&gt;[&lt;/span&gt;6&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt;&lt;sup id=&quot;cite_ref-snyder_6-0&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Longitude#cite_note-snyder-6&quot;&gt;&lt;span&gt;[&lt;/span&gt;7&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt;&lt;/p&gt;
&lt;p&gt;Similarly, an exact expression for the length of an arcdegree of longitude is:&lt;/p&gt;
&lt;dl&gt;&lt;dd&gt;
&lt;dl&gt;&lt;dd&gt;&lt;img class=&quot;tex yui-img&quot; alt=&quot;\frac{\pi}{180^\circ}\cos(\phi)N(\phi).\;\!&quot; src=&quot;http://upload.wikimedia.org/math/a/8/f/a8f454830b8b8f063500688fa6bbbb24.png&quot;&gt;&lt;/dd&gt;&lt;/dl&gt;
&lt;/dd&gt;&lt;/dl&gt;
&lt;p&gt;The arcradius contained here is in the plane of the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Prime_vertical&quot; title=&quot;Prime vertical&quot;&gt;prime vertical&lt;/a&gt;, the east-west plane perpendicular (or &quot;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Orthogonality&quot; title=&quot;Orthogonality&quot;&gt;normal&lt;/a&gt;&quot;) to both the plane of the meridian and the plane tangent to the surface of the ellipsoid, and is known as the &lt;i&gt;normal radius of curvature&lt;/i&gt;, &lt;img class=&quot;tex yui-img&quot; alt=&quot;N\;\!&quot; src=&quot;http://upload.wikimedia.org/math/6/3/1/631fe013c550a2dc153c1017cd15c438.png&quot;&gt;.&lt;sup id=&quot;cite_ref-mathforum_5-1&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Longitude#cite_note-mathforum-5&quot;&gt;&lt;span&gt;[&lt;/span&gt;6&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt;&lt;sup id=&quot;cite_ref-snyder_6-1&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Longitude#cite_note-snyder-6&quot;&gt;&lt;span&gt;[&lt;/span&gt;7&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt;&lt;/p&gt;
&lt;p&gt;Along the equator (east-west), &lt;img class=&quot;tex yui-img&quot; alt=&quot;N\;\!&quot; src=&quot;http://upload.wikimedia.org/math/6/3/1/631fe013c550a2dc153c1017cd15c438.png&quot;&gt; equals the equatorial radius. The radius of curvature at a &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Right_angle&quot; title=&quot;Right angle&quot;&gt;right angle&lt;/a&gt; to the equator (north-south), &lt;img class=&quot;tex yui-img&quot; alt=&quot;M\;\!&quot; src=&quot;http://upload.wikimedia.org/math/0/1/f/01ff7f895fd77d6be1da38f3e913d8ac.png&quot;&gt;,
is 43&amp;nbsp;km shorter, hence the length of an arcdegree of latitude at the
equator is about 1&amp;nbsp;km less than the length of an arcdegree of longitude
at the equator. The radii of curvature are equal at the poles where
they are about 64&amp;nbsp;km greater than the north-south equatorial radius of
curvature &lt;i&gt;because&lt;/i&gt; the polar radius is 21&amp;nbsp;km less than the
equatorial radius. The shorter polar radii indicate that the northern
and southern hemispheres are flatter, making their radii of curvature
longer. This flattening also 'pinches' the north-south equatorial
radius of curvature, making it 43&amp;nbsp;km less than the equatorial radius.
Both radii of curvature are perpendicular to the plane tangent to the
surface of the ellipsoid at all latitudes, directed toward a point on
the polar axis in the opposite hemisphere (except at the equator where
both point toward Earth's center). The east-west radius of curvature
reaches the axis, whereas the north-south radius of curvature is
shorter at all latitudes except the poles.&lt;/p&gt;
&lt;p&gt;The WGS84 ellipsoid, used by all &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Global_Positioning_System&quot; title=&quot;Global Positioning System&quot;&gt;GPS&lt;/a&gt;
devices, uses an equatorial radius of 6378137.0 m and an inverse
flattening, (1/f), of 298.257223563, hence its polar radius is
6356752.3142 m and its first eccentricity squared is 0.00669437999014.&lt;sup id=&quot;cite_ref-7&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Longitude#cite_note-7&quot;&gt;&lt;span&gt;[&lt;/span&gt;8&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt; The more recent but little used &lt;a href=&quot;http://en.wikipedia.org/wiki/IERS&quot; title=&quot;IERS&quot; class=&quot;mw-redirect&quot;&gt;IERS&lt;/a&gt;
2003 ellipsoid provides equatorial and polar radii of 6378136.6 and
6356751.9 m, respectively, and an inverse flattening of 298.25642.&lt;sup id=&quot;cite_ref-8&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Longitude#cite_note-8&quot;&gt;&lt;span&gt;[&lt;/span&gt;9&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt; Lengths of degrees on the WGS84 and IERS 2003 ellipsoids are the same when rounded to six &lt;a href=&quot;http://en.wikipedia.org/wiki/Significant_digit&quot; title=&quot;Significant digit&quot; class=&quot;mw-redirect&quot;&gt;significant digits&lt;/a&gt;. An appropriate calculator for any latitude is provided by the U.S. government's &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/National_Geospatial-Intelligence_Agency&quot; title=&quot;National Geospatial-Intelligence Agency&quot;&gt;National Geospatial-Intelligence Agency&lt;/a&gt; (NGA).&lt;sup id=&quot;cite_ref-9&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Longitude#cite_note-9&quot;&gt;&lt;span&gt;[&lt;/span&gt;10&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt;&lt;/p&gt;
&lt;table class=&quot;wikitable&quot;&gt;
&lt;tbody&gt;&lt;tr&gt;
&lt;th&gt;Latitude&lt;/th&gt;
&lt;th&gt;N-S radius&lt;br&gt;
of curvature&lt;br&gt;
&lt;img class=&quot;tex yui-img&quot; alt=&quot;M\;\!&quot; src=&quot;http://upload.wikimedia.org/math/0/1/f/01ff7f895fd77d6be1da38f3e913d8ac.png&quot;&gt;&lt;/th&gt;
&lt;th&gt;Surface distance&lt;br&gt;
per 1° change&lt;br&gt;
in latitude&lt;/th&gt;
&lt;th&gt;&lt;br&gt;&lt;/th&gt;
&lt;th&gt;E-W radius&lt;br&gt;
of curvature&lt;br&gt;
&lt;img class=&quot;tex yui-img&quot; alt=&quot;N\;\!&quot; src=&quot;http://upload.wikimedia.org/math/6/3/1/631fe013c550a2dc153c1017cd15c438.png&quot;&gt;&lt;/th&gt;
&lt;th&gt;Surface distance&lt;br&gt;
per 1° change&lt;br&gt;
in longitude&lt;/th&gt;
&lt;/tr&gt;
&lt;tr align=&quot;right&quot;&gt;
&lt;td&gt;0°&lt;/td&gt;
&lt;td&gt;6335.44&amp;nbsp;km&lt;/td&gt;
&lt;td&gt;110.574&amp;nbsp;km&lt;/td&gt;
&lt;td&gt;&lt;br&gt;&lt;/td&gt;
&lt;td&gt;6378.14&amp;nbsp;km&lt;/td&gt;
&lt;td&gt;111.320&amp;nbsp;km&lt;/td&gt;
&lt;/tr&gt;
&lt;tr align=&quot;right&quot;&gt;
&lt;td&gt;15°&lt;/td&gt;
&lt;td&gt;6339.70&amp;nbsp;km&lt;/td&gt;
&lt;td&gt;110.649&amp;nbsp;km&lt;/td&gt;
&lt;td&gt;&lt;br&gt;&lt;/td&gt;
&lt;td&gt;6379.57&amp;nbsp;km&lt;/td&gt;
&lt;td&gt;107.551&amp;nbsp;km&lt;/td&gt;
&lt;/tr&gt;
&lt;tr align=&quot;right&quot;&gt;
&lt;td&gt;30°&lt;/td&gt;
&lt;td&gt;6351.38&amp;nbsp;km&lt;/td&gt;
&lt;td&gt;110.852&amp;nbsp;km&lt;/td&gt;
&lt;td&gt;&lt;br&gt;&lt;/td&gt;
&lt;td&gt;6383.48&amp;nbsp;km&lt;/td&gt;
&lt;td&gt;96.486&amp;nbsp;km&lt;/td&gt;
&lt;/tr&gt;
&lt;tr align=&quot;right&quot;&gt;
&lt;td&gt;45°&lt;/td&gt;
&lt;td&gt;6367.38&amp;nbsp;km&lt;/td&gt;
&lt;td&gt;111.132&amp;nbsp;km&lt;/td&gt;
&lt;td&gt;&lt;br&gt;&lt;/td&gt;
&lt;td&gt;6388.84&amp;nbsp;km&lt;/td&gt;
&lt;td&gt;78.847&amp;nbsp;km&lt;/td&gt;
&lt;/tr&gt;
&lt;tr align=&quot;right&quot;&gt;
&lt;td&gt;60°&lt;/td&gt;
&lt;td&gt;6383.45&amp;nbsp;km&lt;/td&gt;
&lt;td&gt;111.412&amp;nbsp;km&lt;/td&gt;
&lt;td&gt;&lt;br&gt;&lt;/td&gt;
&lt;td&gt;6394.21&amp;nbsp;km&lt;/td&gt;
&lt;td&gt;55.800&amp;nbsp;km&lt;/td&gt;
&lt;/tr&gt;
&lt;tr align=&quot;right&quot;&gt;
&lt;td&gt;75°&lt;/td&gt;
&lt;td&gt;6395.26&amp;nbsp;km&lt;/td&gt;
&lt;td&gt;111.618&amp;nbsp;km&lt;/td&gt;
&lt;td&gt;&lt;br&gt;&lt;/td&gt;
&lt;td&gt;6398.15&amp;nbsp;km&lt;/td&gt;
&lt;td&gt;28.902&amp;nbsp;km&lt;/td&gt;
&lt;/tr&gt;
&lt;tr align=&quot;right&quot;&gt;
&lt;td&gt;90°&lt;/td&gt;
&lt;td&gt;6399.59&amp;nbsp;km&lt;/td&gt;
&lt;td&gt;111.694&amp;nbsp;km&lt;/td&gt;
&lt;td&gt;&lt;br&gt;&lt;/td&gt;
&lt;td&gt;6399.59&amp;nbsp;km&lt;/td&gt;
&lt;td&gt;0.000&amp;nbsp;km&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;&lt;/table&gt;
&lt;h2&gt;&lt;span class=&quot;editsection&quot;&gt;&lt;/span&gt;&lt;span class=&quot;mw-headline&quot; id=&quot;Ecliptic_latitude_and_longitude&quot;&gt;Ecliptic latitude and longitude&lt;/span&gt;&lt;/h2&gt;
&lt;p&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Ecliptic&quot; title=&quot;Ecliptic&quot;&gt;Ecliptic&lt;/a&gt;
latitude and longitude are defined for the planets, stars, and other
celestial bodies in a broadly similar way to that in which terrestrial
latitude and longitude are defined, but there is a special difference.&lt;/p&gt;
&lt;p&gt;The plane of zero latitude for celestial objects is not parallel to
the plane of the celestial and terrestrial equator: it is the plane of
the ecliptic. This is inclined to the equator by the &quot;&lt;a href=&quot;http://en.wikipedia.org/wiki/Obliquity_of_the_ecliptic&quot; title=&quot;Obliquity of the ecliptic&quot; class=&quot;mw-redirect&quot;&gt;obliquity of the ecliptic&lt;/a&gt;&quot;, currently about 23° 26'. The closest celestial counterpart to terrestrial latitude is &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Declination&quot; title=&quot;Declination&quot;&gt;declination&lt;/a&gt;, and the closest celestial counterpart to terrestrial longitude is &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Right_ascension&quot; title=&quot;Right ascension&quot;&gt;right ascension&lt;/a&gt;.
These celestial coordinates bear the same relationship to the celestial
equator as terrestrial latitude and longitude do to the terrestrial
equator, and they are also more frequently used in astronomy than
celestial longitude and latitude.&lt;/p&gt;
&lt;p&gt;The polar axis (relative to the celestial equator) is perpendicular
to the plane of the equator, and parallel to the terrestrial polar
axis. But the (north) pole of the ecliptic, relevant to the definition
of ecliptic latitude, is the normal to the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Ecliptic&quot; title=&quot;Ecliptic&quot;&gt;ecliptic&lt;/a&gt; plane nearest to the direction of the celestial north pole of the equator, i.e. 23° 26' away from it.&lt;/p&gt;
&lt;p&gt;Ecliptic latitude is measured from 0° to 90° north (+) or south (−) of the ecliptic. &lt;a href=&quot;http://en.wikipedia.org/wiki/Ecliptic_longitude&quot; title=&quot;Ecliptic longitude&quot; class=&quot;mw-redirect&quot;&gt;Ecliptic longitude&lt;/a&gt;
is measured from 0° to 360° eastward (the direction that the Sun
appears to move relative to the stars), along the ecliptic from the &lt;a href=&quot;http://en.wikipedia.org/wiki/Vernal_equinox&quot; title=&quot;Vernal equinox&quot; class=&quot;mw-redirect&quot;&gt;vernal equinox&lt;/a&gt;. The equinox at a specific date and time is a fixed equinox, such as that in the &lt;a href=&quot;http://en.wikipedia.org/wiki/J2000&quot; title=&quot;J2000&quot; class=&quot;mw-redirect&quot;&gt;J2000&lt;/a&gt; reference frame.&lt;/p&gt;
&lt;p&gt;However, the equinox moves because it is the intersection of two
planes, both of which move. The ecliptic is relatively stationary,
wobbling within a 4° diameter circle relative to the fixed stars over
millions of years under the gravitational influence of the other
planets. The greatest movement is a relatively rapid gyration of
Earth's equatorial plane whose pole traces a 47° diameter circle caused
by the Moon. This causes the equinox to &lt;a href=&quot;http://en.wikipedia.org/wiki/Precession_%28astronomy%29&quot; title=&quot;Precession (astronomy)&quot; class=&quot;mw-redirect&quot;&gt;precess&lt;/a&gt; westward along the ecliptic about 50&quot; per year. This moving equinox is called the &lt;i&gt;equinox of date&lt;/i&gt;.
Ecliptic longitude relative to a moving equinox is used whenever the
positions of the Sun, Moon, planets, or stars at dates other than that
of a fixed equinox is important, as in &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Calendar&quot; title=&quot;Calendar&quot;&gt;calendars&lt;/a&gt;, &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Astrology&quot; title=&quot;Astrology&quot;&gt;astrology&lt;/a&gt;, or &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Celestial_mechanics&quot; title=&quot;Celestial mechanics&quot;&gt;celestial mechanics&lt;/a&gt;. The 'error' of the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Julian_calendar&quot; title=&quot;Julian calendar&quot;&gt;Julian&lt;/a&gt; or &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Gregorian_calendar&quot; title=&quot;Gregorian calendar&quot;&gt;Gregorian calendar&lt;/a&gt; is always relative to a moving equinox. The years, months, and days of the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Chinese_calendar&quot; title=&quot;Chinese calendar&quot;&gt;Chinese calendar&lt;/a&gt; all depend on the ecliptic longitudes &lt;i&gt;of date&lt;/i&gt;
of the Sun and Moon. The 30° zodiacal segments used in astrology are
also relative to a moving equinox. Celestial mechanics (here restricted
to the motion of &lt;a href=&quot;http://en.wikipedia.org/wiki/Solar_system&quot; title=&quot;Solar system&quot; class=&quot;mw-redirect&quot;&gt;solar system&lt;/a&gt; bodies) uses both a fixed and moving equinox. Sometimes in the study of &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Milankovitch_cycles&quot; title=&quot;Milankovitch cycles&quot;&gt;Milankovitch cycles&lt;/a&gt;, the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Invariable_plane&quot; title=&quot;Invariable plane&quot;&gt;invariable plane&lt;/a&gt; of the solar system is substituted for the moving ecliptic. Longitude may be denominated from 0 to &lt;img class=&quot;tex yui-img&quot; alt=&quot;\begin{matrix}2\pi\end{matrix}&quot; src=&quot;http://upload.wikimedia.org/math/5/0/9/50980564a2ef3433ab3a71ea7dae375d.png&quot;&gt; radians in either case.&lt;/p&gt;
&lt;h2&gt;&lt;span class=&quot;editsection&quot;&gt;&lt;/span&gt;&lt;span class=&quot;mw-headline&quot; id=&quot;Longitude_on_bodies_other_than_Earth&quot;&gt;Longitude on bodies other than Earth&lt;/span&gt;&lt;/h2&gt;
&lt;p&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Planet&quot; title=&quot;Planet&quot;&gt;Planetary&lt;/a&gt; co-ordinate systems are defined relative to their mean &lt;a href=&quot;http://en.wikipedia.org/wiki/Axis_of_rotation&quot; title=&quot;Axis of rotation&quot; class=&quot;mw-redirect&quot;&gt;axis of rotation&lt;/a&gt;
and various definitions of longitude depending on the body. The
longitude systems of most of those bodies with observable rigid
surfaces have been defined by references to a surface feature such as a
&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Impact_crater&quot; title=&quot;Impact crater&quot;&gt;crater&lt;/a&gt;. The &lt;a href=&quot;http://en.wikipedia.org/wiki/North_pole&quot; title=&quot;North pole&quot; class=&quot;mw-redirect&quot;&gt;north pole&lt;/a&gt; is that pole of rotation that lies on the north side of the invariable plane of the solar system (near the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Ecliptic&quot; title=&quot;Ecliptic&quot;&gt;ecliptic&lt;/a&gt;).
The location of the prime meridian as well as the position of body's
north pole on the celestial sphere may vary with time due to precession
of the axis of rotation of the planet (or satellite). If the position
angle of the body's prime meridian increases with time, the body has a
direct (or &lt;a href=&quot;http://en.wikipedia.org/wiki/Direct_motion&quot; title=&quot;Direct motion&quot; class=&quot;mw-redirect&quot;&gt;prograde&lt;/a&gt;) rotation; otherwise the rotation is said to be &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Retrograde_motion&quot; title=&quot;Retrograde motion&quot;&gt;retrograde&lt;/a&gt;.&lt;/p&gt;
&lt;p&gt;In the absence of other information, the axis of rotation is assumed to be normal to the mean &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Orbital_plane_%28astronomy%29&quot; title=&quot;Orbital plane (astronomy)&quot;&gt;orbital plane&lt;/a&gt;; &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Mercury_%28planet%29&quot; title=&quot;Mercury (planet)&quot;&gt;Mercury&lt;/a&gt;
and most of the satellites are in this category. For many of the
satellites, it is assumed that the rotation rate is equal to the mean &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Orbital_period&quot; title=&quot;Orbital period&quot;&gt;orbital period&lt;/a&gt;. In the case of the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Gas_giant&quot; title=&quot;Gas giant&quot;&gt;giant planets&lt;/a&gt;, since their surface features are constantly changing and moving at various rates, the rotation of their &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Magnetic_field&quot; title=&quot;Magnetic field&quot;&gt;magnetic fields&lt;/a&gt; is used as a reference instead. In the case of the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Sun&quot; title=&quot;Sun&quot;&gt;Sun&lt;/a&gt;,
even this criterion fails (because its magnetosphere is very complex
and does not really rotate in a steady fashion), and an agreed-upon
value for the rotation of its equator is used instead.&lt;/p&gt;
&lt;p&gt;For &lt;i&gt;planetographic longitude&lt;/i&gt;, west longitudes (i.e.,
longitudes measured positively to the west) are used when the rotation
is prograde, and east longitudes (i.e., longitudes measured positively
to the east) when the rotation is retrograde. In simpler terms, imagine
a distant, non-orbiting observer viewing a planet as it rotates. Also
suppose that this observer is within the plane of the planet's equator.
A point on the equator that passes directly in front of this observer
later in time has a higher planetographic longitude than a point that
did so earlier in time.&lt;/p&gt;
&lt;p&gt;However, &lt;i&gt;planetocentric longitude&lt;/i&gt; is always measured positively to the east, regardless of which way the planet rotates. &lt;i&gt;East&lt;/i&gt;
is defined as the counter-clockwise direction around the planet, as
seen from above its north pole, and the north pole is whichever pole
more closely aligns with the Earth's north pole. Longitudes
traditionally have been written using &quot;E&quot; or &quot;W&quot; instead of &quot;+&quot; or &quot;−&quot;
to indicate this polarity. For example, the following all mean the same
thing:&lt;/p&gt;
&lt;ul&gt;&lt;li&gt;−91°&lt;/li&gt;&lt;li&gt;91°W&lt;/li&gt;&lt;li&gt;+269°&lt;/li&gt;&lt;li&gt;269°E.&lt;/li&gt;&lt;/ul&gt;
&lt;p&gt;The reference surfaces for some planets (such as Earth and &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Mars&quot; title=&quot;Mars&quot;&gt;Mars&lt;/a&gt;) are &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Ellipsoid&quot; title=&quot;Ellipsoid&quot;&gt;ellipsoids&lt;/a&gt;
of revolution for which the equatorial radius is larger than the polar
radius; in other words, they are oblate spheroids. Smaller bodies (&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Io_%28moon%29&quot; title=&quot;Io (moon)&quot;&gt;Io&lt;/a&gt;, &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Mimas_%28moon%29&quot; title=&quot;Mimas (moon)&quot;&gt;Mimas&lt;/a&gt;,
etc.) tend to be better approximated by triaxial ellipsoids; however,
triaxial ellipsoids would render many computations more complicated,
especially those related to &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Map_projection&quot; title=&quot;Map projection&quot;&gt;map projections&lt;/a&gt;.
Many projections would lose their elegant and popular properties. For
this reason spherical reference surfaces are frequently used in mapping
programs.&lt;/p&gt;
&lt;p&gt;The modern standard for maps of Mars (since about 2002) is to use
planetocentric coordinates. The meridian of Mars is located at &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Airy-0&quot; title=&quot;Airy-0&quot;&gt;Airy-0&lt;/a&gt; crater.&lt;sup id=&quot;cite_ref-10&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Longitude#cite_note-10&quot;&gt;&lt;span&gt;[&lt;/span&gt;11&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt;&lt;/p&gt;
&lt;p&gt;&lt;a href=&quot;http://en.wikipedia.org/wiki/Tidal_lock&quot; title=&quot;Tidal lock&quot; class=&quot;mw-redirect&quot;&gt;Tidally-locked&lt;/a&gt; bodies have a natural reference longitude passing through the point nearest to their parent body.&lt;sup id=&quot;cite_ref-11&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Longitude#cite_note-11&quot;&gt;&lt;span&gt;[&lt;/span&gt;12&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt; However, &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Libration&quot; title=&quot;Libration&quot;&gt;libration&lt;/a&gt; due to non-circular orbits or axial tilts causes this point to move around any fixed point on the celestial body like an &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Analemma&quot; title=&quot;Analemma&quot;&gt;analemma&lt;/a&gt;.&lt;/p&gt;&lt;p&gt;__________________________________________________&lt;/p&gt;&lt;p&gt;As with my previous post, have you ever wondered what is that longitude in your GPS? Why did you even bother? Haha!&lt;br&gt;&lt;/p&gt;</description>
            <pubDate>Fri, 13 Nov 2009 07:08:30 +0100</pubDate>
        </item>
        <item>
            <title>GPS, Latitude...</title>
            <link>http://geocachinggpstreasurehunt.yolasite.com/index/index/gps-latitude-</link>
            <description>&lt;p&gt;&lt;b&gt;Latitude&lt;/b&gt;, usually denoted by the Greek letter &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Phi_%28letter%29&quot; title=&quot;Phi (letter)&quot;&gt;phi&lt;/a&gt; (&lt;a href=&quot;http://en.wikipedia.org/wiki/%CE%A6&quot; title=&quot;Φ&quot; class=&quot;mw-redirect&quot;&gt;φ&lt;/a&gt;) gives the location of a place on &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Earth&quot; title=&quot;Earth&quot;&gt;Earth&lt;/a&gt; (or other planetary body) north or south of the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Equator&quot; title=&quot;Equator&quot;&gt;equator&lt;/a&gt;. &lt;b&gt;Lines of Latitude&lt;/b&gt; are the imaginary horizontal lines shown running east-to-west (or west to east) on maps (particularly so in the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Mercator_projection&quot; title=&quot;Mercator projection&quot;&gt;Mercator projection&lt;/a&gt;) that run either north or south of the equator. Technically, latitude is an &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Angle&quot; title=&quot;Angle&quot;&gt;angular measurement&lt;/a&gt; in &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Degree_%28angle%29&quot; title=&quot;Degree (angle)&quot;&gt;degrees&lt;/a&gt; (marked with °) ranging from 0° at the equator (&lt;a href=&quot;http://en.wikipedia.org/wiki/Low_latitude&quot; title=&quot;Low latitude&quot; class=&quot;mw-redirect&quot;&gt;low latitude&lt;/a&gt;) to 90° at the poles (90° N or +90° for the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/North_Pole&quot; title=&quot;North Pole&quot;&gt;North Pole&lt;/a&gt; and 90° S or −90° for the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/South_Pole&quot; title=&quot;South Pole&quot;&gt;South Pole&lt;/a&gt;). The latitude is approximately the angle between straight up at the surface (the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Zenith&quot; title=&quot;Zenith&quot;&gt;zenith&lt;/a&gt;) and the sun at an &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Equinox&quot; title=&quot;Equinox&quot;&gt;equinox&lt;/a&gt;. The &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Complementary_angles&quot; title=&quot;Complementary angles&quot;&gt;complementary angle&lt;/a&gt; of a latitude is called the &lt;b&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Colatitude&quot; title=&quot;Colatitude&quot;&gt;colatitude&lt;/a&gt;&lt;/b&gt;.&lt;/p&gt;&lt;b&gt;&lt;span class=&quot;editsection&quot;&gt;&lt;/span&gt;&lt;span class=&quot;mw-headline&quot; id=&quot;Circles_of_latitude&quot;&gt;Circles of latitude&lt;/span&gt;&lt;/b&gt;

&lt;p&gt;All locations of a given latitude are collectively referred to as a &lt;i&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Circle_of_latitude&quot; title=&quot;Circle of latitude&quot;&gt;circle of latitude&lt;/a&gt;&lt;/i&gt; or &lt;i&gt;line of latitude&lt;/i&gt; or &lt;i&gt;parallel&lt;/i&gt;, because they are &lt;a href=&quot;http://en.wikipedia.org/wiki/Coplanar&quot; title=&quot;Coplanar&quot; class=&quot;mw-redirect&quot;&gt;coplanar&lt;/a&gt;, and all such &lt;a href=&quot;http://en.wikipedia.org/wiki/Plane_%28mathematics%29&quot; title=&quot;Plane (mathematics)&quot; class=&quot;mw-redirect&quot;&gt;planes&lt;/a&gt; are &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Parallel_%28geometry%29&quot; title=&quot;Parallel (geometry)&quot;&gt;parallel&lt;/a&gt; to the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Equator&quot; title=&quot;Equator&quot;&gt;equator&lt;/a&gt;. Lines of latitude other than the Equator are approximately &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Small_circle&quot; title=&quot;Small circle&quot;&gt;small circles&lt;/a&gt; on the surface of the Earth; they are not &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Geodesic&quot; title=&quot;Geodesic&quot;&gt;geodesics&lt;/a&gt;
since the shortest route between two points at the same latitude
involves a path that bulges toward the nearest pole, first moving
farther away from and then back toward the equator (see &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Great_circle&quot; title=&quot;Great circle&quot;&gt;great circle&lt;/a&gt;).&lt;/p&gt;
&lt;div class=&quot;thumb tright&quot;&gt;
&lt;div class=&quot;thumbinner&quot; style=&quot;width: 302px;&quot;&gt;&lt;a href=&quot;http://en.wikipedia.org/wiki/File:Parallel_45.jpg&quot; class=&quot;image&quot;&gt;&lt;img alt=&quot;&quot; src=&quot;http://upload.wikimedia.org/wikipedia/commons/thumb/5/5e/Parallel_45.jpg/300px-Parallel_45.jpg&quot; class=&quot;thumbimage yui-img&quot; width=&quot;300&quot; height=&quot;242&quot;&gt;&lt;/a&gt;&lt;/div&gt;
&lt;/div&gt;
&lt;p&gt;A specific latitude may then be combined with a specific &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Longitude&quot; title=&quot;Longitude&quot;&gt;longitude&lt;/a&gt; to give a precise position on the Earth's surface (see &lt;a href=&quot;http://en.wikipedia.org/wiki/Satellite_navigation_system&quot; title=&quot;Satellite navigation system&quot; class=&quot;mw-redirect&quot;&gt;satellite navigation system&lt;/a&gt;).&lt;/p&gt;
&lt;h3&gt;&lt;span class=&quot;editsection&quot;&gt;I&lt;/span&gt;&lt;span class=&quot;mw-headline&quot; id=&quot;Important_named_circles_of_latitude&quot;&gt;mportant named circles of latitude&lt;/span&gt;&lt;/h3&gt;
&lt;p&gt;Besides the equator, four other lines of latitude are named because
of the role they play in the geometrical relationship with the Earth
and the Sun:&lt;/p&gt;
&lt;ul&gt;&lt;li&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Arctic_Circle&quot; title=&quot;Arctic Circle&quot;&gt;Arctic Circle&lt;/a&gt;: 66° 33′ 39″ N&lt;/li&gt;&lt;li&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Tropic_of_Cancer&quot; title=&quot;Tropic of Cancer&quot;&gt;Tropic of Cancer&lt;/a&gt;: 23° 26′ 21″ N&lt;/li&gt;&lt;li&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Tropic_of_Capricorn&quot; title=&quot;Tropic of Capricorn&quot;&gt;Tropic of Capricorn&lt;/a&gt;: 23° 26′ 21″ S&lt;/li&gt;&lt;li&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Antarctic_Circle&quot; title=&quot;Antarctic Circle&quot;&gt;Antarctic Circle&lt;/a&gt;: 66° 33′ 39″ S&lt;/li&gt;&lt;/ul&gt;
&lt;p&gt;Only at latitudes between the Tropics is it possible for the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Sun&quot; title=&quot;Sun&quot;&gt;sun&lt;/a&gt; to be at the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Zenith&quot; title=&quot;Zenith&quot;&gt;zenith&lt;/a&gt;. Only north of the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Arctic_Circle&quot; title=&quot;Arctic Circle&quot;&gt;Arctic Circle&lt;/a&gt; or south of the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Antarctic_Circle&quot; title=&quot;Antarctic Circle&quot;&gt;Antarctic Circle&lt;/a&gt; is the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Midnight_sun&quot; title=&quot;Midnight sun&quot;&gt;midnight sun&lt;/a&gt; possible.&lt;/p&gt;
&lt;p&gt;The reason that these lines have the values that they do lies in the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Axial_tilt&quot; title=&quot;Axial tilt&quot;&gt;axial tilt&lt;/a&gt; of the Earth with respect to the sun, which is &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Degree_%28angle%29&quot; title=&quot;Degree (angle)&quot;&gt;23° 26′ 21.41″&lt;/a&gt;.&lt;/p&gt;
&lt;p&gt;Note that the Arctic Circle and Tropic of Cancer are colatitudes,
since the sum of their angles is 90°—similarly for the Antarctic Circle
and Tropic of Capricorn.&lt;/p&gt;
&lt;h2&gt;&lt;span class=&quot;editsection&quot;&gt;&lt;/span&gt;&lt;span class=&quot;mw-headline&quot; id=&quot;Subdivisions&quot;&gt;Subdivisions&lt;/span&gt;&lt;/h2&gt;
&lt;p&gt;A degree is divided into 60 &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Minute_of_arc&quot; title=&quot;Minute of arc&quot;&gt;minutes&lt;/a&gt;.
One minute can be further divided into 60 seconds. An example of a
latitude specified in this way is 13°19'43″ N (for greater precision, a
decimal fraction can be added to the seconds). An alternative
representation uses only degrees and minutes, where the seconds are
expressed as a decimal fraction of minutes: the above example would be
expressed as 13°19.717' N. Degrees can also be expressed singularly,
with both the minutes and seconds incorporated as a decimal number and
rounded as desired (decimal degree notation): 13.32861° N. Sometimes,
the north/south suffix is replaced by a negative sign for south (−90°
for the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/South_Pole&quot; title=&quot;South Pole&quot;&gt;South Pole&lt;/a&gt;).&lt;/p&gt;
&lt;h2&gt;&lt;span class=&quot;editsection&quot;&gt;&lt;/span&gt;&lt;span class=&quot;mw-headline&quot; id=&quot;Effect_of_latitude&quot;&gt;Effect of latitude&lt;/span&gt;&lt;/h2&gt;
&lt;div class=&quot;thumb tright&quot;&gt;
&lt;div class=&quot;thumbinner&quot; style=&quot;width: 182px;&quot;&gt;&lt;a href=&quot;http://en.wikipedia.org/wiki/File:Annual_Average_Temperature_Map.jpg&quot; class=&quot;image&quot;&gt;&lt;img alt=&quot;&quot; src=&quot;http://upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Annual_Average_Temperature_Map.jpg/180px-Annual_Average_Temperature_Map.jpg&quot; class=&quot;thumbimage yui-img&quot; width=&quot;180&quot; height=&quot;139&quot;&gt;&lt;/a&gt;&lt;/div&gt;&lt;/div&gt;&lt;p&gt;A region's latitude has a great effect on its &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Climate&quot; title=&quot;Climate&quot;&gt;climate&lt;/a&gt; and &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Weather&quot; title=&quot;Weather&quot;&gt;weather&lt;/a&gt; (see &lt;i&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Effect_of_sun_angle_on_climate&quot; title=&quot;Effect of sun angle on climate&quot;&gt;Effect of sun angle on climate&lt;/a&gt;&lt;/i&gt;). Latitude more loosely determines tendencies in &lt;a href=&quot;http://en.wikipedia.org/wiki/Polar_aurora&quot; title=&quot;Polar aurora&quot; class=&quot;mw-redirect&quot;&gt;polar auroras&lt;/a&gt;, &lt;a href=&quot;http://en.wikipedia.org/wiki/Prevailing_wind&quot; title=&quot;Prevailing wind&quot; class=&quot;mw-redirect&quot;&gt;prevailing winds&lt;/a&gt;, and other physical characteristics of geographic locations.&lt;/p&gt;
&lt;p&gt;Researchers at &lt;a href=&quot;http://en.wikipedia.org/wiki/Harvard&quot; title=&quot;Harvard&quot; class=&quot;mw-redirect&quot;&gt;Harvard&lt;/a&gt;'s Center for International Development (CID) found in 2001 that only three &lt;a href=&quot;http://en.wikipedia.org/wiki/Tropical&quot; title=&quot;Tropical&quot; class=&quot;mw-redirect&quot;&gt;tropical&lt;/a&gt; economies — &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Hong_Kong&quot; title=&quot;Hong Kong&quot;&gt;Hong Kong&lt;/a&gt;, &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Singapore&quot; title=&quot;Singapore&quot;&gt;Singapore&lt;/a&gt;, and &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Taiwan&quot; title=&quot;Taiwan&quot;&gt;Taiwan&lt;/a&gt; — were classified as high-income by the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/World_Bank&quot; title=&quot;World Bank&quot;&gt;World Bank&lt;/a&gt;, while all countries within regions zoned as &lt;a href=&quot;http://en.wikipedia.org/wiki/Temperate&quot; title=&quot;Temperate&quot; class=&quot;mw-redirect&quot;&gt;temperate&lt;/a&gt; had either middle- or high-income economies. &lt;sup id=&quot;cite_ref-0&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Latitude#cite_note-0&quot;&gt;&lt;span&gt;[&lt;/span&gt;1&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt;
The validity of the Harvard report may be questioned because a
different threshold is used for the tropical regions and the World Bank
list fails to include Qatar's, United Arab Emirates', and Kuwait's
economies. Further, countries such as Brazil have far better incomes
than much of the Former Soviet Union and Iron Curtain states&lt;sup class=&quot;noprint Template-Fact&quot; title=&quot;This claim needs references to reliable sources from June 2009&quot; style=&quot;white-space: nowrap;&quot;&gt;[&lt;i&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Wikipedia:Citation_needed&quot; title=&quot;Wikipedia:Citation needed&quot;&gt;citation needed&lt;/a&gt;&lt;/i&gt;]&lt;/sup&gt;.&lt;/p&gt;
&lt;h2&gt;&lt;span class=&quot;editsection&quot;&gt;&lt;/span&gt;&lt;span class=&quot;mw-headline&quot; id=&quot;Elliptic_parameters&quot;&gt;Elliptic parameters&lt;/span&gt;&lt;/h2&gt;
&lt;p&gt;Because most planets (including Earth) are &lt;i&gt;ellipsoids of revolution&lt;/i&gt;, or &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Oblate_spheroid&quot; title=&quot;Oblate spheroid&quot;&gt;spheroids&lt;/a&gt;, rather than &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Sphere&quot; title=&quot;Sphere&quot;&gt;spheres&lt;/a&gt;,
both the radius and the length of arc varies with latitude. This
variation requires the introduction of elliptic parameters based on an
ellipse's &lt;b&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Angular_eccentricity&quot; title=&quot;Angular eccentricity&quot;&gt;angular eccentricity&lt;/a&gt;&lt;/b&gt;, &lt;img class=&quot;tex yui-img&quot; alt=&quot;o\!\varepsilon\,\!&quot; src=&quot;http://upload.wikimedia.org/math/9/d/a/9da837553648b46588ca5d0ef48cdb03.png&quot;&gt; (which equals &lt;img class=&quot;tex yui-img&quot; alt=&quot;\arccos\left(\frac{b}{a}\right)\,\!&quot; src=&quot;http://upload.wikimedia.org/math/5/1/f/51f113ecf7e558f166136da394c92b1e.png&quot;&gt;, where &lt;img class=&quot;tex yui-img&quot; alt=&quot;a\;\!&quot; src=&quot;http://upload.wikimedia.org/math/1/6/f/16f45a094fa9fac788b8dbcc4a699133.png&quot;&gt; and &lt;img class=&quot;tex yui-img&quot; alt=&quot;b\;\!&quot; src=&quot;http://upload.wikimedia.org/math/7/5/d/75dc17277f9ca3ecc36acf3bc475dc09.png&quot;&gt; are the equatorial radius (6378137.0 m for Earth) and the polar radius (6356752.3142 m for Earth), respectively; &lt;img class=&quot;tex yui-img&quot; alt=&quot;\sin^2(o\!\varepsilon)\,\!&quot; src=&quot;http://upload.wikimedia.org/math/b/4/6/b466933e4a014d6264f6e3f28cde69e4.png&quot;&gt; is the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Eccentricity_%28mathematics%29&quot; title=&quot;Eccentricity (mathematics)&quot;&gt;first eccentricity&lt;/a&gt; squared, &lt;img class=&quot;tex yui-img&quot; alt=&quot;{e^2}\,\!&quot; src=&quot;http://upload.wikimedia.org/math/2/e/a/2ea79cdb99cecf9508c474aed06efe9c.png&quot;&gt;; and &lt;img class=&quot;tex yui-img&quot; alt=&quot;2\sin^2\left(\frac{o\!\varepsilon}{2}\right)\;\!&quot; src=&quot;http://upload.wikimedia.org/math/5/9/9/599fc5801123244d70bb2c7181551355.png&quot;&gt; or &lt;img class=&quot;tex yui-img&quot; alt=&quot;1-\cos(o\!\varepsilon)\,\!&quot; src=&quot;http://upload.wikimedia.org/math/b/a/d/bad715b5c03e4ba3dd97fba5530bcbc5.png&quot;&gt; is the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Flattening&quot; title=&quot;Flattening&quot;&gt;flattening&lt;/a&gt;, &lt;img class=&quot;tex yui-img&quot; alt=&quot;{f}\,\!&quot; src=&quot;http://upload.wikimedia.org/math/f/9/a/f9aac88ffba7006939416bd8dedc166b.png&quot;&gt;). Utilized in creating the &lt;a href=&quot;http://en.wikipedia.org/wiki/Integrand#Terminology_and_notation&quot; title=&quot;Integrand&quot; class=&quot;mw-redirect&quot;&gt;integrands&lt;/a&gt; for &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Curvature&quot; title=&quot;Curvature&quot;&gt;curvature&lt;/a&gt; is the inverse of the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Elliptic_integral#Incomplete_elliptic_integral_of_the_second_kind&quot; title=&quot;Elliptic integral&quot;&gt;principal elliptic integrand&lt;/a&gt;, &lt;img class=&quot;tex yui-img&quot; alt=&quot;E'\,\!&quot; src=&quot;http://upload.wikimedia.org/math/a/5/b/a5b0c11f360116a76406e244fb0b1e23.png&quot;&gt;:&lt;/p&gt;
&lt;dl&gt;&lt;dd&gt;
&lt;dl&gt;&lt;dd&gt;&lt;img class=&quot;tex yui-img&quot; alt=&quot; n'(\phi)=\frac{1}{E'(\phi)}
 =\frac{1}{\sqrt{1-(\sin(\phi)\sin(o\!\varepsilon))^2}};\,\!
 &quot; src=&quot;http://upload.wikimedia.org/math/c/6/c/c6c819713594a39ff2e81eb44d45fa8a.png&quot;&gt;&lt;/dd&gt;&lt;dd&gt;&lt;img class=&quot;tex yui-img&quot; alt=&quot;\begin{align}
 M(\phi)&amp;amp;=a\cdot\cos^2(o\!\varepsilon)n'^3(\phi)
 =\frac{(ab)^2}{\Big((a\cos(\phi))^2+(b\sin(\phi))^2\Big)^{3/2}};\\
 N(\phi)&amp;amp;=a{\cdot}n'(\phi)
 =\frac{a^2}{\sqrt{(a\cos(\phi))^2+(b\sin(\phi))^2}}.\end{align}\,\!
 &quot; src=&quot;http://upload.wikimedia.org/math/2/c/5/2c526bd7f96544c5abd66d2d6d5fd98f.png&quot;&gt;&lt;/dd&gt;&lt;/dl&gt;
&lt;/dd&gt;&lt;/dl&gt;
&lt;h2&gt;&lt;span class=&quot;editsection&quot;&gt;&lt;/span&gt;&lt;span class=&quot;mw-headline&quot; id=&quot;Degree_length&quot;&gt;Degree length&lt;/span&gt;&lt;/h2&gt;
&lt;p&gt;On Earth, the length of an &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Degree_%28angle%29&quot; title=&quot;Degree (angle)&quot;&gt;arcdegree&lt;/a&gt; of north–south latitude difference, &lt;img class=&quot;tex yui-img&quot; alt=&quot;\scriptstyle{\Delta\phi}\,\!&quot; src=&quot;http://upload.wikimedia.org/math/9/8/5/98546375864afa1bdfd4768f532ee056.png&quot;&gt;, is about 60 &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Nautical_mile&quot; title=&quot;Nautical mile&quot;&gt;nautical miles&lt;/a&gt;, 111 &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Kilometre&quot; title=&quot;Kilometre&quot;&gt;kilometres&lt;/a&gt; or 69 &lt;a href=&quot;http://en.wikipedia.org/wiki/Statute_mile&quot; title=&quot;Statute mile&quot; class=&quot;mw-redirect&quot;&gt;statute miles&lt;/a&gt; at any latitude. The length of an arcdegree of east-west longitude difference, &lt;img class=&quot;tex yui-img&quot; alt=&quot;\scriptstyle{\cos(\phi)\Delta\lambda}\,\!&quot; src=&quot;http://upload.wikimedia.org/math/e/c/1/ec1ca731651bcc413b1dc9cc0f7e5362.png&quot;&gt;, is about the same at the equator as the north-south, reducing to zero at the poles.&lt;/p&gt;
&lt;p&gt;In the case of a spheroid, a &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Meridian_%28geography%29&quot; title=&quot;Meridian (geography)&quot;&gt;meridian&lt;/a&gt; and its anti-meridian form an &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Ellipse&quot; title=&quot;Ellipse&quot;&gt;ellipse&lt;/a&gt;, from which an exact expression for the length of an arcdegree of latitude difference is:&lt;/p&gt;
&lt;dl&gt;&lt;dd&gt;
&lt;dl&gt;&lt;dd&gt;&lt;img class=&quot;tex yui-img&quot; alt=&quot;\frac{\pi}{180^\circ}M(\phi);\,\!&quot; src=&quot;http://upload.wikimedia.org/math/0/3/4/034683c83208119cd4b503181dd8a85d.png&quot;&gt;&lt;/dd&gt;&lt;/dl&gt;
&lt;/dd&gt;&lt;/dl&gt;
&lt;p&gt;This radius of arc (or &quot;arcradius&quot;) is in the plane of a meridian, and is known as the &lt;i&gt;meridional &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Radius_of_curvature_%28applications%29&quot; title=&quot;Radius of curvature (applications)&quot;&gt;radius of curvature&lt;/a&gt;&lt;/i&gt;, &lt;img class=&quot;tex yui-img&quot; alt=&quot;M\,\!&quot; src=&quot;http://upload.wikimedia.org/math/3/b/6/3b652357e59da356dbb6f2105020406e.png&quot;&gt;.&lt;sup id=&quot;cite_ref-mathforum_1-0&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Latitude#cite_note-mathforum-1&quot;&gt;&lt;span&gt;[&lt;/span&gt;2&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt;&lt;sup id=&quot;cite_ref-snyder_2-0&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Latitude#cite_note-snyder-2&quot;&gt;&lt;span&gt;[&lt;/span&gt;3&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt;&lt;/p&gt;
&lt;p&gt;Similarly, an exact expression for the length of an arcdegree of longitude difference is:&lt;/p&gt;
&lt;dl&gt;&lt;dd&gt;
&lt;dl&gt;&lt;dd&gt;&lt;img class=&quot;tex yui-img&quot; alt=&quot;\frac{\pi}{180^\circ}\cos(\phi)N(\phi);\,\!&quot; src=&quot;http://upload.wikimedia.org/math/9/6/1/9613d13aca7abfc4aaf4be31b859ddb8.png&quot;&gt;&lt;/dd&gt;&lt;/dl&gt;
&lt;/dd&gt;&lt;/dl&gt;
&lt;p&gt;The arcradius contained here is in the plane of the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Prime_vertical&quot; title=&quot;Prime vertical&quot;&gt;prime vertical&lt;/a&gt;, the east-west plane perpendicular (or &quot;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Orthogonality&quot; title=&quot;Orthogonality&quot;&gt;normal&lt;/a&gt;&quot;) to both the plane of the meridian and the plane tangent to the surface of the ellipsoid, and is known as the &lt;i&gt;normal radius of curvature&lt;/i&gt;, &lt;img class=&quot;tex yui-img&quot; alt=&quot;N\,\!&quot; src=&quot;http://upload.wikimedia.org/math/1/c/c/1ccb2fd4de8445c82de205e329c265d5.png&quot;&gt;.&lt;sup id=&quot;cite_ref-mathforum_1-1&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Latitude#cite_note-mathforum-1&quot;&gt;&lt;span&gt;[&lt;/span&gt;2&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt;&lt;sup id=&quot;cite_ref-snyder_2-1&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Latitude#cite_note-snyder-2&quot;&gt;&lt;span&gt;[&lt;/span&gt;3&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt;&lt;/p&gt;
&lt;p&gt;Along the equator (east-west), &lt;img class=&quot;tex yui-img&quot; alt=&quot;N\;\!&quot; src=&quot;http://upload.wikimedia.org/math/6/3/1/631fe013c550a2dc153c1017cd15c438.png&quot;&gt; equals the equatorial radius. The radius of curvature at a &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Right_angle&quot; title=&quot;Right angle&quot;&gt;right angle&lt;/a&gt; to the equator (north-south), &lt;img class=&quot;tex yui-img&quot; alt=&quot;M\;\!&quot; src=&quot;http://upload.wikimedia.org/math/0/1/f/01ff7f895fd77d6be1da38f3e913d8ac.png&quot;&gt;,
is 43&amp;nbsp;km shorter, hence the length of an arcdegree of latitude
difference at the equator is about 1&amp;nbsp;km less than the length of an
arcdegree of longitude difference at the equator. The radii of
curvature are equal at the poles where they are about 64&amp;nbsp;km greater
than the north-south equatorial radius of curvature &lt;i&gt;because&lt;/i&gt; the
polar radius is 21&amp;nbsp;km less than the equatorial radius. The shorter
polar radii indicate that the northern and southern hemispheres are
flatter, making their radii of curvature longer. This flattening also
'pinches' the north-south equatorial radius of curvature, making it
43&amp;nbsp;km less than the equatorial radius. Both radii of curvature are
perpendicular to the plane tangent to the surface of the ellipsoid at
all latitudes, directed toward a point on the polar axis in the
opposite hemisphere (except at the equator where both point toward
Earth's center). The east-west radius of curvature reaches the axis,
whereas the north-south radius of curvature is shorter at all latitudes
except the poles.&lt;/p&gt;
&lt;p&gt;The &lt;a href=&quot;http://en.wikipedia.org/wiki/WGS84&quot; title=&quot;WGS84&quot; class=&quot;mw-redirect&quot;&gt;WGS84&lt;/a&gt; ellipsoid, used by all &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Global_Positioning_System&quot; title=&quot;Global Positioning System&quot;&gt;GPS&lt;/a&gt;
devices, uses an equatorial radius of 6378137.0 m and an inverse
flattening, (1/f), of 298.257223563, hence its polar radius is
6356752.3142 m and its first eccentricity squared is 0.00669437999014.&lt;sup id=&quot;cite_ref-3&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Latitude#cite_note-3&quot;&gt;&lt;span&gt;[&lt;/span&gt;4&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt; The more recent but little used &lt;a href=&quot;http://en.wikipedia.org/wiki/IERS&quot; title=&quot;IERS&quot; class=&quot;mw-redirect&quot;&gt;IERS&lt;/a&gt;
2003 ellipsoid provides equatorial and polar radii of 6378136.6 and
6356751.9 m, respectively, and an inverse flattening of 298.25642.&lt;sup id=&quot;cite_ref-4&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Latitude#cite_note-4&quot;&gt;&lt;span&gt;[&lt;/span&gt;5&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt; Lengths of degrees on the WGS84 and IERS 2003 ellipsoids are the same when rounded to six &lt;a href=&quot;http://en.wikipedia.org/wiki/Significant_digit&quot; title=&quot;Significant digit&quot; class=&quot;mw-redirect&quot;&gt;significant digits&lt;/a&gt;. An appropriate calculator for any latitude is provided by the U.S. government's &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/National_Geospatial-Intelligence_Agency&quot; title=&quot;National Geospatial-Intelligence Agency&quot;&gt;National Geospatial-Intelligence Agency&lt;/a&gt; (NGA).&lt;sup id=&quot;cite_ref-5&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Latitude#cite_note-5&quot;&gt;&lt;span&gt;[&lt;/span&gt;6&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt;&lt;/p&gt;
&lt;table class=&quot;wikitable&quot; border=&quot;1&quot;&gt;
&lt;tbody&gt;&lt;tr&gt;
&lt;th&gt;Latitude&lt;/th&gt;
&lt;th&gt;N-S radius&lt;br&gt;
of curvature&lt;br&gt;
&lt;img class=&quot;tex yui-img&quot; alt=&quot;M\;\!&quot; src=&quot;http://upload.wikimedia.org/math/0/1/f/01ff7f895fd77d6be1da38f3e913d8ac.png&quot;&gt;&lt;/th&gt;
&lt;th&gt;Surface distance&lt;br&gt;
per 1° change&lt;br&gt;
in latitude&lt;/th&gt;
&lt;th&gt;&lt;br&gt;&lt;/th&gt;
&lt;th&gt;E-W radius&lt;br&gt;
of curvature&lt;br&gt;
&lt;img class=&quot;tex yui-img&quot; alt=&quot;N\;\!&quot; src=&quot;http://upload.wikimedia.org/math/6/3/1/631fe013c550a2dc153c1017cd15c438.png&quot;&gt;&lt;/th&gt;
&lt;th&gt;Surface distance&lt;br&gt;
per 1° change&lt;br&gt;
in longitude&lt;/th&gt;
&lt;/tr&gt;
&lt;tr style=&quot;text-align: right;&quot;&gt;
&lt;td&gt;0°&lt;/td&gt;
&lt;td&gt;6335.44&amp;nbsp;km&lt;/td&gt;
&lt;td&gt;110.574&amp;nbsp;km&lt;/td&gt;
&lt;td&gt;&lt;br&gt;&lt;/td&gt;
&lt;td&gt;6378.14&amp;nbsp;km&lt;/td&gt;
&lt;td&gt;111.320&amp;nbsp;km&lt;/td&gt;
&lt;/tr&gt;
&lt;tr style=&quot;text-align: right;&quot;&gt;
&lt;td&gt;15°&lt;/td&gt;
&lt;td&gt;6339.70&amp;nbsp;km&lt;/td&gt;
&lt;td&gt;110.649&amp;nbsp;km&lt;/td&gt;
&lt;td&gt;&lt;br&gt;&lt;/td&gt;
&lt;td&gt;6379.57&amp;nbsp;km&lt;/td&gt;
&lt;td&gt;107.551&amp;nbsp;km&lt;/td&gt;
&lt;/tr&gt;
&lt;tr style=&quot;text-align: right;&quot;&gt;
&lt;td&gt;30°&lt;/td&gt;
&lt;td&gt;6351.38&amp;nbsp;km&lt;/td&gt;
&lt;td&gt;110.852&amp;nbsp;km&lt;/td&gt;
&lt;td&gt;&lt;br&gt;&lt;/td&gt;
&lt;td&gt;6383.48&amp;nbsp;km&lt;/td&gt;
&lt;td&gt;96.486&amp;nbsp;km&lt;/td&gt;
&lt;/tr&gt;
&lt;tr style=&quot;text-align: right;&quot;&gt;
&lt;td&gt;45°&lt;/td&gt;
&lt;td&gt;6367.38&amp;nbsp;km&lt;/td&gt;
&lt;td&gt;111.132&amp;nbsp;km&lt;/td&gt;
&lt;td&gt;&lt;br&gt;&lt;/td&gt;
&lt;td&gt;6388.84&amp;nbsp;km&lt;/td&gt;
&lt;td&gt;78.847&amp;nbsp;km&lt;/td&gt;
&lt;/tr&gt;
&lt;tr style=&quot;text-align: right;&quot;&gt;
&lt;td&gt;60°&lt;/td&gt;
&lt;td&gt;6383.45&amp;nbsp;km&lt;/td&gt;
&lt;td&gt;111.412&amp;nbsp;km&lt;/td&gt;
&lt;td&gt;&lt;br&gt;&lt;/td&gt;
&lt;td&gt;6394.21&amp;nbsp;km&lt;/td&gt;
&lt;td&gt;55.800&amp;nbsp;km&lt;/td&gt;
&lt;/tr&gt;
&lt;tr style=&quot;text-align: right;&quot;&gt;
&lt;td&gt;75°&lt;/td&gt;
&lt;td&gt;6395.26&amp;nbsp;km&lt;/td&gt;
&lt;td&gt;111.618&amp;nbsp;km&lt;/td&gt;
&lt;td&gt;&lt;br&gt;&lt;/td&gt;
&lt;td&gt;6398.15&amp;nbsp;km&lt;/td&gt;
&lt;td&gt;28.902&amp;nbsp;km&lt;/td&gt;
&lt;/tr&gt;
&lt;tr style=&quot;text-align: right;&quot;&gt;
&lt;td&gt;90°&lt;/td&gt;
&lt;td&gt;6399.59&amp;nbsp;km&lt;/td&gt;
&lt;td&gt;111.694&amp;nbsp;km&lt;/td&gt;
&lt;td&gt;&lt;br&gt;&lt;/td&gt;
&lt;td&gt;6399.59&amp;nbsp;km&lt;/td&gt;
&lt;td&gt;0.000&amp;nbsp;km&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;&lt;/table&gt;
&lt;h2&gt;&lt;span class=&quot;editsection&quot;&gt;&lt;/span&gt;&lt;span class=&quot;mw-headline&quot; id=&quot;Types_of_latitude&quot;&gt;Types of latitude&lt;/span&gt;&lt;/h2&gt;
&lt;p&gt;With a spheroid that is slightly flattened by its rotation,
cartographers refer to a variety of auxiliary latitudes to precisely
adapt spherical projections according to their purpose.&lt;br&gt;
For planets other than Earth, such as &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Mars&quot; title=&quot;Mars&quot;&gt;Mars&lt;/a&gt;,
geographic and geocentric latitude are called &quot;planetographic&quot; and
&quot;planetocentric&quot; latitude, respectively. Most maps of Mars since 2002
use planetocentric coordinates.&lt;/p&gt;
&lt;h3&gt;&lt;span class=&quot;editsection&quot;&gt;&lt;/span&gt;&lt;span class=&quot;mw-headline&quot; id=&quot;Common_.22latitude.22&quot;&gt;Common &quot;latitude&quot;&lt;/span&gt;&lt;/h3&gt;
&lt;p&gt;In common usage, &quot;latitude&quot; refers to &lt;b&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Geodetic_system&quot; title=&quot;Geodetic system&quot;&gt;geodetic&lt;/a&gt;&lt;/b&gt; or &lt;b&gt;geographic latitude&lt;/b&gt; &lt;img class=&quot;tex yui-img&quot; alt=&quot;\phi\,\!&quot; src=&quot;http://upload.wikimedia.org/math/b/f/d/bfd070bbf4b8539e9b3af50740384bf6.png&quot;&gt; and is the angle between the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Equator&quot; title=&quot;Equator&quot;&gt;equatorial plane&lt;/a&gt; and a line that is &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Surface_normal&quot; title=&quot;Surface normal&quot;&gt;normal&lt;/a&gt; to the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Reference_ellipsoid&quot; title=&quot;Reference ellipsoid&quot;&gt;reference ellipsoid&lt;/a&gt;,
which approximates the shape of Earth to account for flattening of the
poles and bulging of the equator. This value usually differs from the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Latitude#Geocentric_latitude&quot; title=&quot;Latitude&quot;&gt;geocentric latitude&lt;/a&gt;.&lt;/p&gt;
&lt;p&gt;The expressions following assume elliptical polar sections and that
all sections parallel to the equatorial plane are circular. Geographic
latitude (with longitude) then provides a &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Gauss_map&quot; title=&quot;Gauss map&quot;&gt;Gauss map&lt;/a&gt;. As defined earlier in this article, &lt;img class=&quot;tex yui-img&quot; alt=&quot;o\!\varepsilon\,\!&quot; src=&quot;http://upload.wikimedia.org/math/9/d/a/9da837553648b46588ca5d0ef48cdb03.png&quot;&gt; is the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Angular_eccentricity&quot; title=&quot;Angular eccentricity&quot;&gt;angular eccentricity&lt;/a&gt; of a meridian.&lt;/p&gt;
&lt;h3&gt;&lt;span class=&quot;editsection&quot;&gt;&lt;/span&gt;&lt;span class=&quot;mw-headline&quot; id=&quot;Reduced_latitude&quot;&gt;Reduced latitude&lt;/span&gt;&lt;/h3&gt;
&lt;ul&gt;&lt;li&gt;On a spheroid, lines of &lt;b&gt;reduced&lt;/b&gt; or &lt;b&gt;parametric latitude&lt;/b&gt;, &lt;img class=&quot;tex yui-img&quot; alt=&quot;\beta\,\!&quot; src=&quot;http://upload.wikimedia.org/math/5/b/3/5b320b6d3d3254d936c752ae308dbfd8.png&quot;&gt;,
form circles whose radii are the same as the radii of circles formed by
the corresponding lines of latitude on a sphere with radius equal to
the equatorial radius of the spheroid.&lt;/li&gt;&lt;/ul&gt;
&lt;dl&gt;&lt;dd&gt;
&lt;dl&gt;&lt;dd&gt;&lt;img class=&quot;tex yui-img&quot; alt=&quot;\beta=\arctan\Big(\cos(o\!\varepsilon)\tan(\phi)\Big) = \arctan\Bigg(\frac{b}{a}\tan(\phi)\Bigg);\,\!&quot; src=&quot;http://upload.wikimedia.org/math/c/8/7/c870ce4264d9e03c241b232ad7e08f97.png&quot;&gt;&lt;/dd&gt;&lt;/dl&gt;
&lt;/dd&gt;&lt;/dl&gt;
&lt;h3&gt;&lt;span class=&quot;editsection&quot;&gt;&lt;/span&gt;&lt;span class=&quot;mw-headline&quot; id=&quot;Authalic_latitude&quot;&gt;Authalic latitude&lt;/span&gt;&lt;/h3&gt;
&lt;ul&gt;&lt;li&gt;&lt;b&gt;Authalic latitude&lt;/b&gt;, &lt;img class=&quot;tex yui-img&quot; alt=&quot;\xi\,\!&quot; src=&quot;http://upload.wikimedia.org/math/b/7/e/b7e14d308150288a955359883e39ac3e.png&quot;&gt;, gives an area-preserving transform to the sphere.&lt;/li&gt;&lt;/ul&gt;
&lt;dl&gt;&lt;dd&gt;
&lt;dl&gt;&lt;dd&gt;&lt;img class=&quot;tex yui-img&quot; alt=&quot;\widehat{S}^2(\phi)=\frac{1}{2}b^2\left(\sin(\phi)n'^2(\phi)+\frac{\ln\bigg(n'(\phi)\Big(1+\sin(\phi)\sin(o\!\varepsilon)\Big)\bigg)}{\sin(o\!\varepsilon)}\right);\,\!&quot; src=&quot;http://upload.wikimedia.org/math/7/0/e/70e9de122bdadc15ff563d8dc936bcc4.png&quot;&gt;&lt;/dd&gt;&lt;/dl&gt;
&lt;/dd&gt;&lt;/dl&gt;
&lt;dl&gt;&lt;dd&gt;
&lt;dl&gt;&lt;dd&gt;&lt;img class=&quot;tex yui-img&quot; alt=&quot;\begin{align}\xi&amp;amp;=\arcsin\!\left(\frac{\widehat{S}^2(\phi)}{\widehat{S}^2(90^\circ)}\right),\\
&amp;amp;=\arcsin\!\left(\frac{\sin(\phi)\sin(o\!\varepsilon)n'^2(\phi)+\ln\Big(n'(\phi)\big(1+\sin(\phi)\sin(o\!\varepsilon)\big)\Big)}{\sin(o\!\varepsilon)\sec^2(o\!\varepsilon)+\ln\Big(\sec(o\!\varepsilon)\big(1+\sin(o\!\varepsilon)\big)\Big)}\right);\end{align}\,\!&quot; src=&quot;http://upload.wikimedia.org/math/2/b/e/2beab1a56dc0cb43ccb236966f63eb24.png&quot;&gt;&lt;/dd&gt;&lt;/dl&gt;
&lt;/dd&gt;&lt;/dl&gt;
&lt;h3&gt;&lt;span class=&quot;editsection&quot;&gt;&lt;/span&gt;&lt;span class=&quot;mw-headline&quot; id=&quot;Rectifying_latitude&quot;&gt;Rectifying latitude&lt;/span&gt;&lt;/h3&gt;
&lt;ul&gt;&lt;li&gt;&lt;b&gt;Rectifying latitude&lt;/b&gt;, &lt;img class=&quot;tex yui-img&quot; alt=&quot;\mu\,\!&quot; src=&quot;http://upload.wikimedia.org/math/7/4/b/74b8eddf4b37de80c7c8eed1b64e46fc.png&quot;&gt;, is the surface distance from the equator, scaled so the pole is 90°, but involves elliptic integration:&lt;/li&gt;&lt;/ul&gt;
&lt;dl&gt;&lt;dd&gt;
&lt;dl&gt;&lt;dd&gt;
&lt;dl&gt;&lt;dd&gt;&amp;nbsp;&lt;img class=&quot;tex yui-img&quot; alt=&quot;\mu=\frac{\;\int_{0}^\phi\;M(\theta)\,d\theta}{\frac{2}{\pi}\int_{0}^{90^\circ}M(\phi)\,d\phi}
=\frac{\pi}{2}\cdot\frac{\;\int_{0}^\phi\;n'^3(\theta)\,d\theta}{\int_{0}^{90^\circ}n'^3(\phi)\,d\phi};\,\!&quot; src=&quot;http://upload.wikimedia.org/math/e/b/a/eba3732d036d156a592072917ad8ca57.png&quot;&gt;&lt;/dd&gt;&lt;/dl&gt;
&lt;/dd&gt;&lt;/dl&gt;
&lt;/dd&gt;&lt;/dl&gt;
&lt;h3&gt;&lt;span class=&quot;editsection&quot;&gt;&lt;/span&gt;&lt;span class=&quot;mw-headline&quot; id=&quot;Conformal_latitude&quot;&gt;Conformal latitude&lt;/span&gt;&lt;/h3&gt;
&lt;ul&gt;&lt;li&gt;&lt;b&gt;Conformal latitude&lt;/b&gt;, &lt;img class=&quot;tex yui-img&quot; alt=&quot;\chi\,\!&quot; src=&quot;http://upload.wikimedia.org/math/f/2/5/f259283373d46c5a10db61640455a03b.png&quot;&gt;, gives an angle-preserving (&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Conformal&quot; title=&quot;Conformal&quot;&gt;conformal&lt;/a&gt;) transform to the sphere.&lt;/li&gt;&lt;/ul&gt;
&lt;dl&gt;&lt;dd&gt;
&lt;dl&gt;&lt;dd&gt;&lt;img class=&quot;tex yui-img&quot; alt=&quot;\chi=2\cdot\arctan\left(\sqrt{\frac{1+\sin(\phi)}{1-\sin(\phi)}\cdot\left(\frac{1-\sin(\phi)\sin(o\!\varepsilon)}{1+\sin(\phi)\sin(o\!\varepsilon)}\right)^{\!\!\sin(o\!\varepsilon)}}^{\color{white}|}\;\right)-\frac{\pi}{2};\;\!&quot; src=&quot;http://upload.wikimedia.org/math/7/e/5/7e59bf31a1efc305e5d3fcf06e182470.png&quot;&gt;&lt;/dd&gt;&lt;/dl&gt;
&lt;/dd&gt;&lt;/dl&gt;
&lt;h3&gt;&lt;span class=&quot;editsection&quot;&gt;&lt;/span&gt;&lt;span class=&quot;mw-headline&quot; id=&quot;Geocentric_latitude&quot;&gt;Geocentric latitude&lt;/span&gt;&lt;/h3&gt;
&lt;ul&gt;&lt;li&gt;The &lt;b&gt;geocentric latitude&lt;/b&gt;, &lt;img class=&quot;tex yui-img&quot; alt=&quot;\psi\,\!&quot; src=&quot;http://upload.wikimedia.org/math/4/b/1/4b1c491f938e0f03982ce86761904296.png&quot;&gt;, is the angle between the equatorial plane and a line from the center of Earth.&lt;/li&gt;&lt;/ul&gt;
&lt;dl&gt;&lt;dd&gt;
&lt;dl&gt;&lt;dd&gt;&lt;img class=&quot;tex yui-img&quot; alt=&quot;\psi=\arctan\Big(\cos^2(o\!\varepsilon)\tan(\phi)\Big) = \arctan\Big((b/a)^2\tan(\phi)\Big).\;\!&quot; src=&quot;http://upload.wikimedia.org/math/4/5/4/454c1c7c2c917a75b89d789996d03df5.png&quot;&gt;&lt;/dd&gt;&lt;/dl&gt;
&lt;/dd&gt;&lt;dd&gt;It is the size of the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Central_angle&quot; title=&quot;Central angle&quot;&gt;central angle&lt;/a&gt; between the equator and the point of interest, as measured along a &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Meridian_%28geography%29&quot; title=&quot;Meridian (geography)&quot;&gt;meridian&lt;/a&gt;. This value usually differs from the geographic latitude, as so:&lt;/dd&gt;&lt;/dl&gt;
&lt;div class=&quot;center&quot;&gt;
&lt;div class=&quot;thumb tnone&quot;&gt;
&lt;div class=&quot;thumbinner&quot; style=&quot;width: 277px;&quot;&gt;&lt;a href=&quot;http://en.wikipedia.org/wiki/File:Two-types-of-latitude.png&quot; class=&quot;image&quot;&gt;&lt;img alt=&quot;&quot; src=&quot;http://upload.wikimedia.org/wikipedia/commons/thumb/0/06/Two-types-of-latitude.png/275px-Two-types-of-latitude.png&quot; class=&quot;thumbimage yui-img&quot; width=&quot;275&quot; height=&quot;178&quot;&gt;&lt;/a&gt;&lt;/div&gt;&lt;/div&gt;&lt;/div&gt;&lt;h3&gt;&lt;span class=&quot;mw-headline&quot; id=&quot;Astronomical_latitude&quot;&gt;Astronomical latitude&lt;/span&gt;&lt;/h3&gt;
&lt;p&gt;A more obscure measure of latitude is the &lt;b&gt;astronomical latitude&lt;/b&gt;, which is the angle between the equatorial plane and the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Surface_normal&quot; title=&quot;Surface normal&quot;&gt;normal&lt;/a&gt; to the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Geoid&quot; title=&quot;Geoid&quot;&gt;geoid&lt;/a&gt;
(ie a plumb line). It originated as the angle between horizon and pole
star. It differs from the geodetic latitude only slightly, due to the
slight deviations of the geoid from the reference ellipsoid.&lt;/p&gt;
&lt;p&gt;Astronomical latitude is not to be confused with &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Declination&quot; title=&quot;Declination&quot;&gt;declination&lt;/a&gt;, the coordinate &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Astronomer&quot; title=&quot;Astronomer&quot;&gt;astronomers&lt;/a&gt; use to describe the locations of stars north/south of the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Celestial_equator&quot; title=&quot;Celestial equator&quot;&gt;celestial equator&lt;/a&gt; (see &lt;a href=&quot;http://en.wikipedia.org/wiki/Equatorial_coordinates&quot; title=&quot;Equatorial coordinates&quot; class=&quot;mw-redirect&quot;&gt;equatorial coordinates&lt;/a&gt;), nor with &lt;a href=&quot;http://en.wikipedia.org/wiki/Ecliptic_latitude&quot; title=&quot;Ecliptic latitude&quot; class=&quot;mw-redirect&quot;&gt;ecliptic latitude&lt;/a&gt;, the coordinate that astronomers use to describe the locations of stars north/south of the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Ecliptic&quot; title=&quot;Ecliptic&quot;&gt;ecliptic&lt;/a&gt; (see &lt;a href=&quot;http://en.wikipedia.org/wiki/Ecliptic_coordinates&quot; title=&quot;Ecliptic coordinates&quot; class=&quot;mw-redirect&quot;&gt;ecliptic coordinates&lt;/a&gt;).&lt;/p&gt;
&lt;h3&gt;&lt;span class=&quot;editsection&quot;&gt;&lt;/span&gt;&lt;span class=&quot;mw-headline&quot; id=&quot;Palaeolatitude&quot;&gt;Palaeolatitude&lt;/span&gt;&lt;/h3&gt;
&lt;p&gt;Continents move over time, due to &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Continental_drift&quot; title=&quot;Continental drift&quot;&gt;continental drift&lt;/a&gt;,
taking whatever fossils and other features of interest they may have
with them. Particularly when discussing fossils, it's often more useful
to know where the fossil was when it was laid down, than where it is
when it was dug up: this is called the &lt;i&gt;palæolatitude&lt;/i&gt; of the fossil. The Palæolatitude can be constrained by &lt;a href=&quot;http://en.wikipedia.org/wiki/Pal%C3%A6omagnetism&quot; title=&quot;Palæomagnetism&quot; class=&quot;mw-redirect&quot;&gt;palæomagnetic&lt;/a&gt;
data. If tiny magnetisable grains are present when the rock is being
formed, these will align themselves with Earth's magnetic field like
compass needles. A &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Magnetometer&quot; title=&quot;Magnetometer&quot;&gt;magnetometer&lt;/a&gt; can deduce the orientation of these grains by subjecting a sample to a magnetic field, and the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Magnetic_declination&quot; title=&quot;Magnetic declination&quot;&gt;magnetic declination&lt;/a&gt; of the grains can be used to infer the latitude of deposition.&lt;/p&gt;
&lt;h3&gt;&lt;span class=&quot;editsection&quot;&gt;&lt;/span&gt;&lt;span class=&quot;mw-headline&quot; id=&quot;Comparison_of_selected_types&quot;&gt;Comparison of selected types&lt;/span&gt;&lt;/h3&gt;
&lt;p&gt;The following plot shows the differences between the types of
latitude. The data used are found in the table following the plot.
Please note that the values in the table are in minutes, not degrees,
and the plot reflects this as well. Also observe that the conformal
symbols are hidden behind the geocentric due to being very close in
value. Finally it is important to mention also that these differences
don't mean that the use of one specific latitude will necessarily cause
more distortions than the other (the real fact is that each latitude
type is optimized for achieving a different goal).&lt;/p&gt;
&lt;p&gt;&lt;a href=&quot;http://en.wikipedia.org/wiki/File:Types_of_latitude_difference.png&quot; class=&quot;image&quot;&gt;&lt;img class=&quot;yui-img&quot; alt=&quot;Types of latitude difference.png&quot; src=&quot;http://upload.wikimedia.org/wikipedia/commons/d/dc/Types_of_latitude_difference.png&quot; width=&quot;512&quot; height=&quot;384&quot;&gt;&lt;/a&gt;&lt;/p&gt;
&lt;dl&gt;&lt;dd&gt;
&lt;table class=&quot;wikitable&quot;&gt;
&lt;tbody&gt;&lt;tr&gt;
&lt;th colspan=&quot;6&quot;&gt;Approximate difference from geographic latitude (&quot;Lat&quot;)&lt;/th&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;th&gt;Lat&lt;br&gt;
&lt;img class=&quot;tex yui-img&quot; alt=&quot;\phi\,\!&quot; src=&quot;http://upload.wikimedia.org/math/b/f/d/bfd070bbf4b8539e9b3af50740384bf6.png&quot;&gt;&lt;/th&gt;
&lt;th&gt;Reduced&lt;br&gt;
&lt;img class=&quot;tex yui-img&quot; alt=&quot;\phi-\beta\,\!&quot; src=&quot;http://upload.wikimedia.org/math/7/5/3/7534fbf825ec859a3e87f24573465b01.png&quot;&gt;&lt;/th&gt;
&lt;th&gt;Authalic&lt;br&gt;
&lt;img class=&quot;tex yui-img&quot; alt=&quot;\phi-\xi\,\!&quot; src=&quot;http://upload.wikimedia.org/math/b/4/4/b44db2389065b5ce1a8b0a7e66a03461.png&quot;&gt;&lt;/th&gt;
&lt;th&gt;Rectifying&lt;br&gt;
&lt;img class=&quot;tex yui-img&quot; alt=&quot;\phi-\mu\,\!&quot; src=&quot;http://upload.wikimedia.org/math/a/f/e/afe6668bc4795b66c9b5ce6d3c7ec58a.png&quot;&gt;&lt;/th&gt;
&lt;th&gt;Conformal&lt;br&gt;
&lt;img class=&quot;tex yui-img&quot; alt=&quot;\phi-\chi\,\!&quot; src=&quot;http://upload.wikimedia.org/math/7/0/7/707cf74a46c9d9cbd175a0336dd357c4.png&quot;&gt;&lt;/th&gt;
&lt;th&gt;Geocentric&lt;br&gt;
&lt;img class=&quot;tex yui-img&quot; alt=&quot;\phi-\psi\,\!&quot; src=&quot;http://upload.wikimedia.org/math/7/7/b/77b78087727b404d9c709aa2241a6f9f.png&quot;&gt;&lt;/th&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;0°&lt;/td&gt;
&lt;td&gt;0.00′&lt;/td&gt;
&lt;td&gt;0.00′&lt;/td&gt;
&lt;td&gt;0.00′&lt;/td&gt;
&lt;td&gt;0.00′&lt;/td&gt;
&lt;td&gt;0.00′&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;5°&lt;/td&gt;
&lt;td&gt;1.01′&lt;/td&gt;
&lt;td&gt;1.35′&lt;/td&gt;
&lt;td&gt;1.52′&lt;/td&gt;
&lt;td&gt;2.02′&lt;/td&gt;
&lt;td&gt;2.02′&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;10°&lt;/td&gt;
&lt;td&gt;1.99′&lt;/td&gt;
&lt;td&gt;2.66′&lt;/td&gt;
&lt;td&gt;2.99′&lt;/td&gt;
&lt;td&gt;3.98′&lt;/td&gt;
&lt;td&gt;3.98′&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;15°&lt;/td&gt;
&lt;td&gt;2.91′&lt;/td&gt;
&lt;td&gt;3.89′&lt;/td&gt;
&lt;td&gt;4.37′&lt;/td&gt;
&lt;td&gt;5.82′&lt;/td&gt;
&lt;td&gt;5.82′&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;20°&lt;/td&gt;
&lt;td&gt;3.75′&lt;/td&gt;
&lt;td&gt;5.00′&lt;/td&gt;
&lt;td&gt;5.62′&lt;/td&gt;
&lt;td&gt;7.48′&lt;/td&gt;
&lt;td&gt;7.48′&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;25°&lt;/td&gt;
&lt;td&gt;4.47′&lt;/td&gt;
&lt;td&gt;5.96′&lt;/td&gt;
&lt;td&gt;6.70′&lt;/td&gt;
&lt;td&gt;8.92′&lt;/td&gt;
&lt;td&gt;8.92′&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;30°&lt;/td&gt;
&lt;td&gt;5.05′&lt;/td&gt;
&lt;td&gt;6.73′&lt;/td&gt;
&lt;td&gt;7.57′&lt;/td&gt;
&lt;td&gt;10.09′&lt;/td&gt;
&lt;td&gt;10.09′&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;35°&lt;/td&gt;
&lt;td&gt;5.48′&lt;/td&gt;
&lt;td&gt;7.31′&lt;/td&gt;
&lt;td&gt;8.22′&lt;/td&gt;
&lt;td&gt;10.95′&lt;/td&gt;
&lt;td&gt;10.96′&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;40°&lt;/td&gt;
&lt;td&gt;5.75′&lt;/td&gt;
&lt;td&gt;7.66′&lt;/td&gt;
&lt;td&gt;8.62′&lt;/td&gt;
&lt;td&gt;11.48′&lt;/td&gt;
&lt;td&gt;11.49′&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;45°&lt;/td&gt;
&lt;td&gt;5.84′&lt;/td&gt;
&lt;td&gt;7.78′&lt;/td&gt;
&lt;td&gt;8.76′&lt;/td&gt;
&lt;td&gt;11.67′&lt;/td&gt;
&lt;td&gt;11.67′&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;50°&lt;/td&gt;
&lt;td&gt;5.75′&lt;/td&gt;
&lt;td&gt;7.67′&lt;/td&gt;
&lt;td&gt;8.63′&lt;/td&gt;
&lt;td&gt;11.50′&lt;/td&gt;
&lt;td&gt;11.50′&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;55°&lt;/td&gt;
&lt;td&gt;5.49′&lt;/td&gt;
&lt;td&gt;7.32′&lt;/td&gt;
&lt;td&gt;8.23′&lt;/td&gt;
&lt;td&gt;10.97′&lt;/td&gt;
&lt;td&gt;10.98′&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;60°&lt;/td&gt;
&lt;td&gt;5.06′&lt;/td&gt;
&lt;td&gt;6.75′&lt;/td&gt;
&lt;td&gt;7.59′&lt;/td&gt;
&lt;td&gt;10.12′&lt;/td&gt;
&lt;td&gt;10.13′&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;65°&lt;/td&gt;
&lt;td&gt;4.48′&lt;/td&gt;
&lt;td&gt;5.97′&lt;/td&gt;
&lt;td&gt;6.72′&lt;/td&gt;
&lt;td&gt;8.95′&lt;/td&gt;
&lt;td&gt;8.96′&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;70°&lt;/td&gt;
&lt;td&gt;3.76′&lt;/td&gt;
&lt;td&gt;5.01′&lt;/td&gt;
&lt;td&gt;5.64′&lt;/td&gt;
&lt;td&gt;7.52′&lt;/td&gt;
&lt;td&gt;7.52′&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;75°&lt;/td&gt;
&lt;td&gt;2.92′&lt;/td&gt;
&lt;td&gt;3.90′&lt;/td&gt;
&lt;td&gt;4.39′&lt;/td&gt;
&lt;td&gt;5.85′&lt;/td&gt;
&lt;td&gt;5.85′&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;80°&lt;/td&gt;
&lt;td&gt;2.00′&lt;/td&gt;
&lt;td&gt;2.67′&lt;/td&gt;
&lt;td&gt;3.00′&lt;/td&gt;
&lt;td&gt;4.00′&lt;/td&gt;
&lt;td&gt;4.01′&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;85°&lt;/td&gt;
&lt;td&gt;1.02′&lt;/td&gt;
&lt;td&gt;1.35′&lt;/td&gt;
&lt;td&gt;1.52′&lt;/td&gt;
&lt;td&gt;2.03′&lt;/td&gt;
&lt;td&gt;2.03′&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;90°&lt;/td&gt;
&lt;td&gt;0.00′&lt;/td&gt;
&lt;td&gt;0.00′&lt;/td&gt;
&lt;td&gt;0.00′&lt;/td&gt;
&lt;td&gt;0.00′&lt;/td&gt;
&lt;td&gt;0.00′&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;&lt;/table&gt;
&lt;/dd&gt;&lt;/dl&gt;
&lt;h3&gt;&lt;span class=&quot;editsection&quot;&gt;&lt;/span&gt;&lt;span class=&quot;mw-headline&quot; id=&quot;Corrections_for_altitude&quot;&gt;Corrections for altitude&lt;/span&gt;&lt;/h3&gt;
&lt;div class=&quot;thumb tright&quot;&gt;
&lt;div class=&quot;thumbinner&quot; style=&quot;width: 258px;&quot;&gt;&lt;a href=&quot;http://en.wikipedia.org/wiki/File:Geocentric_vs_geodetic_latitude_with_elevation.svg&quot; class=&quot;image&quot;&gt;&lt;img alt=&quot;&quot; src=&quot;http://upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Geocentric_vs_geodetic_latitude_with_elevation.svg/256px-Geocentric_vs_geodetic_latitude_with_elevation.svg.png&quot; class=&quot;thumbimage yui-img&quot; width=&quot;256&quot; height=&quot;235&quot;&gt;&lt;/a&gt;&lt;/div&gt;&lt;/div&gt;&lt;p&gt;When converting from geodetic (&quot;common&quot;) latitude to other types of
latitude, corrections must be made for altitude for systems which do
not measure the angle from the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Surface_normal&quot; title=&quot;Surface normal&quot;&gt;normal&lt;/a&gt; of the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Spheroid&quot; title=&quot;Spheroid&quot;&gt;spheroid&lt;/a&gt;. For example, in the figure at right, point &lt;i&gt;H&lt;/i&gt; (located on the surface of the spheroid) and point &lt;i&gt;H'&lt;/i&gt; (located at some greater elevation) have different &lt;i&gt;geocentric&lt;/i&gt; latitudes (angles &lt;i&gt;β&lt;/i&gt; and &lt;i&gt;γ&lt;/i&gt; respectively), even though they share the same &lt;i&gt;geodetic&lt;/i&gt; latitude (angle &lt;i&gt;α&lt;/i&gt;). Note that the flatness of the spheroid and elevation of point &lt;i&gt;H'&lt;/i&gt;
in the image is significantly greater than what is found on the Earth,
exaggerating the errors inherent in such calculations if left
uncorrected. Note also that the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Reference_ellipsoid&quot; title=&quot;Reference ellipsoid&quot;&gt;reference ellipsoid&lt;/a&gt; used in the geodetic system is itself just an approximation of the true &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Geoid&quot; title=&quot;Geoid&quot;&gt;geoid&lt;/a&gt;, and therefore introduces its own errors, though the differences are less severe. (See &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Latitude#Astronomical_latitude&quot;&gt;Astronomical latitude&lt;/a&gt;, above.)&lt;/p&gt;&lt;p&gt;__________________________________________________&lt;/p&gt;&lt;p&gt;Have you really ever wondered? &quot;Hey, what is this latitude in my GPS? I use it for geocaching treasure hunts. What is it?&quot; Then you wonder, &quot;Why did I even ask it?&quot;. Haha!&lt;br&gt;&lt;/p&gt;</description>
            <pubDate>Fri, 13 Nov 2009 07:05:43 +0100</pubDate>
        </item>
        <item>
            <title>A little Geocaching Humor</title>
            <link>http://geocachinggpstreasurehunt.yolasite.com/index/index/a-little-geocaching-humor</link>
            <description>&lt;img class=&quot;yui-img&quot; src=&quot;http://geocachinggpstreasurehunt.yolasite.com/index/resources/geocaching-gps-treasure-hunt.jpeg&quot; style=&quot;width: 325px;&quot;&gt;&lt;br&gt;&lt;br&gt;&lt;span style=&quot;background-color: rgb(255, 255, 255);&quot;&gt;&quot;Geocachers, please don’t take offensive to this t-shirt&quot;&lt;/span&gt;&lt;br&gt;&lt;br&gt;__________________________________________________&lt;br&gt;&lt;br&gt;Hahahaha! This is a good one from Crunchgear. But for the geocachers, it's probably more like &quot;Thank you for paying tax for the satellites that we use for our hobby&quot;. Hahaha!&lt;span style=&quot;background-color: rgb(255, 255, 255);&quot;&gt;&lt;/span&gt;</description>
            <pubDate>Fri, 13 Nov 2009 07:02:48 +0100</pubDate>
        </item>
        <item>
            <title>IPhone Apps for the Geocaching enthusiast</title>
            <link>http://geocachinggpstreasurehunt.yolasite.com/index/index/iphone-apps-for-the-geocaching-enthusiast</link>
            <description>Geocaching is becoming more a popular hobby for the outdoor activities seeker and &quot;treasure hunting&quot;&amp;nbsp; enthusiast. Most often people are unfamiliar with the concept, and some assume that you need expensive equipment to have an enjoyable geocaching experience. Thankfully, you can go geocaching with your iPhone! without having to spend too much. Yahoo! As long as you are not addicted to your couch, you are going to enjoy experiencing different geocaching missions.&lt;br&gt;&lt;br&gt;Let us check out these some useful Apps:&lt;br&gt;&lt;br&gt;Geosphere: Geosphere is yet another cool geo-caching iPhone app that enables you to get outdoors and have fun. What I like about this app is the fact that it lets you search for missions based on difficulty and other factors.&lt;br&gt;&lt;br&gt;iGeocacher: a sophisticated geo-caching app for iPhone that makes it so easy to go outdoors without having to use a single piece of paper. The interface is easy to use and the app works offline as well.&lt;br&gt;&lt;br&gt;Geocaching: one of the most popular geo-caching apps for iPhone. Comes with 895,000 geo-caches that can keep you entertained forever.&lt;br&gt;&lt;br&gt;Geocaching Buddy: more of an add on for iGeocacher. It integrates well with that app and makes it easier to complete your missions. It helps you remember your clues and get more done outdoors.&lt;br&gt;&lt;br&gt;GPS Mission Pro: a cool app that lets you play games all around your neighborhood and quit your couch addiction.&lt;br&gt;&lt;br&gt;MotionX GPS Sport: a complete GPS app that not only lets you get around using your phone, it makes it easy to go geocaching as well. Gives you great bang for your buck.&lt;br&gt;&lt;br&gt;&lt;a class=&quot;&quot; title=&quot;&quot; href=&quot;http://www.iphoneness.com/iphone-apps/5-cool-geocaching-applications-for-iphone/&quot;&gt;Geocaching GPS Treasure Hunt Information Source&lt;/a&gt;&lt;br&gt;&lt;br&gt;__________________________________________________&lt;br&gt;&lt;br&gt;This are real great tips on IPhone Apps for the geocaching experience. Thanks! GPS Mission Pro sounds fun.&lt;br&gt;</description>
            <pubDate>Fri, 13 Nov 2009 06:51:13 +0100</pubDate>
        </item>
        <item>
            <title>Hiking, Exercise can be so Rewarding: Geocaching</title>
            <link>http://geocachinggpstreasurehunt.yolasite.com/index/index/hiking-exercise-can-be-so-rewarding-geocaching</link>
            <description>&lt;h1&gt;Cache In, Trash Out: The New Geocaching Mantra of Eco-Resorts&lt;/h1&gt;&lt;br&gt;&lt;h2&gt;Take a hike; get a gift-not a bad way to spend a green day.&lt;/h2&gt;By&lt;span style=&quot;text-decoration: none;&quot;&gt; Laurel House&lt;br&gt;&lt;br&gt;&lt;/span&gt;&lt;p&gt;Forget about golf, hotels are getting savvy when it comes to keeping
their guests engaged in green activities that not only help clean up
the environment, but give them a gift in return. Yes, there are two
things that the average human being loves: the &quot;hunt,&quot; and presents.
Mix the two with the great outdoors and exercise and you've got &lt;a class=&quot;&quot; href=&quot;http://planetgreen.discovery.com/travel-outdoors/geocaching-green-pastime.html&quot;&gt;GeoCaching&lt;/a&gt;--a form of high-tech treasure hunting that's inviting a childlike exuberance to emerge from even the most stale adults. &lt;/p&gt;
&lt;p&gt;The outdoor game has players using GPS tracking systems to coordinate hidden treasure &lt;a class=&quot;&quot; href=&quot;http://planetgreen.discovery.com/home-garden/reuse-altoids-tins.html&quot;&gt;caches hidden in little boxes&lt;/a&gt;
in obscure spots all over the world. From rarely explored waterfalls to
city street corners, the world-wide scavenger hunt is getting people of
all ages and abilities outside and into this greener exercise activity.
Each cache consists of a visitor's log so that gamers can mark their
territory and even leave a note for the next cache guest. Many caches
also have little gifts with a take-one, leave-one concept that can be
anything from dice to paper airplanes, jewelry and even tickets to
sporting events. &lt;/p&gt;
&lt;p&gt;No geocaches in your immediate area? Create, hide and register one
yourself http://www.wikihow.com/Create-and-Hide-a-Geocache! It's a
great way to change up your work out and even get kids to exercise
without knowing it! With over 933,945 &lt;a class=&quot;&quot; href=&quot;http://www.geocaching.com/&quot;&gt;active geocaches around the world&lt;/a&gt;,
you are almost certain to have a green adventure in your area. Or take
a trip to one of these resorts to learn how the game works first:&lt;/p&gt;
&lt;h3&gt;Where Can You Learn to GeoCache?&lt;/h3&gt;
&lt;p&gt;&lt;br&gt;
&lt;a class=&quot;&quot; href=&quot;http://www.ojairesort.com/&quot;&gt;Ojai Valley Inn and Spa,&lt;/a&gt; an
environmentally conscious resort in Southern California, is a great
place to learn the basics of geocaching with a guide-led hike complete
with all of the accouterments including a backpack, GPS unit, energy
bars, water, and maps. Highfalutin guests scour the surrounding
mountains for secret caches while encouraging each person to remove any
spotted trash. The idea is &quot;cache in, trash out&quot;--essentially
incentive-driven trail clean-ups. The resort's geocaching crew makes
sure that caches are stocked with fun little gifts like locally made
bracelets and crafts to up the ante and keep the crowds scouring the
trails for cache and trash. &lt;/p&gt;
&lt;p&gt;Red Mountain Spa in Utah provides GPS units to interested guests
then teaches the newbie geo-adventurers how to log and read coordinates
(longitude and latitude), and finally lead them on a search of hidden
caches throughout the 55-acre property. The tough terrain offers a very
active trek, as buccaneers forge through streams, jump ravines and
scale rocky hillsides all for the sake of treasure hunting! Since the
caches are contained on the Red Mountain property and its surrounding,
caches can include gift certificates to the spa, resort skincare
products, and fitness gear!&lt;/p&gt;
&lt;p&gt;Who knew exercise could be so rewarding! &lt;br&gt;&lt;/p&gt;&lt;p&gt;&lt;a class=&quot;&quot; title=&quot;&quot; href=&quot;http://planetgreen.discovery.com/food-health/cache-trash-geocaching-resorts.html&quot;&gt;Geocaching GPS Treasure Hunt Information Source&lt;/a&gt;&lt;/p&gt;&lt;p&gt;__________________________________________________&lt;/p&gt;&lt;p&gt;&quot;Who knew exercise could be so rewarding&quot; indeed. This could make hiking even more an enjoyable experience. This is great for the young and even greater for the young at heart and spirit.&lt;br&gt;&lt;/p&gt;&lt;br&gt;</description>
            <pubDate>Fri, 13 Nov 2009 06:42:35 +0100</pubDate>
        </item>
        <item>
            <title>Trackable Treasures Collectors: Geocoins</title>
            <link>http://geocachinggpstreasurehunt.yolasite.com/index/index/trackable-treasures-collectors-geocoins</link>
            <description>&lt;p&gt;A &lt;b&gt;geocoin&lt;/b&gt; is a metal or wooden coin minted in similar fashion to a &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Medallion&quot; title=&quot;Medallion&quot;&gt;medallion&lt;/a&gt;, &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Token_coin&quot; title=&quot;Token coin&quot;&gt;token coin&lt;/a&gt;, military &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Challenge_coin&quot; title=&quot;Challenge coin&quot;&gt;challenge coin&lt;/a&gt; or &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Wooden_nickel&quot; title=&quot;Wooden nickel&quot;&gt;wooden nickel&lt;/a&gt;, for use in &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Geocaching&quot; title=&quot;Geocaching&quot;&gt;geocaching&lt;/a&gt;. Some geocoins are trackable on the internet using a serial number and website address engraved on the coin.&lt;/p&gt;
&lt;p&gt;Personal geocoins are a personal signature item bearing the geocacher's &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Pseudonym&quot; title=&quot;Pseudonym&quot;&gt;handle&lt;/a&gt; and personal design, similar to a &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Heraldry&quot; title=&quot;Heraldry&quot;&gt;heraldic&lt;/a&gt; device. Geocoins are often minted by caching organizations and as fund-raisers for geocaching events.&lt;/p&gt;
&lt;p&gt;Geocoins with tracking numbers that have been registered on their
associated websites are said to be &quot;activated&quot;, whereas geocoins that
are still unregistered are termed &quot;unactivated&quot;. Activated geocoins
that have been left in a cache are meant to be moved from cache to
cache like a &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Travel_Bug&quot; title=&quot;Travel Bug&quot;&gt;Travel Bug&lt;/a&gt;, whereas unactivated geocoins may be placed in geocaches to be found by others and kept as &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Trophy&quot; title=&quot;Trophy&quot;&gt;trophies&lt;/a&gt;.
Unactivated coins may be also traded or given to other cachers like a
calling card, as prizes, as awards, or merely sold and collected.&lt;/p&gt;&lt;h2&gt;&lt;span class=&quot;mw-headline&quot; id=&quot;Other_Geocoin-tracking_Sites&quot;&gt;Trackable Geocoins&lt;br&gt;&lt;/span&gt;&lt;/h2&gt;

&lt;p&gt;When a cache listed at geocaching.com contains a geocoin, an icon
(often unique to the coin) is shown on the cache page's &quot;Inventory&quot;
section. This icon will also appear in the inventory of any cacher
holding one as well as in each cacher's historical trackable item
listing. Icons will also remain in the inventory of cachers who log the
'discovery' of a geocoin's number without physically removing it from a
cache. &quot;Icon collecting&quot; -- the act of having these icons listed in
one's trackables listing -- is an associated hobby. Many people bring
geocoins with unique icons to geocaching events so that others may see
the coins and use the tracking number to collect the icons online, and
it is not uncommon for collectors to activate some or all of the coins
in their collections in order to have a matching online collection of
icons associated with their geocaching.com accounts.&lt;/p&gt;&lt;h2&gt;&lt;span class=&quot;mw-headline&quot; id=&quot;History_of_Geocaching.com_Trackable_Geocoins&quot;&gt;Geocoin Theft&lt;br&gt;&lt;/span&gt;&lt;/h2&gt;

&lt;p&gt;It is not uncommon for activated, released geocoins to go missing,
whether because a cacher is unfamiliar with the logging and tracking
process or due to outright theft. Some geocoin owners will purposefully
attempt to destroy the resale value of the coin by drilling and tagging
it with an extra tag, marker, or other item that is intended to
underscore the fact that the geocoin is meant to travel, not to be kept&lt;sup id=&quot;cite_ref-0&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Geocoin#cite_note-0&quot;&gt;&lt;span&gt;[&lt;/span&gt;1&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt;.
Another somewhat controversial anti-theft measure is to create a copy
of the geocoin, releasing the copy and keeping the original&lt;sup id=&quot;cite_ref-1&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Geocoin#cite_note-1&quot;&gt;&lt;span&gt;[&lt;/span&gt;2&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt;.&lt;/p&gt;
&lt;h2&gt;&lt;span class=&quot;editsection&quot;&gt;&lt;/span&gt;&lt;span class=&quot;mw-headline&quot; id=&quot;History_of_Geocaching.com_Trackable_Geocoins&quot;&gt;History of the Trackable Geocoins&lt;/span&gt;&lt;/h2&gt;
&lt;ul&gt;&lt;li&gt;&lt;span class=&quot;mw-formatted-date&quot; title=&quot;2001-09-30&quot;&gt;&lt;span class=&quot;mw-formatted-date&quot; title=&quot;09-30&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/September_30&quot; title=&quot;September 30&quot;&gt;September 30&lt;/a&gt;&lt;/span&gt;, &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/2001&quot; title=&quot;2001&quot;&gt;2001&lt;/a&gt;&lt;/span&gt; The first trackable geocoin released was the Moun10Bike Version 1 Geocoin #002.&lt;sup id=&quot;cite_ref-2&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Geocoin#cite_note-2&quot;&gt;&lt;span&gt;[&lt;/span&gt;3&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt;
The Moun10Bike Version 1 Geocoins are the most sought-after geocoins in
existence. They are all displayed on geocaching.com as owned by
Moun10Bike and he has strictly forbidden their sale; however,
unscrupulous or ignorant persons may list the coin for sale on auction
sites such as eBay, fetching prices in the thousands of USD. When he
finds that a coin has been sold without permission, he has the coin
locked so it is no longer trackable.&lt;sup id=&quot;cite_ref-3&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Geocoin#cite_note-3&quot;&gt;&lt;span&gt;[&lt;/span&gt;4&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt;&lt;/li&gt;&lt;/ul&gt;
&lt;ul&gt;&lt;li&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/2003&quot; title=&quot;2003&quot;&gt;2003&lt;/a&gt;
The first USAGeocoin was released for sale, making it one of the first
geocoins that one can buy, release, and track online without minting an
exclusive personal design. The proposed 2002 design was never made. &lt;sup id=&quot;cite_ref-4&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Geocoin#cite_note-4&quot;&gt;&lt;span&gt;[&lt;/span&gt;5&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt;&lt;/li&gt;&lt;/ul&gt;
&lt;ul&gt;&lt;li&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/2005&quot; title=&quot;2005&quot;&gt;2005&lt;/a&gt; &lt;a href=&quot;http://en.wikipedia.org/wiki/Geocaching.com&quot; title=&quot;Geocaching.com&quot; class=&quot;mw-redirect&quot;&gt;Geocaching.com&lt;/a&gt;
permitted any geocaching.com user to purchase tracking numbers for
approved designs, fueling a sudden surge in number of coins. Minimum
purchase was initially set at 1000 tracking numbers.&lt;/li&gt;&lt;/ul&gt;
&lt;ul&gt;&lt;li&gt;&lt;a href=&quot;http://en.wikipedia.org/wiki/Fall&quot; title=&quot;Fall&quot; class=&quot;mw-redirect&quot;&gt;Fall&lt;/a&gt; &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/2006&quot; title=&quot;2006&quot;&gt;2006&lt;/a&gt;
Groundspeak reduced the minimum purchase of tracking numbers, and the
minimum number of coins minted to obtain a unique icon, to 250. The
drop in the cost to create a geocoin with a unique icon fueled a
'geocoin craze' with hundreds of new personal, group and increasingly
purely commercial designs minted.&lt;sup id=&quot;cite_ref-5&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Geocoin#cite_note-5&quot;&gt;&lt;span&gt;[&lt;/span&gt;6&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt;&lt;/li&gt;&lt;/ul&gt;
&lt;ul&gt;&lt;li&gt;&lt;span class=&quot;mw-formatted-date&quot; title=&quot;2007-02-17&quot;&gt;&lt;span class=&quot;mw-formatted-date&quot; title=&quot;02-17&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/February_17&quot; title=&quot;February 17&quot;&gt;February 17&lt;/a&gt;&lt;/span&gt;, &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/2007&quot; title=&quot;2007&quot;&gt;2007&lt;/a&gt;&lt;/span&gt; The First Annual Geocoinfest was held in &lt;a href=&quot;http://en.wikipedia.org/wiki/Temecula,_CA&quot; title=&quot;Temecula, CA&quot; class=&quot;mw-redirect&quot;&gt;Temecula, CA&lt;/a&gt;.
This event brought hundreds of geocoin collectors together for the
first time in a mass event, with many exclusive coins being given away
or traded.&lt;sup id=&quot;cite_ref-6&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Geocoin#cite_note-6&quot;&gt;&lt;span&gt;[&lt;/span&gt;7&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt;&lt;/li&gt;&lt;/ul&gt;
&lt;ul&gt;&lt;li&gt;&lt;span class=&quot;mw-formatted-date&quot; title=&quot;2009-03-04&quot;&gt;&lt;span class=&quot;mw-formatted-date&quot; title=&quot;03-04&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/March_4&quot; title=&quot;March 4&quot;&gt;March 4&lt;/a&gt;&lt;/span&gt;, &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/2009&quot; title=&quot;2009&quot;&gt;2009&lt;/a&gt;&lt;/span&gt;
Geocaching.com further reduced the minimum number of codes for purchase
to 50, and the minimum number of coins eligible for a custom icon to
50. &lt;sup id=&quot;cite_ref-7&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Geocoin#cite_note-7&quot;&gt;&lt;span&gt;[&lt;/span&gt;8&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt;&lt;/li&gt;&lt;/ul&gt;
&lt;h2&gt;&lt;span class=&quot;editsection&quot;&gt;&lt;/span&gt;&lt;span class=&quot;mw-headline&quot; id=&quot;Geocoin_Terminology&quot;&gt;Geocoin Terminology&lt;/span&gt;&lt;/h2&gt;&lt;b&gt;&lt;span class=&quot;mw-headline&quot; id=&quot;Coin_Finishes&quot;&gt;Coin Finishes&lt;/span&gt;&lt;/b&gt;
&lt;ul&gt;&lt;li&gt;Antique Finish: A finish applied to copper, gold, or silver to give
it a darker look. This finish is used often to have the fine details in
a coin stand out more clearly.&lt;/li&gt;&lt;li&gt;Foggy Painting: Paint finish simulating metal applied surface. Can
has gloss, shine or lustre but lacking definition (foggy details).&lt;/li&gt;&lt;li&gt;Matte: see Satin Finish.&lt;/li&gt;&lt;li&gt;Misty: Silver or gold finish simulating effect of unpolished areas of a proof coin.&lt;/li&gt;&lt;li&gt;Proof-like: Effect attained on high quality die stuck coins by high
pressure and multiple strikes producing mirror finish background with
satin finish relief areas&lt;/li&gt;&lt;li&gt;Satin Finish: A finish giving a matte (non-glossy) look to the
metal. A misused term as traditionally (in fabric) a satin finish often
has a level of gloss associated with it.&lt;/li&gt;&lt;li&gt;Silver: 1. plated with silver 2. .999 solid silver 3. silver-like nickel plated (shiny nickel).&lt;/li&gt;&lt;/ul&gt;
&lt;h3&gt;&lt;span class=&quot;editsection&quot;&gt;&lt;/span&gt;&lt;span class=&quot;mw-headline&quot; id=&quot;Collecting_Terms&quot;&gt;Collecting Terms&lt;/span&gt;&lt;/h3&gt;
&lt;ul&gt;&lt;li&gt;AE: Artists Edition: type of SE; a version of a retail commercial geocoin only made available to the designer of the coin.&lt;/li&gt;&lt;li&gt;LE: Limited Edition: Typically a different version (color, metal,
etc.) than the main run of coins. Produced in a limited quantity one
time only.&lt;/li&gt;&lt;li&gt;RE: Regular edition not produced in a limited in number thus may be
reprised according to demand as dies are held by the mint for minimum
of three years.&lt;/li&gt;&lt;li&gt;SE: Special Edition: Typically a different version to the main run
of coins but unlike LE, XLE or XXLE no limit on the number minted, and
they may be reminted at any time.&lt;/li&gt;&lt;li&gt;XLE: Extra Limited Edition: Same as LE only fewer.&lt;/li&gt;&lt;li&gt;XXLE: Extremely Limited Edition: Same as XLE only fewer.&lt;/li&gt;&lt;li&gt;HTF: Hard to Find; refers to ease of acquiring through purchase or trade not total mint numbers&lt;/li&gt;&lt;li&gt;VHTF: Very Hard to Find; refers to ease of acquiring through purchase or trade not total mint numbers&lt;/li&gt;&lt;li&gt;Proof Coin: 1.the sample coins provided by the mint 2.Effect
attained on high quality die stuck coins by high pressure and multiple
strikes producing mirror finish background with satin finish relief
areas.&lt;/li&gt;&lt;li&gt;Sample Coin: The sample coins provided by the mint. Some sample geocoins do not have tracking numbers.&lt;/li&gt;&lt;/ul&gt;
&lt;h3&gt;&lt;span class=&quot;editsection&quot;&gt;&lt;/span&gt;&lt;span class=&quot;mw-headline&quot; id=&quot;Geocaching_Terms&quot;&gt;Geocaching Terms&lt;/span&gt;&lt;/h3&gt;
&lt;ul&gt;&lt;li&gt;Custom Icon: 16 x 16 px or 32 x 32 px GIF files that are associated
to the coin or coin series by geocaching.com trackable coins.&lt;/li&gt;&lt;li&gt;Micro: A geocoin that is smaller than ~1.25 inches in diameter.
Generally recognized as a coin that would fit inside a 35mm film
canister.&lt;/li&gt;&lt;li&gt;Non-trackable: A geocoin produced without a tracking number.&lt;/li&gt;&lt;li&gt;Personal: A geocoin produced or designed by an individual or team
of geocachers featuring team or cacher's nickname (&quot;geonick&quot;)
prominently on the coin.&lt;/li&gt;&lt;li&gt;Pathtag: Pathtags are a geocoin about the size of a U.S. quarter.
They are used for trading, collecting and personal signature items.
They are trackable at the www.pathtags.com website but not at
geocaching.com.&lt;/li&gt;&lt;/ul&gt;
</description>
            <pubDate>Fri, 13 Nov 2009 06:33:05 +0100</pubDate>
        </item>
        <item>
            <title>Geocaching Challenge in Molalla!</title>
            <link>http://geocachinggpstreasurehunt.yolasite.com/index/index/geocaching-challenge-in-molalla-</link>
            <description>&lt;h2&gt;Molalla to launch geocaching challenge&lt;/h2&gt;&lt;span&gt;By Pioneer Staff&lt;br&gt;&lt;br&gt;&lt;/span&gt;&lt;span id=&quot;ctl00_ctl00_MainContent_MainContent_lblNewsContentText&quot;&gt;The Molalla Geocaching Challenge launches this weekend, sponsored by the city of Molalla and Molalla Area Chamber of Commerce. &lt;br&gt;
&lt;br&gt;
Geocaching is a high-tech treasure hunt that has become a popular hobby
worldwide, with participants using GPS devices and clues posted online
to locate hidden containers (caches). &lt;br&gt;
&lt;br&gt;
“It’s a fun way to attract visitors to Molalla,” Mayor Mike Clarke said
in a press release. “While they’re here looking for hidden caches, they
may discover our elk farm, our train park, our BMX track, or our nature
park and want to come back for another visit.” &lt;br&gt;
&lt;br&gt;
The first 250 participants who complete the challenge will receive a free Molalla medallion at the chamber of commerce office. &lt;br&gt;
&lt;br&gt;
Ten caches have been hidden as part of the challenge and the locations
of each cache, along with clues for tracking them down, will be posted
on &lt;a class=&quot;&quot; href=&quot;http://www.geocaching.com&quot;&gt;www.geocaching.com&lt;/a&gt;
by Friday, Nov. 13. Each cache will include a code word, which
participants must correctly identify if they wish to receive the
medallion. &lt;br&gt;
&lt;br&gt;
Those who find all 10 code words will be entered in a drawing for a $100 gift certificate at the Farmstead Restaurant and Pub. &lt;br&gt;
&lt;br&gt;
“Here’s yet another way to celebrate Oregon’s 150th birthday with a
Molalla spin,” Molalla City Manager John Atkins said in a press
release. “We’re giving people the chance to see where we have come from
and where we are now—the hunt should prove as gratifying as the coins.”
&lt;br&gt;
&lt;br&gt;
Each medallion, also known as a geocoin, is inscribed with a unique
code, allowing the owner to register the coin online if they choose and
hide it in another cache. The coin’s whereabouts can then be tracked
online as geocachers move it from cache to cache. &lt;br&gt;
&lt;br&gt;
Brochures about the treasure hunt will be available at Molalla City
Hall, the Molalla Area Chamber of Commerce and on the city’s Web site, &lt;a class=&quot;&quot; href=&quot;http://www.cityofmolalla.com&quot;&gt;www.cityofmolalla.com&lt;/a&gt;. &lt;br&gt;
&lt;br&gt;
Funding for the coins was provided by the Clackamas County Tourism and Cultural Affairs Department, Atkins said.&lt;br&gt;&lt;br&gt;&lt;a class=&quot;&quot; title=&quot;&quot; href=&quot;http://www.molallapioneer.com/news/2009/November/09/Local.News/molalla.to.launch.geocaching.challenge/news.aspx&quot;&gt;Geocaching GPS Treasure Hunt News Source&lt;/a&gt;&lt;br&gt;&lt;br&gt;__________________________________________________&lt;br&gt;&lt;br&gt;This is great news for the tachie in Oregon! Thank you Molalla!&lt;br&gt;__________________________________________________&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;/span&gt;&lt;h1&gt;Molalla is hosting a Geocaching Challenge&lt;/h1&gt;By Vickie Kavanagh, The Oregonian&lt;br&gt;&lt;br&gt;The City of Molalla and its chamber of commerce have teamed up to host
a Geocaching Challenge -- a high-tech treasure hunting game designed
for Global Positioning System device owners. &lt;br&gt;&lt;br&gt;People are
challenged to locate 10 caches -- each with a unique code word inside
-- hidden in and around Molalla. The prize for seven out of 10 is a
commemorative medallion or &quot;geocoin.&quot; Geocoin owners can register the
coins on an international site and, if they choose, hide them somewhere
else and track their position as they are found and rehidden by other
geocachers. &lt;br&gt;&lt;br&gt;Those who identify all 10 code words correctly
will be entered in a drawing for a $100 gift certificate to the
Farmstead Restaurant and Pub at the Arrowhead Golf Club, 28301 S.
Oregon 213. &lt;br&gt;&lt;br&gt;The locations and clues will be revealed on or
before Friday. For details, pick up a brochure at city hall, 117 N.
Molalla Ave., or the chamber, 105 E. Main St.; visit the &lt;a class=&quot;&quot; href=&quot;mailto:vickiekavanagh@news.oregonian.com&quot;&gt;Web site&lt;/a&gt;; or call John Atkins at 503-829-6855.&lt;br&gt;&lt;br&gt;&lt;span id=&quot;ctl00_ctl00_MainContent_MainContent_lblNewsContentText&quot;&gt;&lt;a class=&quot;&quot; title=&quot;&quot; href=&quot;http://www.oregonlive.com/clackamascounty/index.ssf/2009/11/molalla_is_hosting_a_geocachin.html&quot;&gt;Geocaching GPS Treasure Hunt News Source&lt;/a&gt;&lt;/span&gt;&lt;br&gt;&lt;br&gt;&lt;span id=&quot;ctl00_ctl00_MainContent_MainContent_lblNewsContentText&quot;&gt;__________________________________________________&lt;br&gt;&lt;br&gt;Geocoins! Geocoins! Good luck to those who will be participation in these. Find 7 of 10 hidden caches you get a Geocoin.&lt;br&gt;&lt;/span&gt;</description>
            <pubDate>Fri, 13 Nov 2009 06:29:14 +0100</pubDate>
        </item>
        <item>
            <title>Geocaching sounds fun, what is GPS anyway?</title>
            <link>http://geocachinggpstreasurehunt.yolasite.com/index/index/geocaching-sounds-fun-what-is-gps-anyway-</link>
            <description>&lt;p&gt;The &lt;b&gt;Global Positioning System&lt;/b&gt; (&lt;b&gt;GPS&lt;/b&gt;) is a U.S. space-based &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Global_navigation_satellite_system&quot; title=&quot;Global navigation satellite system&quot;&gt;global navigation satellite system&lt;/a&gt;.
It provides reliable positioning, navigation, and timing services to
worldwide users on a continuous basis in all weather, day and night,
anywhere on or near the Earth.&lt;/p&gt;
&lt;p&gt;GPS is made up of three parts: between 24 and 32 satellites orbiting
the Earth, four control and monitoring stations on Earth, and the GPS &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Receiver_%28radio%29&quot; title=&quot;Receiver (radio)&quot;&gt;receivers&lt;/a&gt; owned by users. GPS satellites &lt;a href=&quot;http://en.wikipedia.org/wiki/Broadcast_signal&quot; title=&quot;Broadcast signal&quot; class=&quot;mw-redirect&quot;&gt;broadcast signals&lt;/a&gt;
from space that are used by GPS receivers to provide three-dimensional
location (latitude, longitude, and altitude) plus the time.&lt;/p&gt;
&lt;p&gt;GPS has become a widely used &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Radio_navigation&quot; title=&quot;Radio navigation&quot;&gt;aid to navigation&lt;/a&gt; worldwide, and a useful tool for &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Cartography&quot; title=&quot;Cartography&quot;&gt;map-making&lt;/a&gt;, &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Surveying&quot; title=&quot;Surveying&quot;&gt;land surveying&lt;/a&gt;, commerce, scientific uses, tracking and surveillance, and hobbies such as &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Geocaching&quot; title=&quot;Geocaching&quot;&gt;geocaching&lt;/a&gt; and &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Waymarking&quot; title=&quot;Waymarking&quot;&gt;waymarking&lt;/a&gt;. Also, the precise &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Time_transfer&quot; title=&quot;Time transfer&quot;&gt;time reference&lt;/a&gt;
is used in many applications including the scientific study of
earthquakes and as a time synchronization source for cellular network
protocols.&lt;/p&gt;
&lt;p&gt;GPS has become a mainstay of transportation systems worldwide,
providing navigation for aviation, ground, and maritime operations.
Disaster relief and emergency services depend upon GPS for location and
timing capabilities in their life-saving missions. Everyday activities
such as banking, mobile phone operations, and even the control of power
grids, are facilitated by the accurate timing provided by GPS. Farmers,
surveyors, geologists and countless others perform their work more
efficiently, safely, economically, and accurately using the free and
open GPS signals.&lt;/p&gt;&lt;h2&gt;&lt;span class=&quot;mw-headline&quot; id=&quot;History&quot;&gt;History&lt;/span&gt;&lt;/h2&gt;
&lt;p&gt;The first satellite navigation system, &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Transit_%28satellite%29&quot; title=&quot;Transit (satellite)&quot;&gt;Transit&lt;/a&gt;, used by the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/United_States_Navy&quot; title=&quot;United States Navy&quot;&gt;United States Navy&lt;/a&gt;,
was first successfully tested in 1960. It used a constellation of five
satellites and could provide a navigational fix approximately once per
hour. In 1967, the U.S. Navy developed the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Timation&quot; title=&quot;Timation&quot;&gt;Timation&lt;/a&gt;
satellite which proved the ability to place accurate clocks in space, a
technology that GPS relies upon. In the 1970s, the ground-based &lt;a href=&quot;http://en.wikipedia.org/wiki/Omega_Navigation_System&quot; title=&quot;Omega Navigation System&quot; class=&quot;mw-redirect&quot;&gt;Omega Navigation System&lt;/a&gt;, based on &lt;a href=&quot;http://www.jproc.ca/hyperbolic/omega.html&quot; class=&quot;external text&quot; rel=&quot;nofollow&quot;&gt;phase comparison of signal transmission from pairs of stations&lt;/a&gt;, became the first worldwide radio navigation system. &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Friedwardt_Winterberg&quot; title=&quot;Friedwardt Winterberg&quot;&gt;Friedwardt Winterberg&lt;/a&gt;&lt;sup id=&quot;cite_ref-0&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Global_Positioning_System#cite_note-0&quot;&gt;&lt;span&gt;[&lt;/span&gt;1&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt; proposed a test of &lt;a href=&quot;http://en.wikipedia.org/wiki/General_Relativity&quot; title=&quot;General Relativity&quot; class=&quot;mw-redirect&quot;&gt;General Relativity&lt;/a&gt; using accurate &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Atomic_clock&quot; title=&quot;Atomic clock&quot;&gt;atomic clocks&lt;/a&gt;
placed in orbit in artificial satellites. To achieve accuracy
requirements, GPS uses principles of general relativity to correct the
satellites' atomic clocks.&lt;/p&gt;
&lt;p&gt;The design of GPS is based partly on similar ground-based radio navigation systems, such as &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/LORAN&quot; title=&quot;LORAN&quot;&gt;LORAN&lt;/a&gt; and the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Decca_Navigator_System&quot; title=&quot;Decca Navigator System&quot;&gt;Decca Navigator&lt;/a&gt; developed in the early 1940s, and used during &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/World_War_II&quot; title=&quot;World War II&quot;&gt;World War II&lt;/a&gt;. Additional inspiration for the GPS came when the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Soviet_Union&quot; title=&quot;Soviet Union&quot;&gt;Soviet Union&lt;/a&gt; launched the first man-made satellite, &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Sputnik_program&quot; title=&quot;Sputnik program&quot;&gt;Sputnik&lt;/a&gt;
in 1957. A team of U.S. scientists led by Dr. Richard B. Kershner were
monitoring Sputnik's radio transmissions. They discovered that, because
of the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Doppler_effect&quot; title=&quot;Doppler effect&quot;&gt;Doppler effect&lt;/a&gt;,
the frequency of the signal being transmitted by Sputnik was higher as
the satellite approached, and lower as it continued away from them.
They realized that since they knew their exact location on the globe,
they could pinpoint where the satellite was along its orbit by
measuring the Doppler distortion (see &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Transit_%28satellite%29&quot; title=&quot;Transit (satellite)&quot;&gt;Transit (satellite)&lt;/a&gt;).&lt;/p&gt;
&lt;p&gt;After &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Korean_Air_Lines_Flight_007&quot; title=&quot;Korean Air Lines Flight 007&quot;&gt;Korean Air Lines Flight 007&lt;/a&gt; was shot down in 1983 after straying into the USSR's &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Prohibited_airspace&quot; title=&quot;Prohibited airspace&quot;&gt;prohibited airspace&lt;/a&gt;,&lt;sup id=&quot;cite_ref-1&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Global_Positioning_System#cite_note-1&quot;&gt;&lt;span&gt;[&lt;/span&gt;2&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt; President &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Ronald_Reagan&quot; title=&quot;Ronald Reagan&quot;&gt;Ronald Reagan&lt;/a&gt; issued a directive making GPS freely available for civilian use, once it was sufficiently developed, as a common good.&lt;sup id=&quot;cite_ref-KAL007_2-0&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Global_Positioning_System#cite_note-KAL007-2&quot;&gt;&lt;span&gt;[&lt;/span&gt;3&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt; The first satellite was launched in 1989 and the 24th and last satellite was launched in 1994.&lt;/p&gt;
&lt;p&gt;Initially the highest quality signal was reserved for military use,
and the signal available for civilian use intentionally degraded
(&quot;Selective Availability&quot;, SA). Selective Availability was ended in
2000, improving the precision of civilian GPS from about 100m to about
20m.&lt;/p&gt;&lt;h2&gt;&lt;span class=&quot;mw-headline&quot; id=&quot;History&quot;&gt;Basic Concepts&lt;br&gt;&lt;/span&gt;&lt;/h2&gt;

&lt;p&gt;A GPS receiver calculates its position by precisely timing the signals sent by the GPS &lt;a href=&quot;http://en.wikipedia.org/wiki/Satellites&quot; title=&quot;Satellites&quot; class=&quot;mw-redirect&quot;&gt;satellites&lt;/a&gt; high above the Earth. Each satellite continually transmits messages which include&lt;/p&gt;
&lt;ul&gt;&lt;li&gt;the time the message was sent&lt;/li&gt;&lt;li&gt;precise orbital information (the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Ephemeris&quot; title=&quot;Ephemeris&quot;&gt;ephemeris&lt;/a&gt;)&lt;/li&gt;&lt;li&gt;the general system health and rough orbits of all GPS satellites (the almanac).&lt;/li&gt;&lt;/ul&gt;
&lt;p&gt;The receiver measures the transit time of each message and computes the distance to each satellite. Geometric &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Trilateration&quot; title=&quot;Trilateration&quot;&gt;trilateration&lt;/a&gt;
is used to combine these distances with the satellites' locations to
obtain the position of the receiver. This position is then displayed,
perhaps with a moving map display or latitude and longitude; elevation
information may be included. Many GPS units also show derived
information such as direction and speed, calculated from position
changes.&lt;/p&gt;
&lt;p&gt;Three satellites might seem enough to solve for position, since
space has three dimensions. However, even a very small clock error
multiplied by the very large &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Speed_of_light&quot; title=&quot;Speed of light&quot;&gt;speed of light&lt;/a&gt;&lt;sup id=&quot;cite_ref-14&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Global_Positioning_System#cite_note-14&quot;&gt;&lt;span&gt;[&lt;/span&gt;15&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt;—the
speed at which satellite signals propagate—results in a large
positional error. Therefore receivers use four or more satellites to
solve for the receiver's location and time. The very accurately
computed time is effectively hidden by most GPS applications, which use
only the location. A few specialized GPS applications do however use
the time; these include &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Time_transfer&quot; title=&quot;Time transfer&quot;&gt;time transfer&lt;/a&gt;, traffic signal timing, and &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/IS-95#Physical_layer&quot; title=&quot;IS-95&quot;&gt;synchronization of cell phone base stations&lt;/a&gt;.&lt;/p&gt;
&lt;p&gt;Although four satellites are required for normal operation, fewer
apply in special cases. If one variable is already known, a receiver
can determine its position using only three satellites. (For example, a
ship or plane may have known elevation.) Some GPS receivers may use
additional clues or assumptions (such as reusing the last known
altitude, &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Dead_reckoning&quot; title=&quot;Dead reckoning&quot;&gt;dead reckoning&lt;/a&gt;, &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Inertial_navigation_system&quot; title=&quot;Inertial navigation system&quot;&gt;inertial navigation&lt;/a&gt;,
or including information from the vehicle computer) to give a degraded
position when fewer than four satellites are visible (see,&lt;sup id=&quot;cite_ref-15&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Global_Positioning_System#cite_note-15&quot;&gt;&lt;span&gt;[&lt;/span&gt;16&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt; Chapters 7 and 8 of,&lt;sup id=&quot;cite_ref-NAVGPS_16-0&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Global_Positioning_System#cite_note-NAVGPS-16&quot;&gt;&lt;span&gt;[&lt;/span&gt;17&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt; and &lt;sup id=&quot;cite_ref-17&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Global_Positioning_System#cite_note-17&quot;&gt;&lt;span&gt;[&lt;/span&gt;18&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt;).&lt;/p&gt;
&lt;h3&gt;&lt;span class=&quot;editsection&quot;&gt;&lt;/span&gt;&lt;span class=&quot;mw-headline&quot; id=&quot;Position_calculation_introduction&quot;&gt;Position calculation introduction&lt;/span&gt;&lt;/h3&gt;
&lt;p&gt;To provide an introductory description of how a GPS receiver works,
errors will be ignored in this section. Using messages received from a
minimum of four visible satellites, a GPS receiver is able to determine
the times sent and then the satellite positions corresponding to these
times sent. The x, y, and z components of position, and the time sent,
are designated as &lt;img class=&quot;tex yui-img&quot; alt=&quot;\scriptstyle\left [x_i, y_i, z_i, t_i\right ]&quot; src=&quot;http://upload.wikimedia.org/math/c/4/5/c4570c028f7ceffeb5c64bf94bfc7866.png&quot;&gt; where the subscript &lt;i&gt;i&lt;/i&gt; is the satellite number and has the value 1, 2, 3, or 4. Knowing the indicated time the message was received &lt;img class=&quot;tex yui-img&quot; alt=&quot;\scriptstyle\  tr&quot; src=&quot;http://upload.wikimedia.org/math/3/e/e/3ee28b8afe91983cc0b9ffbb45d544c2.png&quot;&gt;, the GPS receiver can compute the transit time of the message as &lt;img class=&quot;tex yui-img&quot; alt=&quot;\scriptstyle\left (tr-t_i\right ) &quot; src=&quot;http://upload.wikimedia.org/math/d/7/9/d7902c626c3478c31f1c7459f363ffaf.png&quot;&gt;. Assuming the message &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Travel_time&quot; title=&quot;Travel time&quot;&gt;traveled&lt;/a&gt; at the speed of light, &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Speed_of_light&quot; title=&quot;Speed of light&quot;&gt;c&lt;/a&gt;, the distance traveled, &lt;img class=&quot;tex yui-img&quot; alt=&quot;\scriptstyle\  p_i&quot; src=&quot;http://upload.wikimedia.org/math/b/5/8/b58afe5f5a5c26fcb87eaa5d1d6c0829.png&quot;&gt; can be computed as &lt;img class=&quot;tex yui-img&quot; alt=&quot;\scriptstyle\left (tr-t_i\right )c&quot; src=&quot;http://upload.wikimedia.org/math/8/b/b/8bb39c1b3b34f3f166d49ad1c021f712.png&quot;&gt;.&lt;/p&gt;
&lt;p&gt;A satellite's position and distance from the receiver define a
spherical surface, centered on the satellite. The position of the
receiver is somewhere on this surface. Thus with four satellites, the
indicated position of the GPS receiver is at or near the intersection
of the surfaces of four spheres. (In the ideal case of no errors, the
GPS receiver would be at a precise intersection of the four surfaces.)&lt;/p&gt;&lt;p&gt;For automobiles and other near-earth-vehicles, the correct position
of the GPS receiver is the intersection closest to the earth's surface.
For space vehicles, the intersection farthest from Earth may be the
correct one.&lt;sup id=&quot;cite_ref-19&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Global_Positioning_System#cite_note-19&quot;&gt;&lt;span&gt;[&lt;/span&gt;20&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt;&lt;/p&gt;
&lt;p&gt;The correct position for the GPS receiver is also the intersection
closest to the surface of the sphere corresponding to the fourth
satellite.&lt;/p&gt;
&lt;h3&gt;&lt;span class=&quot;editsection&quot;&gt;&lt;/span&gt;&lt;span class=&quot;mw-headline&quot; id=&quot;Correcting_a_GPS_receiver.27s_clock&quot;&gt;&lt;/span&gt;&lt;span class=&quot;mw-headline&quot; id=&quot;System_segmentation&quot;&gt;System segmentation&lt;/span&gt;&lt;/h3&gt;&lt;p&gt;The current GPS consists of three major segments. These are the
space segment (SS), a control segment (CS), and a user segment (US).&lt;sup id=&quot;cite_ref-20&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Global_Positioning_System#cite_note-20&quot;&gt;&lt;span&gt;[&lt;/span&gt;21&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt;&lt;/p&gt;
&lt;h4&gt;&lt;span class=&quot;editsection&quot;&gt;&lt;/span&gt;&lt;span class=&quot;mw-headline&quot; id=&quot;Space_segment&quot;&gt;Space segment&lt;/span&gt;&lt;/h4&gt;The space segment (SS) comprises the orbiting GPS satellites, or
Space Vehicles (SV) in GPS parlance. The GPS design originally called
for 24 SVs, eight each in three circular &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Orbital_plane_%28astronomy%29&quot; title=&quot;Orbital plane (astronomy)&quot;&gt;orbital planes&lt;/a&gt;,&lt;sup id=&quot;cite_ref-21&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Global_Positioning_System#cite_note-21&quot;&gt;&lt;span&gt;[&lt;/span&gt;22&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt; but this was modified to six planes with four satellites each.&lt;sup id=&quot;cite_ref-22&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Global_Positioning_System#cite_note-22&quot;&gt;&lt;span&gt;[&lt;/span&gt;23&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt; The orbital planes are centered on the Earth, not rotating with respect to the distant stars.&lt;sup id=&quot;cite_ref-23&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Global_Positioning_System#cite_note-23&quot;&gt;&lt;span&gt;[&lt;/span&gt;24&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt; The six planes have approximately 55° &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Inclination&quot; title=&quot;Inclination&quot;&gt;inclination&lt;/a&gt; (tilt relative to Earth's &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Equator&quot; title=&quot;Equator&quot;&gt;equator&lt;/a&gt;) and are separated by 60° &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Right_ascension&quot; title=&quot;Right ascension&quot;&gt;right ascension&lt;/a&gt; of the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Orbital_node&quot; title=&quot;Orbital node&quot;&gt;ascending node&lt;/a&gt; (angle along the equator from a reference point to the orbit's intersection).&lt;sup id=&quot;cite_ref-GPS_overview_from_JPO_24-0&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Global_Positioning_System#cite_note-GPS_overview_from_JPO-24&quot;&gt;&lt;span&gt;[&lt;/span&gt;25&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt; The orbits are arranged so that at least six satellites are always within &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Line-of-sight_propagation&quot; title=&quot;Line-of-sight propagation&quot;&gt;line of sight&lt;/a&gt; from almost everywhere on Earth's surface.&lt;sup id=&quot;cite_ref-25&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Global_Positioning_System#cite_note-25&quot;&gt;&lt;span&gt;[&lt;/span&gt;26&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt;
&lt;p&gt;Orbiting at an altitude of approximately 20,200 kilometers (about 12,550 miles or 10,900 &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Nautical_mile&quot; title=&quot;Nautical mile&quot;&gt;nautical miles&lt;/a&gt;; orbital radius of approximately 26,600&amp;nbsp;km (about 16,500&amp;nbsp;mi or 14,400 NM)), each SV makes two complete orbits each &lt;a href=&quot;http://en.wikipedia.org/wiki/Sidereal_day&quot; title=&quot;Sidereal day&quot; class=&quot;mw-redirect&quot;&gt;sidereal day&lt;/a&gt;, repeating the same ground track each day.&lt;sup id=&quot;cite_ref-26&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Global_Positioning_System#cite_note-26&quot;&gt;&lt;span&gt;[&lt;/span&gt;27&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt;
This was very helpful during development, since even with just four
satellites, correct alignment means all four are visible from one spot
for a few hours each day. For military operations, the ground track
repeat can be used to ensure good coverage in combat zones.&lt;/p&gt;
&lt;p&gt;As of March 2008&lt;sup class=&quot;plainlinks noprint asof-tag update&quot; style=&quot;display: none;&quot;&gt;&lt;a href=&quot;http://geocachinggpstreasurehunt.yolasite.com/index/http://en.wikipedia.org/w/index.php?title=Global_Positioning_System&amp;amp;action=edit&quot; class=&quot;external text&quot; rel=&quot;nofollow&quot;&gt;[update]&lt;/a&gt;&lt;/sup&gt;,&lt;sup id=&quot;cite_ref-27&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Global_Positioning_System#cite_note-27&quot;&gt;&lt;span&gt;[&lt;/span&gt;28&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt; there are 31 actively broadcasting satellites in the GPS &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Satellite_constellation&quot; title=&quot;Satellite constellation&quot;&gt;constellation&lt;/a&gt;,
and two older, retired from active service satellites kept in the
constellation as orbital spares. The additional satellites improve the
precision of GPS receiver calculations by providing redundant
measurements. With the increased number of satellites, the
constellation was changed to a nonuniform arrangement. Such an
arrangement was shown to improve reliability and availability of the
system, relative to a uniform system, when multiple satellites fail.&lt;sup id=&quot;cite_ref-28&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Global_Positioning_System#cite_note-28&quot;&gt;&lt;span&gt;[&lt;/span&gt;29&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt; About ten satellites are visible from any point on the ground at any one time (see animation at right).&lt;/p&gt;
&lt;h4&gt;&lt;span class=&quot;editsection&quot;&gt;&lt;/span&gt;&lt;span class=&quot;mw-headline&quot; id=&quot;Control_segment&quot;&gt;Control segment&lt;/span&gt;&lt;/h4&gt;
&lt;p&gt;The flight paths of the satellites are tracked by U.S. Air Force monitoring stations in &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Hawaii&quot; title=&quot;Hawaii&quot;&gt;Hawaii&lt;/a&gt;, &lt;a href=&quot;http://en.wikipedia.org/wiki/Kwajalein&quot; title=&quot;Kwajalein&quot; class=&quot;mw-redirect&quot;&gt;Kwajalein&lt;/a&gt;, &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Ascension_Island&quot; title=&quot;Ascension Island&quot;&gt;Ascension Island&lt;/a&gt;, &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Diego_Garcia&quot; title=&quot;Diego Garcia&quot;&gt;Diego Garcia&lt;/a&gt;, and &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Colorado_Springs,_Colorado&quot; title=&quot;Colorado Springs, Colorado&quot;&gt;Colorado Springs, Colorado&lt;/a&gt;, along with monitor stations operated by the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/National_Geospatial-Intelligence_Agency&quot; title=&quot;National Geospatial-Intelligence Agency&quot;&gt;National Geospatial-Intelligence Agency&lt;/a&gt; (NGA).&lt;sup id=&quot;cite_ref-29&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Global_Positioning_System#cite_note-29&quot;&gt;&lt;span&gt;[&lt;/span&gt;30&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt; The tracking information is sent to the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Air_Force_Space_Command&quot; title=&quot;Air Force Space Command&quot;&gt;Air Force Space Command&lt;/a&gt;'s master control station at &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Schriever_Air_Force_Base&quot; title=&quot;Schriever Air Force Base&quot;&gt;Schriever Air Force Base&lt;/a&gt; in Colorado Springs, which is operated by the &lt;a href=&quot;http://en.wikipedia.org/wiki/2nd_Space_Operations_Squadron&quot; title=&quot;2nd Space Operations Squadron&quot; class=&quot;mw-redirect&quot;&gt;2nd Space Operations Squadron&lt;/a&gt; (2 SOPS) of the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/United_States_Air_Force&quot; title=&quot;United States Air Force&quot;&gt;United States Air Force&lt;/a&gt;
(USAF). Then 2 SOPS contacts each GPS satellite regularly with a
navigational update (using the ground antennas at Ascension Island,
Diego Garcia, Kwajalein, and Colorado Springs). These updates
synchronize the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Atomic_clock&quot; title=&quot;Atomic clock&quot;&gt;atomic clocks&lt;/a&gt; on board the satellites to within a few &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Nanosecond&quot; title=&quot;Nanosecond&quot;&gt;nanoseconds&lt;/a&gt; of each other, and adjust the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Ephemeris&quot; title=&quot;Ephemeris&quot;&gt;ephemeris&lt;/a&gt; of each satellite's internal orbital model. The updates are created by a &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Kalman_filter&quot; title=&quot;Kalman filter&quot;&gt;Kalman filter&lt;/a&gt; which uses inputs from the ground monitoring stations, &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Space_weather&quot; title=&quot;Space weather&quot;&gt;space weather&lt;/a&gt; information, and various other inputs.&lt;sup id=&quot;cite_ref-30&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Global_Positioning_System#cite_note-30&quot;&gt;&lt;span&gt;[&lt;/span&gt;31&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt;&lt;/p&gt;
&lt;p&gt;Satellite maneuvers are not precise by GPS standards. So to change
the orbit of a satellite, the satellite must be marked 'unhealthy', so
receivers will not use it in their calculation. Then the maneuver can
be carried out, and the resulting orbit tracked from the ground. Then
the new ephemeris is uploaded and the satellite marked healthy again.&lt;/p&gt;
&lt;h4&gt;&lt;span class=&quot;editsection&quot;&gt;&lt;/span&gt;&lt;span class=&quot;mw-headline&quot; id=&quot;User_segment&quot;&gt;User segment&lt;/span&gt;&lt;/h4&gt;The user's GPS receiver is the user segment (US) of the GPS. In
general, GPS receivers are composed of an antenna, tuned to the
frequencies transmitted by the satellites, receiver-processors, and a
highly-stable clock (often a &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Crystal_oscillator&quot; title=&quot;Crystal oscillator&quot;&gt;crystal oscillator&lt;/a&gt;).
They may also include a display for providing location and speed
information to the user. A receiver is often described by its number of
channels: this signifies how many satellites it can monitor
simultaneously. Originally limited to four or five, this has
progressively increased over the years so that, as of 2007&lt;sup class=&quot;plainlinks noprint asof-tag update&quot; style=&quot;display: none;&quot;&gt;&lt;a href=&quot;http://geocachinggpstreasurehunt.yolasite.com/index/http://en.wikipedia.org/w/index.php?title=Global_Positioning_System&amp;amp;action=edit&quot; class=&quot;external text&quot; rel=&quot;nofollow&quot;&gt;[update]&lt;/a&gt;&lt;/sup&gt;, receivers typically have between 12 and 20 channels.&lt;sup id=&quot;cite_ref-31&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Global_Positioning_System#cite_note-31&quot;&gt;&lt;span&gt;[&lt;/span&gt;32&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt;&lt;br&gt;&lt;br&gt;GPS receivers may include an input for differential corrections, using the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/RTCM&quot; title=&quot;RTCM&quot;&gt;RTCM&lt;/a&gt; SC-104 format. This is typically in the form of a &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/RS-232&quot; title=&quot;RS-232&quot;&gt;RS-232&lt;/a&gt;
port at 4,800 bit/s speed. Data is actually sent at a much lower rate,
which limits the accuracy of the signal sent using RTCM. Receivers with
internal DGPS receivers can outperform those using external RTCM data.
As of 2006, even low-cost units commonly include &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Wide_Area_Augmentation_System&quot; title=&quot;Wide Area Augmentation System&quot;&gt;Wide Area Augmentation System&lt;/a&gt; (WAAS) receivers.&lt;br&gt;&lt;br&gt;Many GPS receivers can relay position data to a PC or other device using the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/NMEA_0183&quot; title=&quot;NMEA 0183&quot;&gt;NMEA 0183&lt;/a&gt; protocol, or the newer and less widely used &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/NMEA_2000&quot; title=&quot;NMEA 2000&quot;&gt;NMEA 2000&lt;/a&gt;.&lt;sup id=&quot;cite_ref-32&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Global_Positioning_System#cite_note-32&quot;&gt;&lt;span&gt;[&lt;/span&gt;33&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt; Although these protocols are officially defined by the &lt;a href=&quot;http://en.wikipedia.org/wiki/NMEA&quot; title=&quot;NMEA&quot; class=&quot;mw-redirect&quot;&gt;NMEA&lt;/a&gt;,&lt;sup id=&quot;cite_ref-33&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Global_Positioning_System#cite_note-33&quot;&gt;&lt;span&gt;[&lt;/span&gt;34&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt; references to these protocols have been compiled from public records, allowing open source tools like &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Gpsd&quot; title=&quot;Gpsd&quot;&gt;gpsd&lt;/a&gt; to read the protocol without violating &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Intellectual_property&quot; title=&quot;Intellectual property&quot;&gt;intellectual property&lt;/a&gt; laws. Other proprietary protocols exist as well, such as the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/SiRF&quot; title=&quot;SiRF&quot;&gt;SiRF&lt;/a&gt; and &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/MediaTek&quot; title=&quot;MediaTek&quot;&gt;MTK&lt;/a&gt; protocols. Receivers can interface with other devices using methods including a serial connection, &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Universal_Serial_Bus&quot; title=&quot;Universal Serial Bus&quot;&gt;USB&lt;/a&gt; or &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Bluetooth&quot; title=&quot;Bluetooth&quot;&gt;Bluetooth&lt;/a&gt;.
&lt;div class=&quot;rellink boilerplate further&quot;&gt;Further information: &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/GPS_navigation_device&quot; title=&quot;GPS navigation device&quot;&gt;GPS navigation device&lt;/a&gt;&lt;/div&gt;
&lt;h2&gt;&lt;span class=&quot;editsection&quot;&gt;&lt;/span&gt;&lt;span class=&quot;mw-headline&quot; id=&quot;Navigation&quot;&gt;Navigation&lt;/span&gt;&lt;/h2&gt;
&lt;p&gt;Aspects of navigation are discussed in this section. The subsection
on navigation signals discusses details of the message content. Carrier
frequencies for the messages are stated. Demodulating the carrier and
decoding to separate the signals from the satellites is described. The
position calculation subsection does not require an understanding of
the other subsections. Basic equations describing the geometry of the
sphere and the fundamental concept that the satellite message travels
at the speed of light are used in the subsection. The subsection on
multidimensional Newton-Raphson may be of interest only to those
readers who want a more detailed understanding on how an algorithm
might be written and is unnecessary for the reader who is uninterested
in this amount of detail.&lt;/p&gt;
&lt;h3&gt;&lt;span class=&quot;editsection&quot;&gt;&lt;/span&gt;&lt;span class=&quot;mw-headline&quot; id=&quot;Navigation_signals&quot;&gt;Navigation signals&lt;/span&gt;&lt;/h3&gt;
&lt;p&gt;Transmission of each 30 second frame begins precisely on the minute
and half minute as indicated by the satellite's atomic clock according
to &lt;a href=&quot;http://gpsinformation.net/gpssignal.htm&quot; class=&quot;external text&quot; rel=&quot;nofollow&quot;&gt;Satellite message format&lt;/a&gt;.
Each frame contains 5 subframes of length 6 seconds and with 300 bits.
Each subframe contains 10 words of 30 bits with length 0.6 seconds each.&lt;/p&gt;
&lt;p&gt;Words 1 and 2 of every subframe have the same type of data. The
first word is the telemetry word which indicates the beginning of a
subframe and is used by the receiver to synch with the navigation
message. The second word is the HOW or handover word and it contains
timing information which enables the receiver to identify the subframe
and provides the time the next subframe was sent.&lt;/p&gt;
&lt;p&gt;Words 3 through 10 of subframe 1 contain data describing the
satellite clock and its relationship to GPS time. Words 3 through 10 of
subframes 2 and 3, contain the &lt;i&gt;ephemeris&lt;/i&gt; data, giving the
satellite's own precise orbit. The ephemeris is updated every 2 hours
and is generally valid for 4 hours, with provisions for updates every 6
hours or longer in non-nominal conditions. The time needed to acquire
the ephemeris is becoming a significant element of the delay to first
position fix, because, as the hardware becomes more capable, the time
to lock onto the satellite signals shrinks, but the ephemeris data
requires 30 seconds (worst case) before it is received, due to the low
data transmission rate.&lt;/p&gt;
&lt;p&gt;The &lt;i&gt;almanac&lt;/i&gt; consists of coarse orbit and status information
for each satellite in the constellation, an ionospheric model, and
information to relate GPS derived time to &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Coordinated_Universal_Time&quot; title=&quot;Coordinated Universal Time&quot;&gt;Coordinated Universal Time&lt;/a&gt;
(UTC). Words 3 through 10 of subframes 4 and 5 contain a new part of
the almanac. Each frame contains 1/25th of the almanac, so 12.5 minutes
are required to receive the entire almanac from a single satellite.&lt;sup id=&quot;cite_ref-34&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Global_Positioning_System#cite_note-34&quot;&gt;&lt;span&gt;[&lt;/span&gt;35&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt;
The almanac serves several purposes. The first is to assist in the
acquisition of satellites at power-up by allowing the receiver to
generate a list of visible satellites based on stored position and
time, while an ephemeris from each satellite is needed to compute
position fixes using that satellite. In older hardware, lack of an
almanac in a new receiver would cause long delays before providing a
valid position, because the search for each satellite was a slow
process. Advances in hardware have made the acquisition process much
faster, so not having an almanac is no longer an issue. The second
purpose is for relating time derived from the GPS (called GPS time) to
the international time standard of &lt;a href=&quot;http://en.wikipedia.org/wiki/UTC&quot; title=&quot;UTC&quot; class=&quot;mw-redirect&quot;&gt;UTC&lt;/a&gt;.
Finally, the almanac allows a single-frequency receiver to correct for
ionospheric error by using a global ionospheric model. The corrections
are not as accurate as augmentation systems like &lt;a href=&quot;http://en.wikipedia.org/wiki/WAAS&quot; title=&quot;WAAS&quot; class=&quot;mw-redirect&quot;&gt;WAAS&lt;/a&gt;
or dual-frequency receivers. However, it is often better than no
correction, since ionospheric error is the largest error source for a
single-frequency GPS receiver. An important thing to note about
navigation data is that each satellite transmits not only its own &lt;i&gt;ephemeris&lt;/i&gt;, but transmits an &lt;i&gt;almanac&lt;/i&gt; for all satellites.&lt;/p&gt;
&lt;p&gt;All satellites broadcast at the same two frequencies, 1.57542&amp;nbsp;GHz
(L1 signal) and 1.2276&amp;nbsp;GHz (L2 signal). The receiver can distinguish
the signals from different satellites because GPS uses a &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Code_division_multiple_access&quot; title=&quot;Code division multiple access&quot;&gt;code division multiple access&lt;/a&gt; (CDMA) spread-spectrum technique where the low-bitrate message data is encoded with a high-rate &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Pseudorandom_number_generator&quot; title=&quot;Pseudorandom number generator&quot;&gt;pseudo-random&lt;/a&gt;
(PRN) sequence that is different for each satellite. The receiver knows
the PRN codes for each satellite and can use this to reconstruct the
actual message data. The message data is transmitted at 50 bits per
second. Two distinct CDMA encodings are used: the coarse/acquisition
(C/A) code (a so-called &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Gold_code&quot; title=&quot;Gold code&quot;&gt;Gold code&lt;/a&gt;) at 1.023 million &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Chip_%28CDMA%29&quot; title=&quot;Chip (CDMA)&quot;&gt;chips&lt;/a&gt;
per second, and the precise (P) code at 10.23 million chips per second.
The L1 carrier is modulated by both the C/A and P codes, while the L2
carrier is only modulated by the P code.&lt;sup id=&quot;cite_ref-35&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Global_Positioning_System#cite_note-35&quot;&gt;&lt;span&gt;[&lt;/span&gt;36&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt;
The C/A code is public and used by civilian GPS receivers, while the P
code can be encrypted as a so-called P(Y) code which is only available
to military equipment with a proper decryption key. Both the C/A and
P(Y) codes impart the precise time-of-day to the user.&lt;/p&gt;&lt;h3&gt;&lt;span class=&quot;mw-headline&quot; id=&quot;Navigation_signals&quot;&gt;Demodulation and Decoding&lt;/span&gt;&lt;/h3&gt;Since all of the satellite signals are modulated onto the same L1
carrier frequency, there is a need to separate the signals after
demodulation. This is done by assigning each satellite a unique binary &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Sequence&quot; title=&quot;Sequence&quot;&gt;sequence&lt;/a&gt; sequence known as a &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Gold_code&quot; title=&quot;Gold code&quot;&gt;Gold code&lt;/a&gt;, and the signals are decoded, after demodulation, using modulo 2 addition of the Gold codes corresponding to satellites &lt;i&gt;n&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt; through &lt;i&gt;n&lt;sub&gt;k&lt;/sub&gt;&lt;/i&gt;, where &lt;i&gt;k&lt;/i&gt; is the number of channels in the GPS receiver and &lt;i&gt;n&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt; through &lt;i&gt;n&lt;sub&gt;k&lt;/sub&gt;&lt;/i&gt; are the PRN identifiers of the satellites. Each satellite's PRN identifier is unique and in the range from 1 through 32.&lt;sup id=&quot;cite_ref-37&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Global_Positioning_System#cite_note-37&quot;&gt;&lt;span&gt;[&lt;/span&gt;38&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt; The results of these modulo 2 additions are the 50 bit/s navigation messages from satellites &lt;i&gt;n&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt; through &lt;i&gt;n&lt;sub&gt;k&lt;/sub&gt;&lt;/i&gt;.
The Gold codes used in GPS are a sequence of 1023 bits with a period of
one millisecond. These Gold codes are highly mutually orthogonal, so
that it is unlikely that one satellite signal will be misinterpreted as
another. As well, the Gold codes have good auto-correlation properties.&lt;sup id=&quot;cite_ref-38&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Global_Positioning_System#cite_note-38&quot;&gt;&lt;span&gt;[&lt;/span&gt;39&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt;
&lt;p&gt;There are 1025 different Gold codes of length 1023 bits, but only 32
are used. These Gold codes are quite often referred to as pseudo random
noise since they contain no data and are said to look like random
sequences&lt;sup id=&quot;cite_ref-39&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Global_Positioning_System#cite_note-39&quot;&gt;&lt;span&gt;[&lt;/span&gt;40&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt;. However, this may be misleading since they are actually deterministic sequences.&lt;/p&gt;
&lt;p&gt;If the almanac information has previously been acquired, the
receiver picks which satellites to listen for by their PRNs. If the
almanac information is not in memory, the receiver enters a search mode
and cycles through the PRN numbers until a lock is obtained on one of
the satellites. To obtain a lock, it is necessary that there be an
unobstructed line of sight from the receiver to the satellite. The
receiver can then acquire the almanac and determine the satellites it
should listen for. As it detects each satellite's signal, it identifies
it by its distinct C/A code pattern.&lt;/p&gt;
&lt;p&gt;The receiver uses the C/A Gold code with the same PRN number as the
satellite to compute an offset, O, that generates the best correlation.
The offset, O, is computed in a trial and error manner. The 1023 bits
of the satellite PRN signal are compared with the receiver PRN signal.
If correlation is not achieved, the 1023 bits of the receiver's
internally generated PRN code are shifted by one bit relative to the
satellite's PRN code and the signals are again compared. This process
is repeated until correlation is achieved or all 1023 possible cases
have been tried.&lt;sup id=&quot;cite_ref-gpslock_40-0&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Global_Positioning_System#cite_note-gpslock-40&quot;&gt;&lt;span&gt;[&lt;/span&gt;41&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt;
If all 1023 cases have been tried without achieving correlation, the
frequency oscillator is offset to the next value and the process is
repeated.&lt;/p&gt;
&lt;p&gt;Since the carrier frequency received can vary due to &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Doppler_effect&quot; title=&quot;Doppler effect&quot;&gt;Doppler&lt;/a&gt;
shift, the points where received PRN sequences begin may not differ
from O by an exact integral number of milliseconds. Because of this,
carrier frequency tracking along with PRN code tracking are used to
determine when the received satellite's PRN code begins.&lt;sup id=&quot;cite_ref-gpslock_40-1&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Global_Positioning_System#cite_note-gpslock-40&quot;&gt;&lt;span&gt;[&lt;/span&gt;41&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt;
Unlike the earlier computation of offset in which trials of all 1023
offsets could potentially be required, the tracking to maintain lock
usually requires shifting of half a pulse width or less. To perform
this tracking, the receiver observes two quantities, phase error and
received frequency offset. The correlation of the received PRN code
with respect to the receiver generated PRN code is computed to
determine if the bits of the two signals are misaligned. Comparisons
with correlation computed with receiver generated PRN code shifted half
a pulse width early and half a pulse width late (see section 1.4.2.4 of
&lt;sup id=&quot;cite_ref-NAVGPS_16-1&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Global_Positioning_System#cite_note-NAVGPS-16&quot;&gt;&lt;span&gt;[&lt;/span&gt;17&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt;)
are used to estimate adjustment required. The amount of adjustment
required for maximum correlation is used in estimating phase error.
Received frequency offset from the frequency generated by the receiver
provides an estimate of phase rate error. The command for the frequency
generator and any further PRN code shifting required are computed as a
function of the phase error and the phase rate error in accordance with
the control law used. The Doppler velocity is computed as a function of
the frequency offset from the carrier nominal frequency. The Doppler
velocity is the velocity component along the line of sight of the
receiver relative to the satellite.&lt;/p&gt;
&lt;p&gt;As the receiver continues to read successive PRN sequences, it will
encounter a sudden change in the phase of the 1023 bit received PRN
signal. This indicates the beginning of a data bit of the navigation
message (see section 1.4.2.5 of &lt;sup id=&quot;cite_ref-NAVGPS_16-2&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Global_Positioning_System#cite_note-NAVGPS-16&quot;&gt;&lt;span&gt;[&lt;/span&gt;17&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt;).
This enables the receiver to begin reading the 20 millisecond bits of
the navigation message. Each subframe of the navigation frame begins
with a Telemetry Word which enables the receiver to detect the
beginning of a subframe and determine the receiver clock time at which
the navigation subframe begins. Also each subframe of the navigation
frame is identified by bits in the handover word (HOW) thereby enabling
the receiver to determine which subframe (see section 1.4.2.6 of &lt;sup id=&quot;cite_ref-NAVGPS_16-3&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Global_Positioning_System#cite_note-NAVGPS-16&quot;&gt;&lt;span&gt;[&lt;/span&gt;17&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt; and section 2.5.4 of &lt;a href=&quot;http://www.u-blox.com/images/stories/Resources/gps_compendiumgps-x-02007.pdf&quot; class=&quot;external text&quot; rel=&quot;nofollow&quot;&gt;&quot;Essentials of Satellite Navigation Compendium&quot;&lt;/a&gt;).
There can be a delay of up to 30 seconds before the first estimate of
position because of the need to read the ephemeris data before
computing the intersections of sphere surfaces.&lt;/p&gt;
&lt;p&gt;After a subframe has been read and interpreted, the time the next
subframe was sent can be calculated through the use of the clock
correction data and the HOW. The receiver knows the receiver clock time
of when the beginning of the next subframe was received from detection
of the Telemetry Word thereby enabling computation of the transit time
and thus the pseudorange. The receiver is potentially capable of
getting a new pseudorange measurement at the beginning of each subframe
or every 6 seconds.&lt;/p&gt;
&lt;p&gt;Then the orbital position data, or &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Ephemeris&quot; title=&quot;Ephemeris&quot;&gt;ephemeris&lt;/a&gt;,
from the navigation message is used to calculate precisely where the
satellite was at the start of the message. A more sensitive receiver
will potentially acquire the ephemeris data more quickly than a less
sensitive receiver, especially in a noisy environment.&lt;sup id=&quot;cite_ref-ephemeris_41-0&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Global_Positioning_System#cite_note-ephemeris-41&quot;&gt;&lt;span&gt;[&lt;/span&gt;42&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt;&lt;/p&gt;
&lt;p&gt;This process is repeated for each satellite to which the receiver is listening.&lt;/p&gt;
&lt;p&gt;&lt;b&gt;&lt;span class=&quot;editsection&quot;&gt;&lt;/span&gt;&lt;span class=&quot;mw-headline&quot; id=&quot;Position_calculation_advanced&quot;&gt;&lt;/span&gt;&lt;span class=&quot;mw-headline&quot; id=&quot;Atmospheric_effects&quot;&gt;Atmospheric effects&lt;/span&gt;&lt;/b&gt;&lt;/p&gt;
&lt;p&gt;Inconsistencies of atmospheric conditions affect the speed of the GPS signals as they pass through the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Earth%27s_atmosphere&quot; title=&quot;Earth's atmosphere&quot;&gt;Earth's atmosphere&lt;/a&gt;, especially the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Ionosphere&quot; title=&quot;Ionosphere&quot;&gt;ionosphere&lt;/a&gt;.
Correcting these errors is a significant challenge to improving GPS
position accuracy. These effects are smallest when the satellite is
directly overhead and become greater for satellites nearer the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Horizon&quot; title=&quot;Horizon&quot;&gt;horizon&lt;/a&gt; since the path through the atmosphere is longer (see &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Airmass&quot; title=&quot;Airmass&quot;&gt;airmass&lt;/a&gt;).
Once the receiver's approximate location is known, a mathematical model
can be used to estimate and compensate for these errors.&lt;/p&gt;
&lt;p&gt;Ionospheric delay of a microwave signal depends on its frequency. This phenomenon is known as &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Dispersion_%28optics%29&quot; title=&quot;Dispersion (optics)&quot;&gt;dispersion&lt;/a&gt;
and can be calculated from measurements of delays for two or more
frequency bands, allowing delays at other frequencies to be estimated.&lt;sup id=&quot;cite_ref-52&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Global_Positioning_System#cite_note-52&quot;&gt;&lt;span&gt;[&lt;/span&gt;53&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt;
Some military and expensive survey-grade civilian receivers calculate
atmospheric dispersion from the different delays in the L1 and L2
frequencies, and apply a more precise correction. This can be done in
civilian receivers without decrypting the P(Y) signal carried on L2, by
tracking the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Carrier_wave&quot; title=&quot;Carrier wave&quot;&gt;carrier wave&lt;/a&gt; instead of the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Modulation&quot; title=&quot;Modulation&quot;&gt;modulated&lt;/a&gt;
code. To facilitate this on lower cost receivers, a new civilian code
signal on L2, called L2C, was added to the Block IIR-M satellites,
which was first launched in 2005. It allows a direct comparison of the
L1 and L2 signals using the coded signal instead of the carrier wave.
(see Atmospheric Effects in &lt;a href=&quot;http://www.kowoma.de/en/gps/errors.htm&quot; class=&quot;external text&quot; rel=&quot;nofollow&quot;&gt;&quot;Sources of Errors in GPS&quot;&lt;/a&gt;)&lt;/p&gt;
&lt;p&gt;The effects of the ionosphere generally change slowly, and can be
averaged over time. Those for any particular geographical area can be
easily calculated by comparing the GPS-measured position to a known
surveyed location. This correction is also valid for other receivers in
the same general location. Several systems send this information over
radio or other links to allow L1-only receivers to make ionospheric
corrections. The ionospheric data are transmitted via satellite in &lt;a href=&quot;http://en.wikipedia.org/wiki/Satellite_Based_Augmentation_System&quot; title=&quot;Satellite Based Augmentation System&quot; class=&quot;mw-redirect&quot;&gt;Satellite Based Augmentation Systems&lt;/a&gt; (SBAS) such as &lt;a href=&quot;http://en.wikipedia.org/wiki/WAAS&quot; title=&quot;WAAS&quot; class=&quot;mw-redirect&quot;&gt;WAAS&lt;/a&gt; (available in North America and Hawaii), &lt;a href=&quot;http://en.wikipedia.org/wiki/EGNOS&quot; title=&quot;EGNOS&quot; class=&quot;mw-redirect&quot;&gt;EGNOS&lt;/a&gt; (Europe and Asia) or &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/MSAS&quot; title=&quot;MSAS&quot;&gt;MSAS&lt;/a&gt;
(Japan), which transmits it on the GPS frequency using a special
pseudo-random noise sequence (PRN), so only one receiver and antenna
are required.&lt;/p&gt;
&lt;p&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Humidity&quot; title=&quot;Humidity&quot;&gt;Humidity&lt;/a&gt; also causes a variable delay, resulting in errors similar to ionospheric delay, but occurring in the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Troposphere&quot; title=&quot;Troposphere&quot;&gt;troposphere&lt;/a&gt;.
This effect both is more localized and changes more quickly than
ionospheric effects, and is not frequency dependent. These traits make
precise measurement and compensation of humidity errors more difficult
than ionospheric effects.&lt;sup class=&quot;noprint Template-Fact&quot; title=&quot;This claim needs references to reliable sources from November 2008&quot; style=&quot;white-space: nowrap;&quot;&gt;[&lt;i&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Wikipedia:Citation_needed&quot; title=&quot;Wikipedia:Citation needed&quot;&gt;citation needed&lt;/a&gt;&lt;/i&gt;]&lt;/sup&gt;&lt;/p&gt;
&lt;p&gt;Changes in receiver altitude also change the amount of delay, due to
the signal passing through less of the atmosphere at higher elevations.
Since the GPS receiver computes its approximate altitude, this error is
relatively simple to correct, either by applying a function regression
or correlating margin of atmospheric error to ambient pressure using a
barometric altimeter.&lt;sup class=&quot;noprint Template-Fact&quot; title=&quot;This claim needs references to reliable sources from November 2008&quot; style=&quot;white-space: nowrap;&quot;&gt;[&lt;i&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Wikipedia:Citation_needed&quot; title=&quot;Wikipedia:Citation needed&quot;&gt;citation needed&lt;/a&gt;&lt;/i&gt;]&lt;/sup&gt;&lt;/p&gt;
&lt;h3&gt;&lt;span class=&quot;editsection&quot;&gt;&lt;/span&gt;&lt;span class=&quot;mw-headline&quot; id=&quot;Multipath_effects&quot;&gt;Multipath effects&lt;/span&gt;&lt;/h3&gt;
&lt;p&gt;GPS signals can also be affected by &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Multipath&quot; title=&quot;Multipath&quot;&gt;multipath&lt;/a&gt;
issues, where the radio signals reflect off surrounding terrain;
buildings, canyon walls, hard ground, etc. These delayed signals can
cause inaccuracy. A variety of techniques, most notably &lt;a href=&quot;http://geocachinggpstreasurehunt.yolasite.com/index/http://en.wikipedia.org/w/index.php?title=Narrow_correlator_spacing&amp;amp;action=edit&amp;amp;redlink=1&quot; class=&quot;new&quot; title=&quot;Narrow correlator spacing (page does not exist)&quot;&gt;narrow correlator spacing&lt;/a&gt;,
have been developed to mitigate multipath errors. For long delay
multipath, the receiver itself can recognize the wayward signal and
discard it. To address shorter delay multipath from the signal
reflecting off the ground, specialized antennas (e.g., a &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Choke_ring_antenna&quot; title=&quot;Choke ring antenna&quot;&gt;choke ring antenna&lt;/a&gt;)
may be used to reduce the signal power as received by the antenna.
Short delay reflections are harder to filter out because they interfere
with the true signal, causing effects almost indistinguishable from
routine fluctuations in atmospheric delay.&lt;/p&gt;
&lt;p&gt;Multipath effects are much less severe in moving vehicles. When the
GPS antenna is moving, the false solutions using reflected signals
quickly fail to converge and only the direct signals result in stable
solutions.&lt;/p&gt;
&lt;h3&gt;&lt;span class=&quot;editsection&quot;&gt;&lt;/span&gt;&lt;span class=&quot;mw-headline&quot; id=&quot;Ephemeris_and_clock_errors&quot;&gt;Ephemeris and clock errors&lt;/span&gt;&lt;/h3&gt;
&lt;p&gt;While the ephemeris data is transmitted every 30 seconds, the information itself may be up to two hours old. If a fast &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Time_to_first_fix&quot; title=&quot;Time to first fix&quot;&gt;time to first fix&lt;/a&gt;
(TTFF) is needed, it is possible to upload a valid ephemeris to a
receiver, and in addition to setting the time, a position fix can be
obtained in under ten seconds. It is feasible to put such ephemeris
data on the web so it can be loaded into mobile GPS devices.&lt;sup id=&quot;cite_ref-53&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Global_Positioning_System#cite_note-53&quot;&gt;&lt;span&gt;[&lt;/span&gt;54&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt; See also &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Assisted_GPS&quot; title=&quot;Assisted GPS&quot;&gt;Assisted GPS&lt;/a&gt;.&lt;/p&gt;
&lt;p&gt;The satellite's atomic clocks experience noise and &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Clock_drift&quot; title=&quot;Clock drift&quot;&gt;clock drift&lt;/a&gt;
errors. The navigation message contains corrections for these errors
and estimates of the accuracy of the atomic clock. However, they are
based on observations and may not indicate the clock's current state.&lt;/p&gt;
&lt;p&gt;These problems tend to be very small, but may add up to a few meters (tens of feet) of inaccuracy.&lt;sup id=&quot;cite_ref-54&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Global_Positioning_System#cite_note-54&quot;&gt;&lt;span&gt;[&lt;/span&gt;55&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt;&lt;/p&gt;
&lt;p&gt;For very precise positioning (e.g., in &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Geodesy&quot; title=&quot;Geodesy&quot;&gt;geodesy&lt;/a&gt;), these effects can be eliminated by &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Differential_GPS&quot; title=&quot;Differential GPS&quot;&gt;differential GPS&lt;/a&gt;: the simultaneous use of two or more receivers at several &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Benchmark_%28surveying%29&quot; title=&quot;Benchmark (surveying)&quot;&gt;survey points&lt;/a&gt;. In the 1990s when receivers were quite expensive, some methods of &lt;i&gt;quasi-differential&lt;/i&gt; GPS were developed, using only &lt;i&gt;one&lt;/i&gt; receiver but reoccupation of measuring points. At the TU Vienna the method was named &lt;i&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/QGPS&quot; title=&quot;QGPS&quot;&gt;qGPS&lt;/a&gt;&lt;/i&gt; and adequate software of post processing was developed.&lt;/p&gt;&lt;b&gt;&lt;span class=&quot;mw-headline&quot; id=&quot;Selective_availability&quot;&gt;Selective availability&lt;/span&gt;&lt;/b&gt;
&lt;p&gt;GPS includes a (currently disabled) feature called &lt;i&gt;Selective Availability&lt;/i&gt; (&lt;i&gt;SA&lt;/i&gt;)
that adds intentional, time varying errors of up to 100 meters (328&amp;nbsp;ft)
to the publicly available navigation signals. This was intended to deny
an enemy the use of civilian GPS receivers for precision weapon
guidance.&lt;/p&gt;
&lt;p&gt;SA errors are actually pseudorandom, generated by a cryptographic algorithm from a classified &lt;i&gt;seed&lt;/i&gt; &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Key_%28cryptography%29&quot; title=&quot;Key (cryptography)&quot;&gt;key&lt;/a&gt;
available only to authorized users (the U.S. military, its allies and a
few other users, mostly government) with a special military GPS
receiver. Mere possession of the receiver is insufficient; it still
needs the tightly controlled daily key.&lt;/p&gt;
&lt;p&gt;Before it was turned off on May 1, 2000, typical SA errors were 10
meters (32&amp;nbsp;ft) horizontally and 30 meters (98&amp;nbsp;ft) vertically. Because
SA affects every GPS receiver in a given area almost equally, a fixed
station with an accurately known position can measure the SA error
values and transmit them to the local GPS receivers so they may correct
their position fixes. This is called &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Differential_GPS&quot; title=&quot;Differential GPS&quot;&gt;Differential GPS&lt;/a&gt; or &lt;i&gt;DGPS&lt;/i&gt;.
DGPS also corrects for several other important sources of GPS errors,
particularly ionospheric delay, so it continues to be widely used even
though SA has been turned off. The ineffectiveness of SA in the face of
widely available DGPS was a common argument for turning off SA, and
this was finally done by order of President Clinton in 2000.&lt;/p&gt;
&lt;p&gt;Another restriction on GPS, antispoofing, remains on. This encrypts the &lt;i&gt;P-code&lt;/i&gt;
so that it cannot be mimicked by an enemy transmitter sending false
information. Few civilian receivers have ever used the P-code, and the
accuracy attainable with the public C/A code is so much better than
originally expected (especially with DGPS) that the antispoof policy
has relatively little effect on most civilian users. Turning off
antispoof would primarily benefit surveyors and some scientists who
need extremely precise positions for experiments such as tracking the
motion of a tectonic plate.&lt;/p&gt;
&lt;p&gt;DGPS services are widely available from both commercial and government sources. The latter include &lt;a href=&quot;http://en.wikipedia.org/wiki/WAAS&quot; title=&quot;WAAS&quot; class=&quot;mw-redirect&quot;&gt;WAAS&lt;/a&gt; and the &lt;a href=&quot;http://en.wikipedia.org/wiki/US_Coast_Guard&quot; title=&quot;US Coast Guard&quot; class=&quot;mw-redirect&quot;&gt;U.S. Coast Guard's&lt;/a&gt; network of &lt;a href=&quot;http://en.wikipedia.org/wiki/LF&quot; title=&quot;LF&quot; class=&quot;mw-redirect&quot;&gt;LF&lt;/a&gt;
marine navigation beacons. The accuracy of the corrections depends on
the distance between the user and the DGPS receiver. As the distance
increases, the errors at the two sites will not correlate as well,
resulting in less precise differential corrections.&lt;/p&gt;
&lt;p&gt;During the 1990-91 &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Gulf_War&quot; title=&quot;Gulf War&quot;&gt;Gulf War&lt;/a&gt;,
the shortage of military GPS units caused many troops and their
families to buy readily available civilian units. This significantly
impeded the U.S. military's own battlefield use of GPS, so the military
made the decision to turn off SA for the duration of the war.&lt;/p&gt;
&lt;p&gt;In the 1990s, the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Federal_Aviation_Administration&quot; title=&quot;Federal Aviation Administration&quot;&gt;FAA&lt;/a&gt;
started pressuring the military to turn off SA permanently. This would
save the FAA millions of dollars every year in maintenance of their own
&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Radio_navigation&quot; title=&quot;Radio navigation&quot;&gt;radio navigation&lt;/a&gt; systems. The amount of error added was &quot;set to zero&quot;&lt;sup id=&quot;cite_ref-OSTP_56-0&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Global_Positioning_System#cite_note-OSTP-56&quot;&gt;&lt;span&gt;[&lt;/span&gt;57&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt; at midnight on May 1, 2000 following an announcement by U.S. President &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Bill_Clinton&quot; title=&quot;Bill Clinton&quot;&gt;Bill Clinton&lt;/a&gt;,
allowing users access to the error-free L1 signal. Per the directive,
the induced error of SA was changed to add no error to the public
signals (C/A code). Clinton's executive order required SA to be set to
zero by 2006; it happened in 2000 once the U.S. military developed a
new system that provides the ability to deny GPS (and other navigation
services) to hostile forces in a specific area of crisis without
affecting the rest of the world or its own military systems.&lt;sup id=&quot;cite_ref-OSTP_56-1&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Global_Positioning_System#cite_note-OSTP-56&quot;&gt;&lt;span&gt;[&lt;/span&gt;57&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt;&lt;/p&gt;
&lt;p&gt;Selective Availability is still a system capability of GPS, and
could, in theory, be reintroduced at any time. In practice, in view of
the hazards and costs this would induce for U.S. and foreign shipping,
it is unlikely to be reintroduced, and various government agencies,
including the &lt;a href=&quot;http://en.wikipedia.org/wiki/FAA&quot; title=&quot;FAA&quot; class=&quot;mw-redirect&quot;&gt;FAA&lt;/a&gt;,&lt;sup id=&quot;cite_ref-57&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Global_Positioning_System#cite_note-57&quot;&gt;&lt;span&gt;[&lt;/span&gt;58&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt; have stated that it is not intended to be reintroduced.&lt;/p&gt;
&lt;p&gt;One interesting side effect of the Selective Availability hardware
is the capability to add corrections to the outgoing signal of the GPS &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Caesium&quot; title=&quot;Caesium&quot;&gt;cesium&lt;/a&gt; and &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Rubidium&quot; title=&quot;Rubidium&quot;&gt;rubidium&lt;/a&gt; &lt;a href=&quot;http://en.wikipedia.org/wiki/Atomic_clocks&quot; title=&quot;Atomic clocks&quot; class=&quot;mw-redirect&quot;&gt;atomic clocks&lt;/a&gt; to an accuracy of approximately 2&amp;nbsp;×&amp;nbsp;10&lt;sup&gt;−13&lt;/sup&gt; This represented a significant improvement over the raw accuracy of the clocks.&lt;sup class=&quot;noprint Template-Fact&quot; title=&quot;This claim needs references to reliable sources from March 2007&quot; style=&quot;white-space: nowrap;&quot;&gt;&lt;i&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Wikipedia:Citation_needed&quot; title=&quot;Wikipedia:Citation needed&quot;&gt;&lt;br&gt;&lt;/a&gt;&lt;/i&gt;&lt;/sup&gt;&lt;/p&gt;
&lt;p&gt;On 19 September 2007, the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/United_States_Department_of_Defense&quot; title=&quot;United States Department of Defense&quot;&gt;United States Department of Defense&lt;/a&gt; announced that future GPS III satellites will not be capable of implementing SA,&lt;sup id=&quot;cite_ref-58&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Global_Positioning_System#cite_note-58&quot;&gt;&lt;span&gt;[&lt;/span&gt;59&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt; eventually making the policy permanent.&lt;sup id=&quot;cite_ref-59&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Global_Positioning_System#cite_note-59&quot;&gt;&lt;span&gt;[&lt;/span&gt;60&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt;&lt;/p&gt;
&lt;h3&gt;&lt;span class=&quot;editsection&quot;&gt;&lt;/span&gt;&lt;span class=&quot;mw-headline&quot; id=&quot;Relativity&quot;&gt;&lt;/span&gt;&lt;span class=&quot;mw-headline&quot; id=&quot;Special_and_general_relativity&quot;&gt;Special and general relativity&lt;/span&gt;&lt;/h3&gt;
&lt;p&gt;According to the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Theory_of_relativity&quot; title=&quot;Theory of relativity&quot;&gt;theory of relativity&lt;/a&gt;, due to their constant movement and height relative to the Earth-centered, non-rotating approximately inertial &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Special_relativity#Reference_frames.2C_coordinates_and_The_Lorentz_transformation&quot; title=&quot;Special relativity&quot;&gt;reference frame&lt;/a&gt;, the clocks on the satellites are affected by their speed. &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Special_relativity&quot; title=&quot;Special relativity&quot;&gt;Special relativity&lt;/a&gt;
predicts that atomic clocks moving at GPS orbital speeds will tick more
slowly than stationary ground clocks by about 7.2&amp;nbsp;μs per day.&lt;/p&gt;
&lt;p&gt;For the GPS satellites, &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/General_relativity&quot; title=&quot;General relativity&quot;&gt;general relativity&lt;/a&gt; predicts that the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Atomic_clock&quot; title=&quot;Atomic clock&quot;&gt;atomic clocks&lt;/a&gt;
at GPS orbital altitudes will tick more rapidly, by about 45.9&amp;nbsp;μs per
day, because they have a higher gravitational potential than atomic
clocks on Earth's surface.&lt;/p&gt;
&lt;p&gt;When combined, the discrepancy is about 38 microseconds per day; a difference of 4.465 parts in 10&lt;sup&gt;10&lt;/sup&gt;.&lt;sup id=&quot;cite_ref-Rizos_61-0&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Global_Positioning_System#cite_note-Rizos-61&quot;&gt;&lt;span&gt;[&lt;/span&gt;62&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt;
To account for this discrepancy, the frequency standard on board each
satellite is given a rate offset prior to launch, making it run
slightly slower than the desired frequency on Earth; specifically, at
10.22999999543&amp;nbsp;MHz instead of 10.23&amp;nbsp;MHz.&lt;sup id=&quot;cite_ref-Nelson_62-0&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Global_Positioning_System#cite_note-Nelson-62&quot;&gt;&lt;span&gt;[&lt;/span&gt;63&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt;
Since the atomic clocks on board the GPS satellites are precisely
tuned, it makes the system a practical engineering application of the
scientific theory of relativity in a real-world environment. Placing
atomic clocks on artificial satellites to test Einstein's general
theory was proposed by &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Friedwardt_Winterberg&quot; title=&quot;Friedwardt Winterberg&quot;&gt;Friedwardt Winterberg&lt;/a&gt; in 1955.&lt;sup id=&quot;cite_ref-63&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Global_Positioning_System#cite_note-63&quot;&gt;&lt;span&gt;[&lt;/span&gt;64&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt;&lt;/p&gt;
&lt;h4&gt;&lt;span class=&quot;editsection&quot;&gt;&lt;/span&gt;&lt;span class=&quot;mw-headline&quot; id=&quot;Sagnac_distortion&quot;&gt;Sagnac distortion&lt;/span&gt;&lt;/h4&gt;
&lt;p&gt;GPS observation processing must also compensate for the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Sagnac_effect&quot; title=&quot;Sagnac effect&quot;&gt;Sagnac effect&lt;/a&gt;. The GPS time scale is defined in an &lt;a href=&quot;http://en.wikipedia.org/wiki/Inertial&quot; title=&quot;Inertial&quot; class=&quot;mw-redirect&quot;&gt;inertial&lt;/a&gt; system but observations are processed in an &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/ECEF&quot; title=&quot;ECEF&quot;&gt;Earth-centered, Earth-fixed&lt;/a&gt; (co-rotating) system, a system in which &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Simultaneity&quot; title=&quot;Simultaneity&quot;&gt;simultaneity&lt;/a&gt; is not uniquely defined. A &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Lorentz_transformation&quot; title=&quot;Lorentz transformation&quot;&gt;Lorentz transformation&lt;/a&gt;
is thus applied to convert from the inertial system to the ECEF system.
The resulting signal run time correction has opposite algebraic signs
for satellites in the Eastern and Western celestial hemispheres.
Ignoring this effect will produce an east-west error on the order of
hundreds of nanoseconds, or tens of meters in position.&lt;sup id=&quot;cite_ref-64&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Global_Positioning_System#cite_note-64&quot;&gt;&lt;span&gt;[&lt;/span&gt;65&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt;&lt;/p&gt;
&lt;h3&gt;&lt;span class=&quot;editsection&quot;&gt;&lt;/span&gt;&lt;span class=&quot;mw-headline&quot; id=&quot;Natural_sources_of_interference&quot;&gt;Natural sources of interference&lt;/span&gt;&lt;/h3&gt;
&lt;p&gt;Since GPS signals at terrestrial receivers tend to be relatively
weak, natural radio signals or scattering of the GPS signals can &lt;a href=&quot;http://en.wikipedia.org/wiki/Desensitize&quot; title=&quot;Desensitize&quot; class=&quot;mw-redirect&quot;&gt;desensitize&lt;/a&gt; the receiver, making acquiring and tracking the satellite signals difficult or impossible.&lt;/p&gt;
&lt;p&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Space_weather&quot; title=&quot;Space weather&quot;&gt;Space weather&lt;/a&gt; degrades GPS operation in two ways, direct interference by solar radio burst noise in the same frequency band&lt;sup id=&quot;cite_ref-65&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Global_Positioning_System#cite_note-65&quot;&gt;&lt;span&gt;[&lt;/span&gt;66&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt; or by scattering of the GPS radio signal in ionospheric irregularities referred to as scintillation.&lt;sup id=&quot;cite_ref-66&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Global_Positioning_System#cite_note-66&quot;&gt;&lt;span&gt;[&lt;/span&gt;67&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt; Both forms of degradation follow the 11 year &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Solar_cycle&quot; title=&quot;Solar cycle&quot;&gt;solar cycle&lt;/a&gt; and are a maximum at sunspot maximum although they can occur at anytime. Solar radio bursts are associated with &lt;a href=&quot;http://en.wikipedia.org/wiki/Solar_flares&quot; title=&quot;Solar flares&quot; class=&quot;mw-redirect&quot;&gt;solar flares&lt;/a&gt;
and their impact can affect reception over the half of the Earth facing
the sun. Scintillation occurs most frequently at tropical latitudes
where it is a night time phenomenon. It occurs less frequently at high
latitudes or mid-latitudes where magnetic storms can lead to
scintillation.&lt;sup id=&quot;cite_ref-67&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Global_Positioning_System#cite_note-67&quot;&gt;&lt;span&gt;[&lt;/span&gt;68&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt;
In addition to producing scintillation, magnetic storms can produce
strong ionospheric gradients that degrade the accuracy of SBAS systems.&lt;sup id=&quot;cite_ref-68&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Global_Positioning_System#cite_note-68&quot;&gt;&lt;span&gt;[&lt;/span&gt;69&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt;&lt;/p&gt;
&lt;h3&gt;&lt;span class=&quot;editsection&quot;&gt;&lt;/span&gt;&lt;span class=&quot;mw-headline&quot; id=&quot;Artificial_sources_of_interference&quot;&gt;Artificial sources of interference&lt;/span&gt;&lt;/h3&gt;
&lt;p&gt;In automotive GPS receivers, metallic features in windshields,&lt;sup id=&quot;cite_ref-69&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Global_Positioning_System#cite_note-69&quot;&gt;&lt;span&gt;[&lt;/span&gt;70&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt; such as defrosters, or car window tinting films&lt;sup id=&quot;cite_ref-70&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Global_Positioning_System#cite_note-70&quot;&gt;&lt;span&gt;[&lt;/span&gt;71&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt; can act as a &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Faraday_cage&quot; title=&quot;Faraday cage&quot;&gt;Faraday cage&lt;/a&gt;, degrading reception just inside the car.&lt;/p&gt;
&lt;p&gt;Man-made &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Electromagnetic_interference&quot; title=&quot;Electromagnetic interference&quot;&gt;EMI&lt;/a&gt; (electromagnetic interference) can also disrupt, or &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Radio_jamming&quot; title=&quot;Radio jamming&quot;&gt;jam&lt;/a&gt;, GPS signals. In one well documented case, the entire harbor of &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Moss_Landing,_California&quot; title=&quot;Moss Landing, California&quot;&gt;Moss Landing&lt;/a&gt;, &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/California&quot; title=&quot;California&quot;&gt;California&lt;/a&gt; was unable to receive GPS signals due to unintentional jamming caused by malfunctioning TV antenna preamplifiers.&lt;sup id=&quot;cite_ref-71&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Global_Positioning_System#cite_note-71&quot;&gt;&lt;span&gt;[&lt;/span&gt;72&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt;&lt;sup id=&quot;cite_ref-72&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Global_Positioning_System#cite_note-72&quot;&gt;&lt;span&gt;[&lt;/span&gt;73&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt;
Intentional jamming is also possible. Generally, stronger signals can
interfere with GPS receivers when they are within radio range, or line
of sight. In 2002, a detailed description of how to build a short range
GPS L1 C/A jammer was published in the online magazine &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Phrack&quot; title=&quot;Phrack&quot;&gt;Phrack&lt;/a&gt;.&lt;sup id=&quot;cite_ref-73&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Global_Positioning_System#cite_note-73&quot;&gt;&lt;span&gt;[&lt;/span&gt;74&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt;&lt;/p&gt;
&lt;p&gt;The &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Federal_government_of_the_United_States&quot; title=&quot;Federal government of the United States&quot;&gt;U.S. government&lt;/a&gt; believes that such jammers were used occasionally during the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/War_in_Afghanistan_%282001%E2%80%93present%29&quot; title=&quot;War in Afghanistan (2001–present)&quot;&gt;2001 war in Afghanistan&lt;/a&gt; and the U.S. military claimed to destroy six GPS jammers during the &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Iraq_War&quot; title=&quot;Iraq War&quot;&gt;Iraq War&lt;/a&gt;, including one that was destroyed ironically with a GPS-guided bomb.&lt;sup id=&quot;cite_ref-74&quot; class=&quot;reference&quot;&gt;&lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Global_Positioning_System#cite_note-74&quot;&gt;&lt;span&gt;[&lt;/span&gt;75&lt;span&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt; Such a jammer is relatively easy to detect and locate, making it an attractive target for &lt;a class=&quot;&quot; href=&quot;http://en.wikipedia.org/wiki/Anti-radiation_missile&quot; title=&quot;Anti-radiation missile&quot;&gt;anti-radiation missiles&lt;/a&gt;. The </description>
            <pubDate>Fri, 13 Nov 2009 06:20:05 +0100</pubDate>
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            <title>Geocaching provides hobby for modern-day treasure hunters</title>
            <link>http://geocachinggpstreasurehunt.yolasite.com/index/index/geocaching-provides-hobby-for-modern-day-treasure-hunters</link>
            <description>By Alexandra Hruz&lt;br&gt;&lt;br&gt;It only took an hour of searching in the dark at a
Confederate fort in Alexandria, La. while looking for a hidden geocache
for Walt Adams to realize his obsession with treasure hunting. On hands
and knees, Adams felt around in the dirt, hoping to get his hands on
the treasure he sought. And while Adams did eventually give up for the
night, he wasn't deterred by his loss. He woke up early, went to the
site, found the cache and managed to catch his morning flight back to
Idaho as well. Combined with a penchant for technology, Adams found the
best of both worlds in geocaching, a modern day hobby that uses GPS
technology to find hidden caches. And while it might not be the
treasure hunting of pirate novels, it does inspire connotations of
modern-day Magellans. Geocachers can travel around the country, or even
around the world, to sate their need for discovery by using a handheld
GPS device and a strong trailblazing energy. Here are a few tips and
suggestions from experienced geocachers on how to jump start this
treasure-hunting hobby.&lt;div class=&quot;body&quot;&gt;&lt;p class=&quot;TINYblockquote&quot;&gt;What is Geocaching?&lt;/p&gt;
&lt;p&gt;Geocaching as a hobby came about in 2000 after satellites that were
originally used for military purposes were made civilian-friendly,
allowing people to use GPS devices to track items to within 10 feet,
according to Tom Dunigan, former adjunct associate professor in
Computer Science at the University of Tennessee. The combination of
Internet technology and the change in accuracy of the GPS unit allowed
geocaching to develop as a serious hobby, Dunigan said. Today, there
are between 2 and 3 million active geocachers worldwide, and more than
900,000 hidden caches.&lt;/p&gt;
&lt;p&gt;&quot;It's based on latitude and longitude, so it's not like the
traditional map,&quot; Dunigan said. &quot;It's up to the individual to figure
out how to get there, and once you get there, often the cache is hidden
in some fashion.&quot;&lt;/p&gt;
&lt;p&gt;Dunigan explained that the caches are typically hidden in old Army
ammo boxes or Tupperware containers, and they sometimes contain
trinkets that past explorers left for others to find.&lt;/p&gt;
&lt;p&gt;According to Dunigan, a log is often placed with the cache for
people to sign after discovering it. Following a find, geocachers can
create an online account on a geocaching Web site to create a virtual
log of their finds.&lt;/p&gt;&lt;p class=&quot;TINYblockquote&quot;&gt;Essentials for Geocaching&lt;/p&gt;&lt;p&gt;While
a strong sense of direction and a taste for adventure can certainly be
helpful while searching for hidden goods, geocaching does require a
handheld GPS device, as well as access to the Internet. For those who
are unsure about how to pick out a proper GPS device, Geocaching.com
provides an informative online tutorial about how to buy the right
equipment.&lt;/p&gt;
&lt;p&gt;Having access to a geocache Web site is crucial, and dozens of sites
are available for those ready to download coordinates onto their GPS
before heading out to search. Most sites offer free membership, and
there are geocache sites dedicated to specific countries around the
world for the globe-trotting geocacher.&lt;/p&gt;
&lt;p&gt;&quot;You need the Internet not only to search for local caches, but also
so you can log in your visits and create your own geocaches,&quot; Dunigan
said.&lt;/p&gt;
&lt;p&gt;For tracking more difficult caches, Dunigan also suggested that a
topographical map be brought along on the hunt, as GPS signal can
sometimes be weak in certain areas.&lt;/p&gt;&lt;p class=&quot;TINYblockquote&quot;&gt;Tales from a trailblazer&lt;/p&gt;&lt;p&gt;While
geocaching might not result in treasure chests filled with gold, hidden
caches still provide plenty of excitement and anticipation for those
searching for them. Not only is this hide-and-seek hobby perfect for
those who are interested in technology, it can also satisfy the desire
to explore new places.&lt;/p&gt;
&lt;p&gt;Walt Adams, an Idaho resident who has geocached around the globe, is
always able to sate his need for travel and his geocaching hobby
simultaneously.&lt;/p&gt;
&lt;p&gt;&quot;I have found 1,115 geocaches to date and not too many of them have
gotten away,&quot; Adams said. &quot;I have seen a lot&amp;nbsp;of country and enjoyed a
lot of local history.&quot;&lt;/p&gt;
&lt;p&gt;Through his geocache journeys, Adams has discovered hidden caches in
air raid bunkers and church cemeteries, as well as ones 20 feet
underground in England and near the USS Arizona memorial in Pearl
Harbor, Hawaii.&lt;/p&gt;&lt;p class=&quot;TINYblockquote&quot;&gt;Tips from the experts&lt;/p&gt;
&lt;p&gt;For those who are less than sure about their technological skills or
don't have a clue how to find their first cache, experienced GPS users
can prove to be the best source of knowledge on the subject.&lt;/p&gt;
&lt;p&gt;&quot;The best thing would be to find someone else who is already doing
it to get an idea if it's really worth investing in,&quot; Dunigan said.
Dunigan, who provides latitudes and longitudes for Tennessee landforms,
said that an interest in historical places and technology is what drew
him to the hobby.&lt;/p&gt;
&lt;p&gt;Through his travels around the world, Adams has also amassed some
helpful advice for those who might be interested in geocaching.&lt;/p&gt;
&lt;p&gt;&quot;Lots of geocaches are hidden in holes or under bridges, or in
hollow logs. Snakes, spiders and sharp objects can be there too,&quot; Adams
said. &quot;I almost always wear a pair of leather gloves when I reach in to
feel around.&quot;&lt;/p&gt;
&lt;p&gt;Adams also emphasized that cachers should carry extra batteries and
a flashlight. He also hinted that new cachers should allow for more
time than they actually think it will take.&lt;/p&gt;
&lt;p&gt;For some, geocaching can bring back memories of earning scouting
patches in orienteering. But for others, it provides an excellent
opportunity to enjoy the outdoors while becoming more versed in the
ways of technology.&lt;/p&gt;&lt;p&gt;&lt;a class=&quot;&quot; title=&quot;&quot; href=&quot;http://tnjn.com/2009/nov/09/geocaching-provides-hobby-for-/&quot;&gt;Geocaching GPS Treasure Hunt News Source&lt;/a&gt;&lt;/p&gt;&lt;/div&gt;__________________________________________________&lt;br&gt;&lt;br&gt;Awesome! This sound like fun for the adventurous gadget technocrat! Great job Alexandra!&lt;br&gt;</description>
            <pubDate>Fri, 13 Nov 2009 06:06:15 +0100</pubDate>
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