Question

A satellite of mass $m$ is moving in a circular orbit of radius $r$. Calculate the angular momentum of the satellite with respect to the centre of the orbit.

Answer 1

The angular momentum of a particle of mass $m$ moving in a circular path of radius $r$ with a constant speed $v$ is given by:
$L=mvr$.
Here, the satellite acts as a particle because its diameter is negligible compared to the diameter of the orbit. Therefore, its angular momentum about the centre of the orbit can be found by putting $v=\sqrt{\frac{2GM}{r}}$ as orbital speed of the satellite to obtain
$L=m\left(\sqrt{\frac{2GM}{r}}\right)r\Rightarrow L=m\sqrt{2GMr}$.