A body of mass m is moving in a circular orbit of radius R about a planet of mass M . At some instant, it splits into two equal masses. The first mass moves in a circular orbit of radius R 2 , and the other mass, in a circular orbit of radius 3 R 2 . The difference between the final and initial total energies is:

Step-by-step solution

Initial gravitational potential energy, E_i=- G M m 2 R Final gravitational potential energy, aligned E_f &=- G M m / 2 2 ( R 2 ) - G M m / 2 2 ( 3 R 2 ) &=- G M m 2 R - G M m 6 R &=- 4 G M m 6 R =- 2 G M m 3 R aligned Difference between initial and final energy, E_f-E_i= G M m R (- 2 3 + 1 2 )=- G M m 6 R