Question

How does the orbital velocity of a satellite depend on the mass of the satellite?

Answer 1

Let us consider a satellite of mass m revolving around the Earth in a circular orbit of radius r at a height h from the surface of the Earth. Suppose M and R are the mass and radius of the Earth respectively, then r = R + h.

To revolve the satellite, a centripetal force of $\frac{m{v}_o^2}{r}$ is needed which is provided by the gravitational force $G\frac{Mm}{r^2}$ between the satellite and the Earth.

Therefore, equating both the equations, we get

$\frac{m{v}_o^2}{r}=G\frac{Mm}{r^2}$

$v_o^2=\frac{GM}{r}=\frac{GM}{R+h}$

Simplifying the above equation further, we get

$v_o=\sqrt{\frac{GM}{R+h}}$.

Thus the orbital velocity of a satellite is independent of its mass.