Hello, I haven't learned a lot of physics and math, but I don't know how I misunderstand the following concepts: Why is the gravitational potential energy of a system of two bodies described in one term instead of two? If each body in a two-body system effects a gravitational force on the other one, wouldn't both objects have their own gravitational potential energy (albeit they would be the same value), instead of sharing one energy? My second question: The derivation for the escape velocity of an object at the Earth's surface (as found for instance on Wikipedia here: http://en.wikipedia.org/wiki/Escape_velocity#Derivation_using_G_and_M), seems to me to assume that the Earth remains static while the object is moving away from it. If the object were sufficiently large, wouldn't the Earth and its gravitational field move after it, making it harder for the object to escape the Earth's gravitational field, so that it would not reach infinity? Why doesn't this happen?