Rotational Reasoning Mystery Cache
Hidden : 2/10/2017
Difficulty:
4 out of 5
Terrain:
1.5 out of 5

Size: Size: micro (micro)

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Geocache Description:

The cache is not at the posted coordinates.

Consider the circles shown below; a stationary blue circle and a green circle rotating around it. In the top figure, the radius of the stationary blue circle (Rs) is longer than the radius of the rotating green circle (Rr). In the bottom figure, the radius of the stationary blue circle (Rs) is shorter than the radius of the rotating green circle (Rr). In both figures, the green circle rotates about the blue circle by an amount defined by the angle (Ac), hereafter referred to as a clock angle. Derive the angle of rotation for the green circle (Ar) in both top and bottom figures to determine the latitude and longitude of the cache. The table below provides a summary of the radius lengths and clock angles for the two figures.

Small Circle Rotating Around a Large Circle

Large Circle Rotating Around a Small Circle
Rs
 Rr
 Ac (deg)
 Ar (deg)
3.1415926...
 1.000000000
 9.044125405
 latitude
0.6180339...
 1.000000000
 75.35483444
 longitude

Additional notes:
1 - The figures are not drawn to scale.
2 - For insight into a similar math problem, search for the "coin rotation paradox" on the internet.
Verify with certitude.
Congratulations to first solver and finder naala007.
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Additional Hints (Decrypt)

[hide] Ehoore gver ghor frpgvba - Haqre fgbarf – Ba Rnfg fvqr.

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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