# The dwarf planet Eris orbits the sun every 557 years. How does its average distance compare to...

## Question:

The dwarf planet Eris orbits the sun every 557 years. How does its average distance compare to that of Pluto?

## Average distance:

The average distance of any object which orbits any other is proportional to the orbital period having power {eq}\left( {\frac{2}{3}} \right) {/eq}. The average distance is well explained in Kepler's third law. The average distance is generally measured in astronomical unit (AU).

Given data

• The orbital period is: {eq}P = 557\;{\rm{yr}} {/eq}

The average distance of dwarf planet Eris is,

{eq}a = \sqrt[3]{{{P^2}}} {/eq}

Substitute the values in above equation.

{eq}\begin{align*} a &= \sqrt[3]{{{{\left( {557} \right)}^2}}}\\ &= 67.7\;AU \end{align*} {/eq}

The average distance of Pluto is {eq}39.5\;{\rm{AU}}. {/eq}

The ratio of average distance of dwarf planet Eris and Pluto is,

{eq}\begin{align*} \dfrac{a}{{{a_p}}} &= \dfrac{{67.7}}{{39.5}}\\ a &= 1.71{a_p} \end{align*} {/eq}

Thus, the average distance of dwarf planet Eris is {eq}1.71 {/eq} times the average distance of Pluto.