The potential energy and electric field?

What happens to a body's potential energy when it leaves the influence of a gravitational field?

• At the last conceivable point at which a gravitational field has influence over a body, that body still has its full potential energy -  it may still be pulled toward the center of the field. However, at the very next point away from the field's center and beyond the ability of the field to move it, the body does not have this potential. What happens to the body's potential energy during this transition?

• Answer:

  There is no distance at which gravity is not strong enough to exert a pull on another object, however weak that pull may be. So the potential energy of an object always depends upon its position -- there is no sudden point at which the effects of gravity can be neglected. We can see this fact from the formula for the gravitational potential energy of an object of mass mmm distance rrr away from another object of mass MMM, U=−GMmrU=−GMmrU = - \frac{G M m}{r}, where GGG is the gravitational constant. As the distance r→ âˆžr→ âˆžr \to\ \infty, the potential energy goes from a negative value smoothly to zero.