Physics - Gravitation Question with Solution | TestHub

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. $\begin{array}{rl}& \therefore F_{\text{centripetal }}=F_{\text{gravitational }}\\ & \Rightarrow \frac{m{v}^2}{r}=\frac{GMm}{r^2}\\ & \Rightarrow v=\sqrt{\frac{GM}{r}}\end{array}$ Angular momentum of satellite about the center of orbit, is $L=mvr=m{\left(\frac{GM}{r}\right)}^{1/2}r={\left(GM{m}^{2}r\right)}^{1/2}$