A particle of mass m is under the influence of the gravitational field of a body of mass M ( m). The particle is moving in a circular orbit of radius r 0 with time period T 0 around the mass M .

Question

A particle of mass m is under the influence of the gravitational field of a body of mass M (>> m). The particle is moving in a circular orbit of radius r 0 ​ with time period T 0 ​ around the mass M . Then, the particle is subjected to an additional central force, corresponding to the potential energy

TestHub · Accepted Answer

Hint: T 0 2 ​ = GM 4 π 2 ​ r 0 3 ​ V C ​ ( r ) = r 3 m α ​ F additional ​ = d r ​ d ​ ( V c ​ ) = r 4 3 m α ​ r 0 ​ 2 GMm ​ + r 0 ​ 4 3 m α ​ = r 0 ​ mV 1 2 ​ ​ V 1 ​ = r 0 ​ GM ​ + r 0 ​ 3 3 α ​ ​ T 1 ​ = V 1 ​ 2 π r 0 ​ ​ T 1 2 ​ T 1 2 ​ − T 0 2 ​ ​ = 1 − ( T 1 ​ T 0 ​ ​ ) 2 Solve (1) (2) & (3)

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