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Density of the moon and earth

  1. Nov 14, 2004 #1

    The mass of the earth is 5.98E+24 kg and its radius is 6370 km. The radius of the moon is 1738 km. The acceleration due to gravity at the surface of the moon is 1.62 m/s2. What is the ratio of the average density of the moon to that of the earth? (no units)
    I am very confused as to how I find the density of planets given the equations and information I have. We are studying kepler's Laws and Newtons Law of Gravity. I feel like maybe I am missing some info or something.

    Thanks for the help!
  2. jcsd
  3. Nov 14, 2004 #2
    density will be denoted p
    [tex]p= \frac{m}{v}[/tex]
    [tex]m_2a = \frac{G m_1 m_2}{r^2}[/tex]

    [tex]1.62 = \frac{G m_1}{(1738*10^3 m)^2}[/tex]
    [tex] m_{moon} = m_1, \ \frac{(1.62)(1738*10^3)^2}{G} = m_1 = 7.33 * 10^{22} kg [/tex]
    [tex]p_{earth} = \frac{(5.98 *10^{24})}{(\frac{4}{3}pi (6370)^2)} = 3.52*10^{16} kg/km [/tex]
    [tex]p_{moon} = 5.79*10^{13} kg/km [/tex]
    [tex] p_{earth} : p_{moon} = 43.34 \ p_{moons} \ to \ every \ 1 \ p_{earth} [/tex]
    Last edited: Nov 14, 2004
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