What is the meaning of the word "between" in the law that the force between two masses at separation $r$ is given by $\frac{GM_1M_2}{r^2}$? I am confused about how can a force be in-between, either it is on body A or on body B, or on both.
Suppose body A exerts force $F$ on Body B, so according to Newton's 3rd law of motion B should also exert a force on A.
Let's consider this case for gravitational force between two bodies. If body A exerts force $g$ on Body B, then B body should also exert a force $g$ on A, but B is also exerting the gravitational force $X$ on A, hence A will also exert force $X$ on B.
So, how are two forces acting?
I have given the representation in this diagram.
Best Answer
Newton's Third Law tells us that the force on A due to B is equal (in magnitude, with opposite direction) to the force on B due to A. Therefore, in any interaction between a pair of objects it is sufficient to describe the force on just one of them, since the other can be deduced by Newton's Third Law. For this reason, it is common to refer to force acting on either object simply as the force "between" the objects. Thus, there should only be one pair of forces, with magnitude $\frac{Gm_Am_B}{r^2}$, to describe the gravitational interaction between a pair of masses.