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TRIGONOMETRY equation derivation [HELP]

  1. Apr 19, 2013 #1
    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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  3. Apr 21, 2013 #2

    tiny-tim

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    ??

    that's the wrong diagram :confused:
     
  4. Apr 21, 2013 #3
    No tiny, that is what i mean :) this is my question
     
  5. Apr 21, 2013 #4
    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. :confused:

    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
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