In class today, we discussed a new (but more general) form for the force of gravity: F = Gm1m2/r2. This expression for the force of gravity replaces the familiar F = mg if you're not very close to the surface of the earth. It perhaps doesn't come as a surprise that our old gravity potential energy expression, PE = mgh, is only good when you're also very close to the surface of the earth. The more general expression for the potential energy due to gravity is PE = -Gm1m2/r (where r is an always-positive distance between the centers of the two masses).
Your job in this essay is to work a quick sample case to show this more general PE expression makes sense. Demonstrate how this new expression still has your gravitational potential energy decreasing as your falling object (say, a 5000kg asteroid) gets closer to the earth. If you're losing PE, then the asteroid must be gaining KE (since there are no other forces at play that can do work on the asteroid). The asteroid must, then, speed up as it approaches earth, which makes sense.