Question

Write the equation for orbital velocity of a satellite orbiting the earth at a height of $h$ from the surface of the earth.

Answer 1

So if the satellite of mass $m$ is moving around earth or any other planet of mass $M$ at distance $h$ from surface of earth with radius $R$ with orbital velocity $v$ then
Gravitational force $\frac{GMm}{(R+h{)}^2}$ and centrifugal force $\frac{m{v}^2}{(R+h)}$
$$\frac{GMm}{(R+h{)}^2}=\frac{m{v}^2}{R+h}$$
$$v=\sqrt{\frac{GM}{R+h}}$$