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Geosynchronous Orbits

  1. Jan 21, 2010 #1
    1. The problem statement, all variables and given/known data

    Communications satellites are placed in a circular orbit where they stay directly over a fixed point on the equator as the earth rotates. The radius of the earth is 6.37 x 106m, and the altitude of a geosynchronous orbit is 3.58 x 107m. What are (a) the speed and (b) the magnitude of the acceleration of a satellite in a geosynchronous orbit?

    2. Relevant equations

    M (mass of the earth) = 5.98 x 1024
    G (gravitational constant) = 6.67 x10-11
    GMm = mv2
    r2........ r

    3. The attempt at a solution

    I understand the problem and how to get the answer. I just do not understand where the units go on the above formula and where it is derived from.
     
  2. jcsd
  3. Jan 21, 2010 #2

    Redbelly98

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    Use MKS (SI) units, so units used are N, kg, and m. You may need to look up the units that go with G; it should be in your textbook.

    The formula is a result of Newton's 2nd law, F = ma.

    Hope that helps.
     
  4. Jan 21, 2010 #3

    Andrew Mason

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    Just elaborating on what Redbelly has said, the correct equation is better written as:

    [tex]\frac{GMm}{r^2} = m\omega_{e}^2r[/tex]

    where [itex]\omega_e[/itex] is the rotational (angular) speed of the earth. Since we know the rotational speed of the earth and m cancels out, the only unknown is r.

    The left side is the force of gravity on a body of mass m at a distance r from the earth's center. The right side is mass x the (centripetal) acceleration on the body. So the equation is simply an application of F=ma, as Redbelly has stated.

    AM
     
    Last edited: Jan 21, 2010
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