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Close orbit around planet

  1. Apr 1, 2013 #1
    A satellite is in a circular orbit very close to the surface of a spherical planet. The period of the orbit is 1.94 hours. What is density of the planet? Assume that the planet has a uniform density.

    density = kg/m^3
    T = 2∏/ω = 2∏r/v
    GMm/r^2 = (mv^2)/r
    v^2 = GM/r
    v = rω

    So I know I need to find the radius and the mass of the planet in order to find the density. Since I don't have r or v I found ω=8.99E-4. I'm not sure where to go from here.
     
  2. jcsd
  3. Apr 1, 2013 #2

    mfb

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    2016 Award

    Staff: Mentor

    You don't need the radius or mass (which is a surprising result, I think). Just use r and M, and you will find some relation between those two (based on the orbit). This can be converted into a density afterwards.
     
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