Whenever two objects are touching, they usually exert forces on each other. The force of gravity, on the other hand, is an example of a force that exists between objects without them having to be in contact.

Objects with mass exert forces on each other via the force of gravity. We will extend our treatment of the force of gravity later, but let’s start by saying that the force of gravity that one object exerts on another is F_G, and points toward the object exerting the force.

One factor that the force of gravity depends on is the mass of the object that feels the force - the force of gravity exerted by one object (like the Earth) on another object, like an apple, is proportional to the mass of the apple.

At the Earth's surface we generally say that the gravitational force exerted on an object of mass m by the Earth has a magnitude mg and is directed down.