Question

An earth's satellite is moved from one stable circular orbit to another higher stable circular orbit. Which one of the following quantities increases for the satellite as a result of this change.

• A. Angular momentum
• B. Kinetic energy
• C. Angular velocity
• D. Linear orbital speed

Answer 1

The correct option is A Angular momentum

Orbital speed of a satellite of mass $m$ revolving around a planet of mass $M$ in the orbit of radius $r$ is given by,$$v=\sqrt{\frac{GM}{r}}$$so, $v\propto \frac{1}{\sqrt{r}}$, means as $r$, increases $v$ decreases.

Angular momentum of the satellite:

$L=mvr=m\left(\sqrt{\frac{GM}{r}}\right)r$

So, $L\propto \sqrt{r}$, means as $r$ increases, $L$ also increases.

Kinetic Energy of the satellite:

$K=\frac{GMm}{2r}$

So, $K\propto \frac{1}{r}$, means as $r$ increases, $K$ decreases.

Angular velocity:

$\omega =\frac{v}{r}=\frac{\sqrt{\left(\frac{GM}{r}\right)}}{r}\propto \frac{1}{r^{\frac{3}{2}}}$

So, as $r$ increases, $\omega$ decreases.

Hence, only the angular momentum increases with the increase in the radius of the circular orbit. So, option (a) is the correct answer.