Kepler's Second Law implies which of the following about a planet's motion?

• A. Planets move faster when they are closest to the Sun.
• B. Planets travel along circular orbits only.
• C. The orbital speed is constant for all points.
• D. As a planet moves around its orbit, it sweeps out equal areas in equal times.

Answer: (D)

Kepler’s second law tells us that the line from the Sun to the planet sweeps out equal areas in equal times. This means the rate at which area is covered is constant, not the planet’s speed. Since area swept in a small time is proportional to r^2 times the angular change, the planet must move faster when it is closer to the Sun and slower when it is farther away to keep that areal rate the same. That’s why planets don’t travel in circles with constant speed: their distance from the Sun changes, and the speed adjusts so the area swept per unit time stays constant. This law naturally applies to elliptical orbits, with the Sun at one focus, and it contradicts the idea of always-constant orbital speed or strictly circular paths.