The average distance from Earth to the sun is defined as one astronomical unit (AU). If an asteroid orbits the sun in 1/3 of a year in a circular orbit, the asteroid's distance from the sun is closest to
A) 0.19 AU
B) 0.48 AU
C) 5.2 AU
D) 2.1 AU
E) 0.33 AU

Question

The average distance from Earth to the sun is defined as one astronomical unit (AU). If an asteroid orbits the sun in  1/3  of a year in a circular orbit, the asteroid's distance from the sun is closest to
A)  0.19 AU
B)  0.48 AU
C)  5.2 AU
D)  2.1 AU
E)  0.33 AU

Quizplus · Accepted Answer

Using Kepler's third law, the square of the orbital period (in years) is proportional to the cube of the semi-major axis (in AU). For an asteroid orbiting in 1/3 of a year: (1/3)^2 = a^3, solving gives a ≈ 0.48 AU.

The Average Distance from Earth to the Sun Is Defined