An artificial Earth satellite of mass m is moved from a circular orbit with radius R to a circular orbit with radius 2R.If the mass of the Earth is M_E, the work done by the gravitational force is: A)zero B)GM_Em/R C)GM_Em/2R D)−GM_Em/R E)−GM_Em/2R

Question

Quizplus · Accepted Answer

When an object is moved from one orbit to another, work is done against the gravitational force. The work done is given by the change in potential energy: ΔU = U(final) - U(initial) For a circular orbit, the potential energy is given by: U = -GmM/R where G is the gravitational constant, M is the mass of the Earth, m is the mass of the satellite, and R is the radius of the orbit. When the satellite is moved from an orbit with radius R to an orbit with radius 2R, the potential energy changes by: ΔU = [-GmM/(2R)] - [-GmM/R] ΔU = -GmM/R Therefore, the work done by the gravitational force is equal to the change in potential energy: W = ΔU W = -GmM/R Substituting the given values, we get: W = -G(M)(m)/(2R) W = -GM_Em/2R Hence, the correct answer is E.

An Artificial Earth Satellite of Mass M Is Moved from a Circular