Can you explain TRIGONOMETRY equation [HELP]

[Rihanna]

The signal length from the satellite to the earth station can be found as


2(hs-he)/[{sin^2(theta)+(2(hs-he)/Re)}^1/2+sin(theta)] if theta < 5 degrees Due to the earth projection

where "hs" is satellite height and "he" is the earth station height and Re is the earth radius=3700 Km

My question is Can you help me to obtain this equation? how they got it?

Regards

 

[abdul991]

" help me to obtain this equation? how they got it?........"

From where did u get this equation.. If there is any background for this or any book reference or any website link. then provide it.

 

[godfreyl]

2(hs-he)/[{sin^2(theta)+(2(hs-he)/Re)}^1/2+sin(theta)]

In your other thread you said:

2(hs-he)/[{sin^2(theta)+(2(hs-he)/Re}^1/2}+sin(theta)]

You need to get the brackets right, otherwise we get nowhere trying to figure this out.

Also:

Re is the earth radius=3700 Km

the earth curvature Re = 8500 Km

No, the radius of the earth is about 6400km.

 

[Rihanna]

You need to get the brackets right, otherwise we get nowhere trying to figure this out.

This is the correct equation

2(hs-he)/[{sin^2(theta)+(2(hs-he)/Re)}^1/2+sin(theta)]

No, the radius of the earth is about 6400km.

yes that is Correct

 

[godfreyl]

This is the correct equation

2(hs-he)/[{sin^2(theta)+(2(hs-he)/Re)}^1/2+sin(theta)]

That seems quite accurate for low earth orbit satellites below about 1000Km, but it's way out for intermediate or high orbit satellites.

I made another spreadsheet comparing this formula to the one I gave in the other thread. I can't absolutely guarantee that my formula is correct, but the results look reasonable. OTOH, this formula is obviously wrong at high altitudes - it gives a path length less than HS - HE.

Here's some results:









P.S. Any answer to abdul's questions?

From where did u get this equation.. If there is any background for this or any book reference or any website link. then provide it.