Can you explain TRIGONOMETRY equation [HELP]

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

" 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.

Rihanna said:

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

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In your other thread you said:

Rihanna said:

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

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

Also:

Rihanna said:

Re is the earth radius=3700 Km

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Rihanna said:

the earth curvature Re = 8500 Km

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

godfreyl said:

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

Click to expand...

This is the correct equation

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

godfreyl said:

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

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yes that is Correct

Rihanna said:

This is the correct equation

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

Click to expand...

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?

abdul991 said:

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.

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