I believe that the answer to Question 25 should be U = - G [(Me)(m) r^2]/(Re)^3 which is not on the answer key.

The answer given is U = -G [(Me)(m) r^2] / [2 (Re)^3].  This answer makes no sense.  When r = Re, we should get the Gravitational PE equation.  Instead we get 1/2 the GPE equation.

Michael, You are correct, the posted answer is wrong. I redid the problem and got a slightly different answer from what you have - I will neaten it up and email to you to see if you agree. Once we agree on an answer, I'll change the multiple choice selections.  Thank you very much for pointing this out. John

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