Re: Numb3rs

[tloc54452]

I didn't reply before because I hadn't gotten a chance to think about it until I got stuck in a traffic jam this morning There actually is a closed-form solution using subsolar points. In the attached sketch, A and B are the subsolar points associated with the date-and-time stamps on the two photos. The red circle and cyan circles are all the points at the shadow angles of the A and B photos from their associated subsolar points. There are two interesection points, C and D. From other information, we can select C.

http://mathworld.wolfram.com/SphericalTrigonometry.html
http://mathworld.wolfram.com/NapiersAnalogies.html



QED

John Bercovitz

Now we have a spherical triangle, ABC which has sides a, b, and c. There are ways to solve this triangle using spherical trig. Here are a couple of Wolfram sites: We have all the side lengths, a, b, and c - these are the angles between points B and C, between points A and C, and between points A and B as subtended at the center of the earth. A, B and C also represent the angles between azimuths from a point to the other points on the triangle. Since we have a, b, and c, we can find A, B, and C.

numb3rs.GIF
Description: GIF image

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