# Is there a connection between Newton's law of universal gravitation and the area of a sphere? [duplicate]

According to Newton, the force between two objects of masses $m$ and $M$ is $$F = \frac{GmM}{r^2},$$ where $r$ is the distance between the two objects. Basically, if distance between the object doubles, the force will reduce to the fourth of it. Also, the area of a 3-dimensional sphere is $$A = 4\pi r^2.$$

My guess is that both the object "radiate" gravity particles (gravitons?) uniformly in all possible directions. Now, when these gravity particles have advanced from distance $r$ to distance $2r$, the result area of the "wave" will increase $2^2 = 4$ times, which will make that "wave" $4$ times weaker per area unit, which is reflected in the law.

My question is: can somebody tell whether my intuition makes any sense?