Question

A satellite orbits the moon far from its surface in a circle of radius $r$. If a second satellite has a greater speed, yet still needs to maintain a circular orbit around the moon, how should the second satellite orbit?

• A. With a radius $r$
• B. With a radius greater than $r$
• C. With radius less than $r$
• D. Only an eccentric elliptical orbit can be maintained with a larger speed

Answer 1

The correct option is C With radius less than $r$

For a satellite revolving in circular orbit, centripetal force is provided by the gravitational force. Hence,

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

$r\propto \frac{1}{v^2}$

If speed is higher, then the radius must be reduced.