Question

A satellite of mass m is revolving in circular orbit of radius $r$ around the earth. Its angular momentum w.r.t. the centre of its orbit is

(M= mass of earth, G = universal gravitational constant)

• A. $(GMmr{)}^{1/2}$
• B. $(GM{m}^{2}r{)}^{1/2}$
• C. $(GM{m}^2{r}^2{)}^{1/2}$
• D. $(G{M}^2{m}^{2}r{)}^{1/2}$

Answer 1

Answer: (B)

$(GM{m}^{2}r{)}^{1/2}$

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 earth.

$\therefore$ $F_{centripetal}=F_{gravitational}$

$\Rightarrow \frac{m{v}^2}{r}=\frac{GMm}{r^2}$

$\Rightarrow v=\sqrt{\frac{GM}{r}}$

Angular momentum of satellite about the centre of orbit, $L=mvr$

$L=m(\frac{GM}{r}{)}^{1/2}r$

$⟹$ $L=(GM{m}^{2}r{)}^{1/2}$