Outage Notification

MCQ Question 16. The answer shows A, that a planet with a higher radius will have a higher escape velocity. However, the question also states that both planets have the same surface gravity. That would mean that the increase in mass must be equal to the increase in radius^2. Am I missing something?

Katherine, it's not quite that simple as both M and r increase, but we're not sure in what proportions they are to each other and to each planet.

Start with the escape velocities and set a ratio of v1/v2. After cancelling out constants, we get:

v1/v2 = sqrt [(m1/m2)/r2/r1)]

Since surface gravity, g, is the same on both planets:

(Gm1/r1^2) = (Gm2/r2^2)

Combine those two equations and find: v2 = (r1/r2) v1

So, the escape velocity only depends on the radius when g is the same for both.

John