Question

Two moons orbit a planet in nearly circular orbits. Moon A has orbital radius r, and moon B has orbital radius 16r. Moon A takes 10 days to complete one orbit. How long does it take moon B to complete an orbit

Answer 1

Kepler's Third Law: The square of the period of any planet about the sun is proportional to cube of its mean distance from the sun.

Mathematically: T^2 = K R^3

So (TA / TB)^2 = (RA / RB)^3

TB^2 = TA^2 * (RB / RA)^3

TB^2 = 10^2 * 16^3

TB = (409600)^1/2 = 640 days