Which statement describes Kepler's Second Law?

Which statement describes Kepler's Second Law?

• A. Gravity is a central force.
• B. The line from the Sun to the planet sweeps out equal areas in equal times.
• C. Planets travel in circular orbits only.
• D. The orbital period is proportional to the semi-major axis.

Answer: (B)

Kepler's Second Law says the line from the Sun to a planet sweeps out equal areas in equal times. In other words, the areal velocity (the rate at which area is swept) is constant as the planet moves. This happens because gravity is a central force that exerts no torque about the Sun, so angular momentum is conserved. With angular momentum fixed, the planet must speed up when it is closer to the Sun and slow down when it is farther away so that the same amount of area is covered in any equal time interval. That’s why faster near perihelion and slower near aphelion, yet the area swept per unit time stays the same. The other statements don’t describe the second law: gravity being central is true but describes a cause, not the equal-area effect; planets don’t have to travel in circular orbits (ellipse is allowed); and the orbital period’s relation to size is Kepler’s Third Law, not the second.

Kepler's Second Law says the line from the Sun to a planet sweeps out equal areas in equal times. In other words, the areal velocity (the rate at which area is swept) is constant as the planet moves. This happens because gravity is a central force that exerts no torque about the Sun, so angular momentum is conserved. With angular momentum fixed, the planet must speed up when it is closer to the Sun and slow down when it is farther away so that the same amount of area is covered in any equal time interval. That’s why faster near perihelion and slower near aphelion, yet the area swept per unit time stays the same. The other statements don’t describe the second law: gravity being central is true but describes a cause, not the equal-area effect; planets don’t have to travel in circular orbits (ellipse is allowed); and the orbital period’s relation to size is Kepler’s Third Law, not the second.