TeXes Science Practice Test

Which of Kepler's Planetary Laws of Motion indicates the conservation of angular momentum?

1. Kepler's First Law

2. Kepler's Second Law

3. Kepler's Third Law

4. Kepler's Fourth Law

The correct answer is: Kepler's Second Law

Kepler's Second Law, often referred to as the Law of Equal Areas, indicates the conservation of angular momentum in the motion of planets. This law states that a line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time. This means that a planet moves faster when it is closer to the Sun and slower when it is farther away, resulting in a constant angular momentum as it orbits. The principle of conservation of angular momentum explains how the speed of a planet changes in relation to its distance from the Sun, ensuring that the angular momentum remains constant in the absence of external torques. As planets are not influenced by outside forces in their simplistic elliptical orbits, the second law highlights this consistent motion in relation to a central body (like the Sun), emphasizing the relationship between area swept out and speed. Unlike the first law, which describes the elliptical nature of orbits, or the third law, which relates the orbital periods of planets to their distances from the Sun, the second law explicitly connects to the idea of angular momentum conservation through its focus on the speed of the planets as they traverse their elliptical paths. There is no fourth law in Kepler's original formulation, reinforcing the correctness of the second law in this context