m द्रव्यमान के एक उपग्रह की कक्षा की त्रिज

Given, $M$ is mass of planet, $m$ is mass of satellite, $r$ is radius of orbit.

Let, $v$ be velocity of the satellite

Now, for the satellite to revolve in the orbit the centripetal force must be balanced by gravitational force i.e.,

$F_{c}=F_{g} \rightarrow(1)$

we know that,

$F_{c}=\frac{m v^{2}}{r}$ and $F_{g}=G M m r^{2}$

substituting these values in $(1)$

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

After solving this equation we get

$v^{2}=\frac{G M}{r}$