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Help with a Proof

  1. Oct 16, 2004 #1
    How can i mathematically prove the following equation:
    I have to prove that the minimum speed required to maintain orbit around the Earth is (given the mass of the earth and universal gravitation constant)

    v = 2.00x10^7
    (root)r

    I have to basically prove this equation:

    v = GmE
    r

    P.S. the whole equation to the above is square rooted, and the r should be UNDER GmE).
     
  2. jcsd
  3. Oct 16, 2004 #2

    Clausius2

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    In order to mantain the equilibrium of the body the centrifugal force has to be equal to the gravitational one:

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

    [tex]v=\sqrt{\frac{GM}{r}}[/tex]
     
  4. Oct 16, 2004 #3
    So if this were a question on an assignment out of 6 marks, all i would have to is show the relationship between the two equations (it would be a pretty short proof). Thanx a lot
     
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