Let's assume for a moment that equation being applied to gravity simply because it's cosmetically similar isn't total bullshit. There would still be a massive gap in the equation: the mass of the second body. Gravity is the force of attraction between multiple bodies. The fact that your equation leaves that out reveals its uselessness.
No, it is treating gravity just like a field, like electrostatic fields.
You determine the field strength at a given location.
To then determine the force on an object you multiple the field strength by the particles "charge" which in this case is its mass.
As an example, again with electrostatic fields, there are 2 ways to determine the force on an object.
Assuming there are only 2, the simple way is using the formula:
F=kq
1q
2/r
2.
But this isn't always practical, such as when considering the force on a particle between 2 parallel plates.
To do that you would need to add up all the interactions from every point on the plate.
Another way is to calculate the field (ignoring the particle), which varies depending upon the nature of objects.
For a spherically symmetric object, outside the object, the electric field is given by:
E=kq/r
2For a single plate it is given by (you can use Gauss' law to figure it out as per John's link):
E=s/2e, where s is the charge density of the plate, and e is the permittivity of free space (if you use a medium instead it changes, just like k would, k=1/(4*pi*e)).
Between 2 parallel, oppositely charged plates of |charge density| s, the field will be E=s/e.
Then to find the force on a particle it is simply:
F=Eq.
In the case of a particle in a symmetric field this becomes:
F=(kq
1/r
2)*q
2=kq
1q
2/r
2.
The exact same can be done with gravity.
However, because gravity has mass as its "charge", you end up with force=mass*field strength, and as F=mass*acceleration, you can have acceleration=field strength, e.g. a=g.
This is important when considering things like light. Light has no mass so if you try to determine the force due to gravity acting on it you end up with 0, yet light is still bent by gravity.