In this video , Concept of "Hill sphere" is explored from a question which has recently appeared in score test . Hill radius can be approximately calculated just by writing simple equations from rotation frame of reference .
This question is highly probable for JEE Advanced 2022.

This is the question statement :
The Hill Sphere (named after American astronomer George Hill) of a secondary body (e.g. the earth) revolving around another primary body (such as the sun) is defined as the largest possible sphere in which a satellite of the secondary body (such as the moon) will remain captive to the secondary body and not be lost to the primary body. If the moon goes outside the earth's Hill sphere, it will be revolving directly about the sun. The Hill radius, i.e. the radius of the Hill Sphere can be found by applying Newton's first law to the satellite in a frame of reference attached to earth, but revolving around the primary body with the same angular velocity with which the secondary body revolves around the primary body. The earth's Hill Sphere is much smaller than its orbital radius around the sun. Hence approximations can be used. The earth's mass is m= 6 x 1024 kg. The sun's mass is 2 × 1030 kg. The earth's orbital radius is R = 1.5 x 10" m.

(A) The Hill radius of the earth is 1.5 million km

(B) The Hill radius of the earth is 2.5 million km

(C) A massive planet further away from the sun will have a greater Hill Radius than a light planet

(D) A stable satellite of the earth must have a time period of revolution of less than 7 months.

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