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(D) The correct answer is $D$.When a star shrinks without losing its mass,its gravitational acceleration on its surface increases,but there is no chan

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The radius of the orbit will not change

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(D) The correct answer is $D$.When a star shrinks without losing its mass,its gravitational acceleration on its surface increases,but there is no change in the gravitational force exerted by this star on a distant object like a planet.The force of gravitational attraction of the star on the planet is given by:$F = \frac{G M m}{r^2}$where $M$ is the mass of the star,$m$ is the mass of the planet,and $r$ is the orbital radius of the planet.Since the mass of the star $(M)$,the mass of the planet $(m)$,and the distance between them $(r)$ remain unchanged,the gravitational force $F$ remains constant.Because the centripetal force required to maintain the circular orbit depends only on the mass of the star and the distance $r$,and neither of these has changed,there will be no change in the orbital radius of the planet.

$A$ 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?

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