# TRIGONOMETRY equation derivation [HELP]

1. Apr 19, 2013

### hgphtgi

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?

Regards

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2. Apr 21, 2013

### tiny-tim

??

that's the wrong diagram

3. Apr 21, 2013

### hgphtgi

No tiny, that is what i mean :) this is my question

4. Apr 21, 2013

### Mandelbroth

What is theta in the diagram? I don't see it. Also, I'm assuming that $\stackrel{\frown}{AC}$ doesn't contain B, correct?

You aren't being very specific. If you want our help, give us the necessary information.

I'm thinking your equation is $||\stackrel{\frown}{AC}||=\frac{2h}{\sqrt{\sin^2\theta+\frac{2h}{r}}+\sin(\theta)}$.

Edit:
Preliminarily (I don't know what theta is in the diagram), I'm thinking the rough outline of a proof might be along the lines of this:

1. Consider O (the center of earth) as the center of a coordinate system.
2. Defining points A, B, and C in terms of the earth as a circle (set of all points equidistant from O)
3. Noting that arc AC is on a circle centered at some new point $(x_1,y_1)$ with radius $\sqrt{x^2+(r+h-y_1)^2}$.
4. $s=r\theta$

Last edited: Apr 21, 2013