Energy required for moving a body of mass m from a circular orbit of radius 3R to a higher orbit of radius 4R around the earth is.

Step-by-step solution

The total mechanical energy E of a body of mass m in a circular orbit of radius r around the Earth of mass M is given by the expression E = - GMm 2r . The energy in the initial orbit of radius r₁ = 3R is E₁ = - GMm 2(3R) = - GMm 6R . The energy in the final orbit of radius r₂ = 4R is E₂ = - GMm 2(4R) = - GMm 8R . The energy required to move the body from the initial orbit to the final orbit is the change in total mechanical energy, E = E₂ - E₁ . Substituting the values, E = - GMm 8R - (- GMm 6R ) = GMm 6R - GMm 8R