Which law describes Kepler's Third Law?

• A. Kepler's First Law
• B. Kepler's Second Law
• C. Kepler's Third Law
• D. Newton's Law of Gravitation

Answer: (C)

Relating how long an object takes to complete an orbit to the size of that orbit is described by Kepler's Third Law. The law states that the square of the orbital period T is proportional to the cube of the semi-major axis a of the orbit (for planets around the Sun, T^2 = (4π^2/GM) a^3). This direct link between time and distance is what makes it the best description of Kepler's Third Law. The first law is about the shape of orbits being ellipses with the Sun at a focus. The second law says a line from the Sun to the planet sweeps out equal areas in equal times. Newton's Law of Gravitation explains the force that governs motion and can be used to derive Kepler's laws, but it doesn't by itself state the specific T–a relationship for solar-system orbits.