Kepler's Second Law implies which statement about the area swept by a line from the Sun to the planet?

• A. Planets move faster near far from the Sun.
• B. The area swept varies with position in the orbit.
• C. The orbital path is a circle.
• D. The area swept in a given time is constant, independent of position.

Answer: (D)

Kepler's second law says equal areas are swept out in equal times by the line from the Sun to the planet. This means the rate at which area is swept is constant, no matter where the planet is in its orbit. When the planet is closer to the Sun, it moves faster along its path, but the radius from the Sun is smaller, so the sector of area grows by the same amount per unit time. When it’s farther away, the radius is larger but the angular motion is slower, and again the same amount of area is swept in the same time. So, the area swept in a given time is constant and independent of position.