# Newton's third law in relation to field forces

## Main Question or Discussion Point

I need some help understanding how Newton's third law applies to field forces (namely gravitation).

The third law in contact forces seems straightforward to me. Billiard ball A, which is moving, hits billiard ball B. The collision exerts a force on Ball B, resulting in its acceleration. Simultaneously, the collision exerts an equal and opposite force on Ball A, causing it to accelerate as well (in the opposite direction) and come to a stop. Action/reaction pairs are obvious in this scenario.

Now let's take a comet flying into a solar system which only has a star and no other objects. At some point, the star will exert a gravitational force on the comet. This force will accelerate the comet and in some manner alter its trajectory. The star should experience an equal and opposite force as well, and be accelerated in the opposite direction (negligible amount, but present nonetheless).

However, doesn't the comet have mass, and doesn't it exert a gravitational pull on the star as well? And while this is small and may not affect the star, shouldn't the comet feel and equal and opposite reaction as well?

I guess I'm having a hard time finding out what the action/reaction pairs are in the case of field forces. Two scenarios come to mind:

Scenario A) The star exerts a force on the comet. Action is on the comet, reaction is on the star. Simultaneously, the comet exerts a force on the star. Action is on the star, and reaction is on the comet. When considering what forces are acting on the comet, both the action from the star and the reaction from the comet-on-the-star must be considered.

Scenario B) Field forces only make sense when two points are considered. A star (or a comet) does not exert a gravitational force in the absence of another object (to "feel" it). Treating the force of the star on the comet and the force of the comet on the star as different is non-sensical (akin to counting a single force twice). Newton's law of universal gravitation seems to support this idea. But in this case, it is difficult to determine what is "action" and "reaction", and the action/reaction diagram is not as clear.

Can anyone clarify this for me? I hope I have my question clear.

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Well in a two body system, the same force of gravitation acts on both the bodies. The star exerts a force on the comet and causes it to accelerate. Similarly, the comet exerts a force on the star and causes it to accelerate. If you consider one force as the action, the other is the reaction to it. The magnitude of both, however, is the same, which is-
FG = mstar.mcometG/r2 (where 'G' is the gravitational constant)

How much the force will affect each object depends on their mass.

Dale
Mentor
it is difficult to determine what is "action" and "reaction", and the action/reaction diagram is not as clear
The designation of one force as "action" and the other as "reaction" is irrelevant. The important thing is that forces come in pairs. In any Newtonian interaction there will be a force on some object which is paired with an equal and opposite force acting on a different object.

So the sun and the comet interact gravitationally meaning that there is a gravitational force from the sun acting on the comet and there is an equal and opposite gravitational force from the comet acting in the sun.

Designate whichever you like as "action" or "reaction", it doesn't matter. It only matters that both are present and that they are equal and opposite.