The dwarf planet Eris has a moon called Dysomia,which is much smaller in mass than Eris.If Dysomia has an orbital period of 16 days and orbits Eris at a distance of 40,000 km,then what is the mass of Eris?

Question

Quizplus · Accepted Answer

Using Newton's form of Kepler's Third Law, we can find the mass of Eris:
$P^2 = \frac{4\pi^2}{GM}a^3$
Where P is the orbital period, G is the gravitational constant, M is the mass of Eris, and a is the distance between Eris and Dysomia.
Plugging in the given values:
$(16	ext{ days})^2 = \frac{4\pi^2}{G}\frac{(40,000	ext{ km})^3}{M}$
Solving for M, we get:
$M = \frac{4\pi^2}{G}\frac{(40,000	ext{ km})^3}{(16	ext{ days})^2}$
$M = 1.66 	imes 10^{22}$ kg
This is closest to answer choice B.

The Dwarf Planet Eris Has a Moon Called Dysomia,which Is