I think you're referring to the gravitational force exerted on an object by a planet. And in a Newtonian rather than relativistic sense. You can calculate the gravitational force between any 2 objects by F = G*m1*m2/r^2, where G is the universal gravitational constant. This is Newton's formulation. When you're talking about a 2-body system, this is simple.

But when you're talking about something floating in space where position is defined by its relationship to more than 1 object, this becomes more difficult. For example, the moon experiences the gravitational pull of the Earth. But it also experiences the gravitational pull of other massive objects nearby, like other planets. These are other vectors that all act on the object. Fortunately, other than things that are pretty close (astronomically speaking) together, the effect of r^2 is to dilute the effect of gravity out to near zero for things that are relatively far apart, to the point where it's negligible.