TRIGONOMETRY equation derivation [HELP]

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

[Walter Roberson]

The square root suggests an arc-length calculation to me.

[Image Analyst]

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.

Answer 1

[Image Analyst]

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.

Answer 2

[sese]

Anyone wants to share the solution with me please? Really I'll appreciate it.

// i trust in this website members too much