A satellite of mass ' $m$ ' is revolving around the earth of mass ' $M$ ' in an orbit of radius ' $r$ ' with…
A satellite of mass ' $m$ ' is revolving around the earth of mass ' $M$ ' in an orbit of radius ' $r$ ' with constant angular velocity ' $\omega$ '. The angular. momentum of satellite is
( $\mathrm{G}=$ Universal constant of gravitation)
$\mathrm{m}(\mathrm{GMr})^{3 / 2}$
$\mathrm{m}(\mathrm{GMr})$
$\mathrm{m}(\mathrm{GMr})^{1 / 2}$
$\quad \mathrm{m}(\mathrm{GMr})^{-1 / 2}$
Solution
$\begin{aligned} \frac{m^2}{r} & =\frac{G M m}{r^2} \\ \therefore \quad V & =\sqrt{\frac{G M}{r}} \\ L & =m v r=m \sqrt{\frac{G M}{r}} r \\ & =m(G M r)^{1 / 2}\end{aligned}$