GPS R You Mystery Cache
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Difficulty:
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Terrain:
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Size: 
(micro)
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in our disclaimer.
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.
Assume you are on a distant planet named Cacheland. Furthermore,
assume that there are GPS satellites orbiting this planet which are
emitting signals that your GPS receiver can receive to determine
your position on the planet's surface. Your GPS receiver measures
the distance to the satellites. Your GPS receiver also knows the
locations of the satellites very accurately because of the orbital
information and time information it receives. This distance
measurement places your location on a sphere centered at that
satellite with a radius equal to your distance to the satellite.
That sphere around the satellite intersects the planet's surface in
a circle. The center of the circle is directly beneath the
satellite and your position is somewhere on this circle on the
planet's surface.
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. |
You can check your answers for this puzzle on
Geochecker.com.
Congrats to RonTon for FTF.
Additional Hints
(Decrypt)
Hfr pbbeqvangr genafyngvba.
V'z nggenpgrq gb sreebhf zrgnyf.