Question

A satellite is placed in a circular orbit about Earth with a radius equal to 49% the radius of the Moon's orbit. What is its period of revolution in lunar months? (A lunar month is the period of revolution of the Moon.)

Answer 1

A body orbiting at half the moon's distance would have a period of 0.343 lunar months.

Explanation:

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:

T2=a^3

For the Moon T=1 and a=1.

For a body orbiting at half the Moon's radius, a=0.49. Then by Kepler's third law:

T^2=0.49^3=0.117649

Taking the square root gives T=0.324 lunar months.