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)2.1 AU.
D)5.2 AU.
E)0.33 AU.

Question

Quizplus · Accepted Answer

According to Kepler's Third Law, the square of the orbital period of a planet (or asteroid in this case) is directly proportional to the cube of the semi-major axis of its orbit. This law can be simplified to $T^2 \propto R^3$, where $T$ is the orbital period in years and $R$ is the semi-major axis in astronomical units (AU). If an asteroid orbits the sun in 1/3 of a year, we can set $T = 1/3$. To find $R$, we rearrange the formula to $R^3 = T^2$, giving us $R^3 = (1/3)^2$. Solving for $R$, we find $R \approx 0.48$ AU, making option B the closest answer.

The Average Distance from Earth to the Sun Is Defined