## College Physics (4th Edition)

The expression for gravitational potential energy is: $U_g = -\frac{GMm}{r}$ At perihelion, the magnitude of the gravitational potential energy is at its maximum value since $r$ is at a minimum. However, since $U_g \lt 0$, the gravitational potential energy is at its most negative value, that is its minimum value, at perihelion. By conservation of energy, the sum of the kinetic energy and the gravitational potential energy is constant. Since the gravitational potential energy is at its minimum value at perihelion, the kinetic energy must be at its maximum value. The correct answer is: (a) its maximum value