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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).

Answer and Explanation:


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.


Learn more about this topic:

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Kepler's Three Laws of Planetary Motion

from Basics of Astronomy

Chapter 22 / Lesson 12
47K

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