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Homework Help: Finding the mass of a planet using gravitational acceleration and radius

  1. Nov 22, 2008 #1
    1. The problem statement, all variables and given/known data

    Planet Z is 5000 km in diameter. The free-fall acceleration on Planet Z is 7.00 m/s^2. What is the mass of Planet Z?

    2. Relevant equations

    Well Newton's gravitational law G(M1M2)/R^2
    And I cannot think of much else

    3. The attempt at a solution

    On one of the earlier homeworks we were given a table in which there were fictional planets and their ratios of mass and radius to earth so I tried using

    gG M(earth)/(R(earth))^2 = gG M(z)/(R(z))^2
    Where the "g"s are each planet's free fall acceleration.
    so that the Gravitational constant would cancel and I'd have the Mass of planet Z

    For the mass of the earth I used 5.97E34, for the radius of the earth I used 6387.1 km
    I know that the radius needs to be in meters and would be correctly notated as 6.3871E6

    I don't know how to figure this one out
  2. jcsd
  3. Nov 22, 2008 #2


    User Avatar
    Homework Helper

    Welcome to PF.

    F = ma = GMm/r2

    a = GM/r2
  4. Nov 22, 2008 #3
    Thank you very much
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