Question

Ceres has an orbital semi-major axis = 2.768 AU. What is Ceres’ orbital period?

Answer 1

Answer: 4.6 years

Explanation:

According to Kepler’s Third Law of Planetary motion “The square of the orbital period $T$ of a planet is proportional to the cube of the semi-major axis $a$ (size) of its orbit”:

$T^{2}\propto a^{3}$ (1)  

However, if $T$ is measured in Earth years, and $a$ is measured in astronomical units (unit equivalent to the distance between the Sun and the Earth), equation (1) becomes:  

$T^{2}=a^{3}$ (2)  

Knowing $a=2.768 AU$ and isolating $T$ from (2):  

$T=\sqrt{a^{3}}$ (3)  

$T=\sqrt{(2.768 AU)^{3}}$ (4)  

Finally:  

$T=4.6 years$ This is Ceres' orbital period