I don't have an exact quesiton here. But for example, there is a 10kg mass at a distance of 2R from the centre of mass of the Earth. It's gravitational potential energy is equal (or so it's been preached by teachers) to mgh. The local gravity at 2R is approximately 2.5ms^-2. So let's say the object falls down a little bit. The height has decreased by a certain amount, and the local gravity at this point is higher. I'm pretty sure that the increase in local gravity means that the Ep worked out at 2R is wrong. I'm pretty sure that mgh ONLY applies when the h is small enough that the g doesn't change. That it's meant for a UNIFORM acceleration. The thing is, gravity isn't a uniform acceleration. So how do we find the true potential energy of an object in a gravitational field? If by some virtue, you can prove that mgh IS correct for gravitational fields (which I HIGHLY HIGHLY HIGHLY doubt), then how can you find the Ep of a mass in a uniform acceleration field?