If an asteroid was moving in a circular orbit around the Sun with an orbital period of 1/5 that of Jupiter, what would be the radius of its orbit? The semimajor axis of Jupiter's orbit is 5.2 au.

Question

Quizplus · Accepted Answer

According to Kepler's third law, the square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit. If the asteroid's orbital period is 1/5 that of Jupiter, then (T_asteroid/T_Jupiter)^2 = (R_asteroid/R_Jupiter)^3, where T is the orbital period and R is the semi-major axis (or radius for circular orbits). Substituting T_asteroid = 1/5 T_Jupiter and R_Jupiter = 5.2 au, we find R_asteroid ≈ 1.78 au.

If an Asteroid Was Moving in a Circular Orbit Around