Starting from Newton’s law of universal gravitation, show how to find the speed of the moon in its orbit from the earth-moon distance of 3.9 × 108 m and the earth’s mass. Assume the orbit is a circle.

Answer 1

Let V be the velocity. Assume the earth's velocity is much larger and that the moon goes around the Earth at the center. Actually, both revolve about the center of mass of the pair, at a speed that depends upon the sum of the masses.

Let M be the Earth's mass.
R = 3.9*10^8 m
G = universal constant of gravity

GM/R^2 = V^2/R

Solve for V