Question

a planet takes 8 years to orbit the sun. according to keplers third law, what is the approximate average distance of this planet from the sun?
a 16 astronomical units (au)
b 8 astronomical units (au)
c 4 astronomical units (au)
d 2 astronomical units (au)

Explanation:

Step1: Recall Kepler's Third Law

$T^{2}=a^{3}$, where $T$ is the orbital - period in years and $a$ is the semi - major axis (average distance) in astronomical units (AU).

Step2: Substitute the given value of $T$

Given $T = 8$ years. Substitute $T$ into the formula: $(8)^{2}=a^{3}$. So, $64=a^{3}$.

Step3: Solve for $a$

Take the cube - root of both sides. $\sqrt[3]{64}=a$. Since $4\times4\times4 = 64$, $a = 4$ AU.

Answer:

C. 4 astronomical units (AU)