Question

Kepler's third law, p2 = a3, means that

a) a planet's period does not depend on the eccentricity of its orbit.
b) the period of a planet does not depend on its mass.
c) all orbits with the same semimajor axis have the same period.
d) planets that are farther from the Sun move at slower average speeds than nearer planets.
e) All of the above are correct.

Answer 1

Kepler's third law correctly implies that all orbits with the same semimajor axis have the same period, regardless of a planet's mass or the eccentricity of its orbit.

Step-by-step explanation:

Kepler's third law states that the square of a planet's orbital period (P²) is directly proportional to the cube of the semimajor axis (a³) of its orbit, where the semimajor axis is the longest diameter of the orbital ellipse and the orbital period is the time it takes a planet to complete one orbit around the Sun. From the options provided, the correct interpretation of Kepler's third law is that all orbits with the same semimajor axis have the same period. This is because the law is based only on the distance (semimajor axis), not on the mass of the planet, the center body (like the Sun), or the shape of the orbit (eccentricity). Therefore, planets further from the Sun do indeed move at slower average speeds.