Question 13.7: ORBITAL SPEEDS At what point in an elliptical orbit (see Fig...

Mechanical energy is conserved as a planet moves in its orbit. The planet’s kinetic energy K=\frac{1}{2} m v^{2} is maximum when the potential energy U=-G m_{\mathrm{S}} m / r is minimum (that is, most negative; see Fig. 13.11), which occurs when the sun–planet distance r is a minimum. Hence the speed v is greatest at perihelion. Similarly, K is minimum when r is maximum, so the speed is slowest at aphelion.
Your intuition about falling bodies is helpful here. As the planet falls inward toward the sun, it picks up speed, and its speed is maximum when closest to the sun. The planet slows down as it moves away from the sun, and its speed is minimum at aphelion.