or

## GPS R You

A cache by UnderTheGun_y2k Message this owner
Hidden : 11/25/2008
In Iowa, United States
Difficulty:
Terrain:

Size:  (micro)

#### Watch

How Geocaching Works

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### Geocache Description:

The cache is NOT located at the above location. You need to solve the puzzle to obtain the cache coordinates.

Most of us use one every time we venture out to locate a cache. Do you even give it a second thought? It just works and provides you with the information you need. Yes, I'm referring to our ubiquitous GPSr. Do you know how one works? After you sign this log, you will have a better appreciation of how the GPS receiver does its job to find its (and your) position. You will probably need a calculator that computes square roots to at least 8 decimal places to solve this puzzle.

To make the math problem easier, we will assume we are dealing with a flat region of Cacheland and that you are located on the surface of the planet. Also assume that the planet's surface is a plane and the intersection of the satellite sphere and this plane traces out a circle. This eliminates the vertical axis making the problem easier though still challenging to solve. The best part about this is that when you are done, you will know a little bit about what is going on inside that device you hold in your hands while caching.

Your GPS has given you the following information:
 Circle Number X Coordinate of circle's center Y Coordinate of circle's center Radius of circle 1 -106.97515 61.881302 25.0 2 -56.97515 61.881302 40.0 3 -125.1760152 91.881302 60.0

Your task is to take these three circles which have been created by the GPS satellites and find the point where they intersect. The coordinates of this intersection are the coordinates of the real cache here on planet Earth. To get you started on the right foot, the equation for a circle in a plane can be represented by:
(x - xcenter)2 + (y - ycenter)2 = r2;
where r = radius of the circle; and the center of the circle is (xcenter, ycenter).
Once you have the answer for the intersection, convert x and y into DDD MM.MMM to get the actual cache coordinates.
One more thing, most GPS receivers do this calculation once per second in 3 dimensions with the 4 best satellites. Now maybe you will be amazed the next time you pick up that GPSr to find that next new cache.

Congrats to RonTon for FTF.

Hfr pbbeqvangr genafyngvba.
V'z nggenpgrq gb sreebhf zrgnyf.

Decryption Key

A|B|C|D|E|F|G|H|I|J|K|L|M
-------------------------
N|O|P|Q|R|S|T|U|V|W|X|Y|Z

(letter above equals below, and vice versa)

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