A particle of mass m is under the influence of the gravitational field of a body of mass M(≫ m). The particle is moving …

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 r₀ with time period T₀ around the mass M. Then, the particle is subjected to an additional central force, corresponding to the potential energy V_c(r) = mα/r³, where α is a positive constant of suitable dimensions and r is the distance from the center of the orbit. If the particle moves in the same circular orbit of radius r₀ in the combined gravitational potential due to M and V_c(r), but with a new time period T₁, then\(\left({\mathrm{T}}_{1}^{2}-{\mathrm{T}}_{0}^{2}/{\mathrm{T}}_{1}^{2}\right)\) is given by
[G is the gravitational constant.]