Hi all,
So, in Physics, we are taught two equations for gravitational potential energy:
U = mgh, assuming that the gravitational field is constant, and
U = -GMm/r
Now, I've come across numerous questions in textbooks and Trial papers which say something to the effect: "If the orbital radius of a satellite is doubled, what happens to gravitational potential energy?". Using the first equation, you can conclude that gravitational potential energy doubles. However, for the second equation, since U is inversely proportional to r, this implies that U will actually halve (though this still ends up being an increase as U becomes less negative). Yet, most, if not all solutions I've seen to such questions (most often multiple choice), will align with the former - radius doubles, gravitational potential energy increases by a factor of 2.
How can we reconcile these two equations? Which one is correct?
Any assistance is very much appreciated!