Question

A planet of mass $m$ is moving around a star of mass $M$ and radius $R$ in a circular orbit of radius $r$. The star abruptly shrinks to half its radius without any loss of mass. What change will be there in the orbit of the planet ?

• A. The planet will escape from the star
• B. The radius of the orbit will increase
• C. The radius of the orbit will decrease
• D. The radius of the orbit will not change

Answer 1

The correct option is D The radius of the orbit will not change

Answer is D.
The radius of the orbit will not change. The force of gravity that the planet feels is only a function of the star's mass, the planet's mass, the distance between the centers of the objects, and the gravitational constant. The star's radius has no part in the equation and shrinking the radius of the star does not change where its center is located. The planet won't notice a thing.