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A planet of mass 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
A planet of mass 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 is : (d) The radius of the orbit will not change
When star shrinks without losing its mass, its gravitational acceleration on its surface increases but there is no change in force exerted by this star on a distant object like a planet. Force of gravitational attraction of star on planet is
F = GMm/r2
where, M = mass of star, m = mass of planet and r = orbital radius of planet. As, this force remains same there is no change in orbital radius of planet.