A satellite is put in a circular orbit about Earth with a radius equal to one-half the radius of the Moon's orbit. What is its period of revolution in lunar months?

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Answer 1 · 2016-05-30T12:34:14

A body orbiting at half the moon's distance would have a period of 0.35355 lunar months.

Kepler's third law can be used to calculate the period of a body orbiting the Earth.

Taking the units of period #T# in lunar months and orbit radius #a# in lunar orbit radii. Then Kepler's third law states that:

#T^2=a^3#

For the Moon #T=1# and #a=1#.

For a body orbiting at half the Moon's radius, #a=0.5#. Then by Kepler's third law:

#T^2=0.5^3=0.125#

Taking the square root gives #T=0.35355# lunar months.