A satellite of mass $m$ is moving in a circular orbit of radius $r$ around the earth. The angular momentum…
A satellite of mass $m$ is moving in a circular orbit of radius $r$ around the earth. The angular momentum of the satellite about the center of orbitis ( $M=$ mass of earth, $G=$ gravitational constant)
$\left(G M m^2 r^2\right)^{1 / 2}$
$(G M m r)$
$\left(G M m^2 r\right)^{1 / 2}$
$\left(G M^2 m r\right)^{1 / 2}$
Solution
Let the satellite revolves in a circular orbit of radius $r$ with a linear velocity $v$.
The centripetal force of acting on the satellite is balanced by the gravitational force due to the earth.
$\begin{aligned} & \therefore F_{\text {centripetal }}=F_{\text {gravitational }} \\ & \Rightarrow \frac{m v^2}{r}=\frac{G M m}{r^2} \\ & \Rightarrow v=\sqrt{\frac{G M}{r}}\end{aligned}$
Angular momentum of satellite about the center of orbit, is
$L=m v r=m\left(\frac{G M}{r}\right)^{1 / 2} r=\left(G M m^2 r\right)^{1 / 2}$