Posted by Amelia on Sunday, November 22, 2009 at 12:48am.
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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