Answer to Question #137563 in Physics for Muhammad

Question

A moon orbits planet X at a speed of 6.68x10^3 m/s. If planet X has a mass of 8.68x10^25 kg, what is the radius of the moon's orbit around planet X?

(G=6.67x10^-11 N.m^2 /Kg^2)

Answer 1

Gravitational force between the moon and the planet is $F = G \frac{m M}{R^2}$, where $m$ is the mass of the moon, $M$ is the mass of the planet, R is the distance between the two, G is the gravitational constant.

Since the motion of the moon is along the circular path, this force is equal to centripetal force $F = m \frac{v^2}{R}$. Equating last two equations, obtain $G \frac{M m}{R^2} = m \frac{v^2}{R}$, from where $v^2 = \frac{G M}{R}$, and $R = \frac{G M}{v^2} \approx 1.3 \cdot 10^8 m$.