According to Kepler's laws, when is a planet's orbital speed greatest?

• A. At aphelion
• B. At the semi-major axis
• C. At the center of its orbit
• D. At perihelion

Answer: (D)

In an elliptical orbit the speed varies due to conservation of angular momentum: equal areas are swept in equal times. This means the areal velocity, which is proportional to r times the orbital speed, stays constant. When the planet is close to the Sun (r is small), it must move faster along its path to sweep the same area in the same time. So the orbital speed is greatest at the closest point to the Sun, perihelion. Conversely, at the farthest point, aphelion, the radius is large and the speed is smallest. The center of the orbit or the point where the radius equals the semi-major axis isn’t where the speed peaks.