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Gravitational Potential and Satellite Motion

  1. Dec 4, 2005 #1
    Astronomers observing a distant solar system have noticed a planet orbiting a star with a period of 4.44x107 s. The distance from the planet to the star is 4.28x1011 m. Calculate the mass of the star, in kg.

    ihave used v = 2*pi*r/T and v=(2Gm/r)^1/2
    i get 8.75e18
    is this the way to calculate m
    thanks in advance
     
  2. jcsd
  3. Dec 5, 2005 #2

    mezarashi

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    The more logical thing to do (imho) is:

    [tex] F = \frac{mv^2}{R} = \frac{GMm}{R^2}[/tex]

    Which simplify into Kepler's law, with the subsitution: [tex]v = \frac{2\pi R}{T}[/tex]
     
  4. Dec 5, 2005 #3

    BobG

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    Why are you finding velocity if the problem asked for the mass of the star?

    You can use Kepler's third law, or:

    [tex]\tau^2=\frac{4 \pi^2 a^3}{G(M+m)}[/tex]
    Unless the planet is very, very big for a planet, it can be disregarded, eliminating the little m from the equation. The rest is rearranging the equation to solve for big M.
     
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