If you have two moons that have the same radius, but Moon A is denser and has 2 times the mass of Moon B, how do their escape velocities from their respective surfaces compare?
A) Moon A has an escape velocity that is 1.4 times larger than Moon B.
B) Moon A has an escape velocity that is 1.4 times smaller than Moon B.
C) Moon A has an escape velocity that is 2 times smaller than Moon B.
D) Moon A has an escape velocity that is 2 times larger than Moon B.
E) Because gravity affects all masses the same, the escape velocities are the same.

Question

Quizplus · Accepted Answer

Escape velocity is proportional to the square root of the mass. Since Moon A has twice the mass of Moon B, its escape velocity is √2 times that of Moon B, which is approximately 1.4 times larger.

If You Have Two Moons That Have the Same Radius