From Kepler's third law,an asteroid with an orbital period of 8 years lies at an average distance from the Sun equal to
A)2 astronomical units.
B)4 astronomical units.
C)8 astronomical units.
D)16 astronomical units.
E)It depends on the asteroid's mass.

Question

Quizplus · Accepted Answer

Kepler's third law states that the square of the orbital period of a planet (or asteroid) is directly proportional to the cube of the semi-major axis of its orbit. This can be simplified to $P^2 \propto a^3$, where $P$ is the orbital period in years and $a$ is the average distance from the sun in astronomical units (AU). For an orbital period of 8 years, $8^2 = 64$, which when solved for $a$ in the context of Earth's orbit (where $P = 1$ year and $a = 1$ AU) gives us $a^3 = 64$, thus $a = 4$ AU. The mass of the asteroid does not factor into Kepler's third law, which applies universally.

From Kepler's Third Law,an Asteroid with an Orbital Period of 8