# 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?

Jun 5, 2018

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.