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