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The Moon's period of revolution around the Earth is 27.3 d. How far away is the moon?

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  1. You need to know the mass of the earth (M) to answer that question. You can look it up or use the relation

    g = G M/r^2,

    where g is the universal constant of gravity, r is the Earth's radius and g is the acceleration of gravity at the Earth's surface.

    To get the radius R of the moon's orbit, use Kepler's third law.

    G M/R^2 = V^2/R = [(2 pi R)/P]^2/R
    which rearranges to
    R^3/P^2 = M G/(4 pi^2)
    where P is the period in seconds.

    For another explanation see
    http://www-istp.gsfc.nasa.gov/stargaze/Skepl3rd.htm

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