A satellite orbits the earth. The point in orbit farthest from the earth is the apogee and the point nearest the earth the perigee. With respect to the earth, at which of these points does the satellite have the greatest gravitational potential energy? The greatest kinetic energy? The greatest total energy?

The greatest gravitational potential energy is at apogee. The greatest kinetic energy is at perigee. Total Energy is constant.

Explanation:

The gravitational potential energy is at its greatest when the satellite is farthest  from the earth, this point is called the apogee. And at this point the kinetic energy will be at its minimum.

The kinetic energy is greatest when the satellite is closest to the earth, this point is the perigee. And at this point the gravitational potential energy will be at a minimum level.

the total energy is the sum of the gravitational potential energy and the kinetic energy.As the satellite orbits the earth, the kinetic energy and the gravitational potential energymay be interchanged but the total energy will remain unchanged.