Watch the Astro Tour on Kepler’s Laws and choose the statement below that directly follows from Kepler’s second law of planetary motion. Choose one:
A. Venus is traveling faster when it is at perihelion (the closest distance to the Sun) than when it is at aphelion (the farthest distance from the Sun).
B. The area swept out by the orbit of Jupiter in five days is the same as the area swept out by Mars in five days.
C. Mercury’s year (the time it takes to orbit the Sun once) is shorter than Saturn’s year.
D. All the planets travel in elliptical orbits around the Sun.
The correct answer and explanation is:
The correct answer is A: Venus is traveling faster when it is at perihelion (the closest distance to the Sun) than when it is at aphelion (the farthest distance from the Sun).
Kepler’s second law, also known as the law of equal areas, states that a line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time. This implies that when a planet is closer to the Sun (at perihelion), it moves faster in its orbit to sweep out the same area in the same time as when it is farther away (at aphelion).
As the planet moves along its elliptical orbit, the distance from the Sun changes. When the planet is near perihelion, the gravitational pull from the Sun is stronger, so the planet accelerates. Conversely, when the planet is near aphelion, the Sun’s gravitational pull is weaker, and the planet moves slower. Despite this, the planet’s motion adjusts so that the area swept out by the line joining the planet and the Sun remains constant over time.
Thus, Venus, being closer to the Sun at perihelion, will travel faster compared to its speed at aphelion, as it needs to cover a larger distance in the same time to maintain the equal area swept out.
Option B refers to the equal areas swept out, but it does not directly follow from Kepler’s second law as it compares two different planets over the same period. Option C is related to orbital periods, not to the second law. Option D is a statement about elliptical orbits, which is Kepler’s first law, not the second.