TRIGONOMETRY equation derivation [HELP]

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sese
sese 2013-4-20
The signal length from satellite to the earth station (AC) can be found as
2(H)/[{sin^2(theta)+(2(H)/R)}^1/2+sin(theta)] Due to the earth projection
where "H" is satellite height and and R is the earth radius
My question is Can you help me to derive this equation? how they have obtained it? http://www.mediafire.com/view/?0frta8fx6x1zxds
Regards
  2 个评论
Walter Roberson
Walter Roberson 2013-4-21
The square root suggests an arc-length calculation to me.
Image Analyst
Image Analyst 2013-4-21
Isn't arc length radius times angle (s=r*theta)? But then I thought that it's probably not just a simple circular arc since the index changes as you change altitude. Though it's possible that equation did make the assumption of a perfect circular arc to make the math easier.

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回答（2 个）

Image Analyst
Image Analyst 2013-4-20
No. I'm sure it's very complicated because the index of refraction changes as a function of elevation (density of atmosphere) so it probably involves derivatives and integrals and equations of index of refraction as a function of elevation. Anyway, deriving the equation itself doesn't involve MATLAB so instead of asking here you should ask a physicist or engineer who works in that field.
sese
sese 2013-4-21
Anyone wants to share the solution with me please? Really I'll appreciate it.
// i trust in this website members too much

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