Suppose an asteroid is discovered with an elliptical orbit, a period of exactly 1 year, and perihelion 0.5 au from the Sun. Using Kepler's third law, how far from the Sun is this asteroid at aphelion? (Drawing a diagram of the orbit, including the Sun, will help.)
A) 2.5 au
B) 2.0 au
C) 1.0 au
D) 1.5 au

Question

Quizplus · Accepted Answer

Kepler's third law states that the square of the orbital period is proportional to the cube of the semi-major axis. Since the period is 1 year, the semi-major axis is 1 au. The semi-major axis is the average of the perihelion and aphelion distances. Given the perihelion is 0.5 au, the aphelion must be 1.5 au to average to 1 au.

Suppose an Asteroid Is Discovered with an Elliptical Orbit, a Period