An artificial satellite of mass m is moved from an initial circular orbit at a height R above the Earth's surface to a higher circular orbit at a height 3R , where R is the radius of the Earth. If M is the mass of the Earth, the change in the gravitational potential energy of the satellite is:

Step-by-step solution

The distance of the initial orbit from the center of the Earth is r₁ = R + R = 2R . The initial gravitational potential energy is U_i = - GMm 2R . The distance of the final orbit from the center of the Earth is r₂ = R + 3R = 4R . The final gravitational potential energy is U_f = - GMm 4R . The change in gravitational potential energy is: U = U_f - U_i = - GMm 4R - (- GMm 2R ) = GMm 4R . Answer: GMm 4R