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Homework Help: Kepler's laws and orbits question?

  1. Jan 26, 2012 #1
    1. The problem statement, all variables and given/known data

    An imaginary planet has a diameter twice that of our earth. The planet has one moon with an orbital radius of 5.0x10^7 km and orbital period of 10 earth days.
    Determine the strength of the gravitational field at the surface of the planet.

    Radius of earth = 6.38 x 10^6m
    Orbital radius of moon = 5x10^10m
    orbital period = 8.64 x 10^5 s

    2. Relevant equations

    r^3/T^2 = GM/4pi^2
    g = GM/r^2

    i think that's all..?...

    3. The attempt at a solution

    GM = (4pi^2(5x10^10)^3)/(8.64x10^5)^2
    = 6.61 x 10^21

    g = 6.61x10^21/(12.76x10^6)^2
    = 40597576.67N/kg

    this number is massive!!! I must be doing something wrong. any help?
  2. jcsd
  3. Jan 26, 2012 #2


    User Avatar

    Staff: Mentor

    Your calculation looks fine. I wouldn't want to live there!
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