Question

1. Pluto has an orbital period of 248 years, and the dwarf planet Eris has an orbital period of 557 years. What is the average distance (semimajor axis) of Eris from the Sun, and how does it compare to the average distance between Pluto and the Sun? Express your answers in astronomical units (AU).

Answer 1

For this problem we have to Kepler's third law where T^2directly proportional to A^3

T=Time period in years

A=Distance or semi major axis in Au

Pluto Given T=248 years

T^2=A^3

A=T^2/3=248^(2/3)=39.47Au(average distance between sun and Pluto)

For dwarf planet Eris T=557 years

A=557^2/3=67.69 years (average distance between Eris and Sun)

If we divide bothA2(Eris semi major axis )/A1(Pluto semi major axis)=67.69/39.47=1.71 that mean Eris 1.71 times more distance than Pluto or semi major axis of Eris 1.71 time more than Pluto.