How is the potential energy at infinity zero?

In fact, push them into a hole and you will see some of that energy being converted into kinetic energy. Where is the gravitational force between objects zero? The force between objects due to gravity reduces as the distance separating the objects increases. So the force finally becomes zero at infinity. read more

Some forms of potential energy have obvious zeroes, like a spring: leave it alone, not stored spring energy. But others have zeroes that are a bit more arbitrary. One convention we use is to say “if the force tied to the energy drops off with distance, let the zero be infinitely far away.” Zero force, zero potential energy. read more

In this case we generally choose the zero of gravitational potential energy at infinity, since the gravitational force approaches zero at infinity. This is a logical way to define the zero since the potential energy with respect to a point at infinity tells us the energy with which an object is bound to the earth. read more

When we say r = \infty, we are implicitly implying the limit of r as it approaches infinity. Still, like I stated above, we only really care about the changes in the potential. So having a non-zero potential is immaterial to our problem. read more