Question

if a planet has an average distance from the sun (semi - major axis of its orbit) of 4 astronomical units, what is the period of its orbit? (hint: use keplers 3rd law)
a 8 years
b 1 year
c 12 years
d 4 years
e 64 years

Explanation:

Step1: Recall Kepler's 3rd Law

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

Step2: Substitute the given value of \( a \)

We are given that \( a = 4 \) AU. Substitute \( a = 4 \) into the formula \( T^2=a^3 \). So we have \( T^2=4^3 \).

Step3: Calculate \( T^2 \) and then \( T \)

First, calculate \( 4^3=4\times4\times4 = 64 \). So \( T^2 = 64 \). Then, take the square root of both sides. Since \( T \) represents a period (a positive quantity), \( T=\sqrt{64}=8 \) years.

Answer:

A. 8 years