A Matter of Datums 3: The Hypothetical Mystery Cache
A Matter of Datums 3: The Hypothetical
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Difficulty:
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Terrain:
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Size: 
(small)
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This cache is not at the given coordinates. You will have to solve the puzzle below to obtain the final coordinates of the cache.
Introduction
This is the third of a series of geocaches I placed in the Las Cruces area inspired by geodesy. The first GC2XCYE was a wild goose hunt requiring searching a set of coordinates in many many different geodetic datums. The second, GC3HJ9R, was a multi in which the clues at stages would inform one as to which datum the next stage was in. This one is similar to those, but takes a different more computational tack. As in the previous ones, the final is indeed at the posted coordinates, but not in the posted datum.
What is a geodetic datum?
After placing the first two caches of this series, where seekers had to guess or deduce which datum was used to place the geoacache (or stages), I wanted to go a little deeper into what a datum really is. There are several good websites which explore the science of Geodesy. In a nutshell, the datum referred to by the GPS is a reference ellipsoid that roughly matches the shape and size of the earth. Early map makers used rudimentary measurements, usually for a given local area, to describe the shape of the earth. These would describe a surface pretty accurate near the origin of the measurements (say around England) but would tend to lose their accuracy the further away they were used. Modern datums referenced by the GPS have a more global nature, and can maintain accuracy all over the globe. The WGS84 datum is one of these.
The Problem
This geocache was placed using a hypothetical datum, that I'll call the Fugads Datum. The Fugads Datum uses a different reference ellipse than current datums (ie different semi-major and semi minor axis). The Fugads datum also has a center offset, but here I've simplified and used a single offset value for each of the X, Y and Z directions. I've converted the coordinates of several worldwide geocaches to the Fugads datum and listed them below. In order to find geocache GC3WBYE, you must figure out how to solve for the ellipsoid parameters of the Fugads datum, and the offset value used. Armed with that information you should be able to perform the calculations necessary to convert the Fugads coordinates back to WGS84 and make the find. GOOD LUCK!
| Geocache |
WGS84
Latitude |
WGS84
Longitude |
WGS84
Height (m) |
Fugads Datum
Latitude |
Fugads Datum
Longitude |
Fugads Datum
Height (m) |
| GC3WBYE |
?? |
?? |
?? |
32.419688 |
-106.6230597 |
1575.1118
|
GC7CED
(Australia) |
-25.60878 |
134.36188 |
308.0 |
-25.60381276 |
134.3603878 |
491.9658951
|
GC1R4N3
(England) |
51.50418 |
0.0 |
4.0 |
51.49891187
|
0.001526584
|
132.8939378
|
GC12EH4
(Ecuador) |
-.19087 |
-78.54 |
3856.0 |
-0.189879587
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-78.53887824
|
4109.816788
|
Some Helpful reference info
-Use WGS84 datum parameters of:
--Semi-major axis (a) = 6378137.0m
--Semi-minor axis (b) = 6356752.314m
--Inverse flattening (1/f) = 298.25722293287
Additional Hints
(No hints available.)