Earth is a distance of 1 Astronomical Unit (AU) from the Sun, whereas Pluto is 39.5 AU form the Sun. How long, in Earth years, does it take Pluto to complete one orbit of the Sun?

Question

Earth is a distance of 1 Astronomical Unit (AU) from the Sun, whereas Pluto is 39.5 AU form the Sun. How long, in Earth years, does it take Pluto to complete one orbit of the Sun?

I don't quite understand what to do, should I draw a diagram?

What equations do I use? How do I solve? Please help!!

Answer 1

I had to help a student earlier this semester with a similar problem. This is based on Kepler's third law. In this case, all we need is the equation that relates the period (P) with the size of the orbit (a).

Kepler's third law states:

P² = a³

So in this case

P = √39.5³