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Orbit of Planet (KVPY '10)

Let's discuss a problem where we will find the change in the orbit of the planet. Give it a try first, then read the solution.

The Problem:

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 there in the orbit of the planet?

Discussion:

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.

As we know, the formula for centripetal force is $$ F=\frac{mv^2}{r}$$

Since the radius of the star is decreasing without any change in mass will not have any effect on force exerted by star on planet which is the required centripetal force.

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