I'm really confused pls help

Question

Ceres, the largest asteroid and a dwarf planet, has a semi-major axis of about 2.67 AU. What is Ceres’ orbital period in years about the Sun?

Answer 1

For this question the first thing to grasp is that this is a Kepler's 3rd law question.

When given a period or a distance, we can find what is missing, in this case that is the period by using the distance.

Our equation is P²=A³

First we plugin what we know which in this case is the distance in AU or "A"

P²=2.67³

-> P²=19.034

->then we take the square root to get rid of the exponent of 2 on P

->P=4.4 years

I hope this helped!