Physics

Problem

For the planets in a solar system, where

T

is the orbital period of a planet and

r

is the radius of circular orbit of planet about its sun: a. Show that

T \propto r^{\frac{3}{2}}

. b. Outline what is meant by one astronomical unit (1 AU). c. Pluto is a dwarf planet of the Sun that orbits at a distance of

5.9 \times 10^9

km from the Sun. Determine, in years, the orbital period of Pluto.