Hmm...

The Gravitational Force = where G is the gravitational force constant, M is the big mass of the earth and m is the mass of whatever is falling (me, an apple or a ball.) R is the distance apart the two items are (from the center of mass). In the case of stuff on earth, it is the radius of earth.

Here on earth, the only thing that changes is the mass of (me, an apple or a ball). The earth has the same mass and same radius.

= gm

We use F=mg when we are talking about objects on or close to earth.

Small g is only used when we are talking about the effects of gravity on objects close to earth. It doesn’t work in space (the distance apart is too large) and it doesn’t work unless one of the objects is earth.

The other equation, , can be used when we are looking at the gravitational attraction of the earth and the sun or a spaceship and saturn.