Question

The dwarf planet Pluto has an average orbital radius of 40 AU. Using Kepler's third law of planetary motion, what is Pluto's orbit in Earth-years?

Answer 1

Pluto's period is 253 years using Kepler's third law.

Explanation:

In our solar system, anything orbiting the Sun obeys a simplified form of Kepler's third law if the period `T` is measured in years and the semi-major axis `a` distance is measured in AU.

$$T^2=a^3$$

If Pluto has a semi-major axis distance `a=40` then `T^2=40^3` which gives `T=253` years.

The actual period os Pluto is 248 years which is close.