How does gravity work?

Because gravity acts on all objects through Newtons law of gravitation we can find the total resultant force of any object, F_total = Sum( F_1i ) for i=2 to n for n = number of bodies.

But the real world isn't made up of discrete particles. It is made up of continous material. calculating the gravitational force between all the atoms of two objects would take forever, But if we can pretend that all of the mass of an object is located at its center. We only need to calculate the forces on an objects center of mass.

But what if we want to know the gravitational force on a person who is splunking. The majority of the earth's mass is below the splunker but some is above him. Newton found that the sumation of the forces go to zero for all paticles with radius greater than the splunkers. That is to say the shell above te splunker doesn't effect the force of gravity on the splunker.

Gravity is action at a distance. That is to say that unlike other forces the two objects don't need to be in contact with each other. In fact gravity is inversly proportional to the distance squared. meaning the greater the distance between two objects the smaller the magnatuide of the force.

Not only does force decrease with distance but also potential energy. W = F*d, we know F and d and that potential energy is -Work. From here we get U= -Gm₁m₂/r