A satellite is orbiting the earth in a circular orbit of radius $r$. If the earth suddenly shrinks to half its radius without changing its mass, what will happen to the orbit of the satellite?

Solution

1. The gravitational force on a satellite at distance $r$ from the center of the Earth is given by $F=\frac{GMm}{r^2}$.
2. The orbital velocity required for a circular orbit is $v=\sqrt{\frac{GM}{r}}$.
3. Since the mass $M$ of the Earth and the orbital radius $r$ remain unchanged, the gravitational force and the required orbital velocity remain constant.
4. The physical radius of the Earth does not affect the gravitational field at any point where $r$ is greater than the Earth's radius.
5. Hence the answer is (A).