The dwarf planet Eris orbits the Sun every 557 years. 1. What is your average distance (semi-major axis) from the Sun? Response in —–Semi-major axis of Eris=? AU 2. How does its average distance compare to that of Pluto? Answer in —–aEris/aPluto=?
1) Let: Orbital period of Eris (P) = 557 years.
Semi-major axis (a) = ?
From Kepler’s third law, P2 =
a 3
Where, P is the orbital period in years and a is the semi-major
axis in the AU.
or, a3 = (557)2 = 310249 AU
where, a = 67.697 AU
2) Semi-major axis of Pluto = 39,482 AU.
Semi-major axis of Eris = 67,697 AU
So a/aaPluto =
67.697/39.482 = 1.714
So one Eris = 1.714 one Pluto.