The orbits of asteroids in the asteroid belt have typical semimajor axes of 2.8 au. According to Kepler's law, the approximate sidereal period of these asteroids is
A) 2.8 years.
B) 46.8 years.
C) 1.99 years.
D) 4.68 years.

Question

Quizplus · Accepted Answer

The sidereal period $P$ of an asteroid can be calculated using Kepler's third law, which states $P^2 = a^3$, where $P$ is the period in Earth years and $a$ is the semimajor axis in astronomical units (au). For an asteroid with a semimajor axis of 2.8 au, $P^2 = 2.8^3 = 21.952$, so $P = \sqrt{21.952} \approx 4.68$ years.

The Orbits of Asteroids in the Asteroid Belt Have Typical