In my Intermediate Mechanics class, we’ve been talking about gravitational potential. Gravitational potential is a nice mathematical way to describe the effects of gravity on an object.
You can get an idea of how gravitational potential is related to gravity by imaging a ball on field of rolling hills. The potential at a given point is the height of the ground. The gravitational force can be determined by calculating how the ground varies. If ground is perfectly flat in some region, then a ball placed there would remain at rest, so there is no gravitational force. If the ground decreases in height as you travel eastward, then a ball placed in that region would roll eastward, thus there is a gravitational force in the eastward direction.
Gravitational potential can also be useful in visualizing gravity. In the figure below, I’ve plotted a contour plot of the gravitational potential around two orbiting bodies. This contour plot is similar to a topological map where each dotted line represents a uniform potential. I’ve also plotted dots where the potential is flat. These are points where the gravitational and rotational forces just cancel out, so that the effective force is zero.