Question

if a planets average distance from the sun is 9 astronomical units, how long does it take to complete one orbit around the sun?
a 81 years
b 27 years
c 18 years
d 9 years

Explanation:

Step1: Recall Kepler's third - law

Kepler's third law states that $T^{2}=a^{3}$, where $T$ is the orbital period of a planet in years and $a$ is the semi - major axis of the planet's orbit in astronomical units.

Step2: Substitute the given value of $a$

Given $a = 9$ astronomical units. Substitute $a$ into the formula $T^{2}=a^{3}$. So $T^{2}=9^{3}=729$.

Step3: Solve for $T$

Take the square root of both sides of the equation $T^{2}=729$. So $T=\sqrt{729}=27$ years.

Answer:

B. 27 years