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Finding Density of a Planet Using Period of Orbit

  1. Oct 16, 2009 #1
    1. The problem statement, all variables and given/known data

    A satellite is in a circular orbit very close to the surface of a spherical planet. The period of the orbit is T = 1.78 hours.
    What is density (mass/volume) of the planet? Assume that the planet has a uniform density.


    2. Relevant equations

    T[tex]^{2}[/tex]=4*PI^2*r^3/G*M
    Density = Mass/Volume
    Volume of Sphere = 4/3*PI*r^2

    3. The attempt at a solution
    I converted T into seconds, which I get 6408 seconds,

    I have tried to solve for a single variable, but when I put it back into the equation, everything cancels out......

    What should I do, I'm just super confused..... :(
     
  2. jcsd
  3. Oct 16, 2009 #2

    rock.freak667

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    Homework Helper

    So we have


    [tex]T^2=\frac{4\pi^2 r^3}{GM}[/tex]

    and we know [itex]V=\frac{4}{3}\pi r^3[/itex]


    So if we divide the equation with T2 by 3, can we somehow factor out (4/3)πr3?
     
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