What is the reaction to gravity's pull in a vacuum?

[brand1130x]

I am trying to understand something. Let me pitch a scenario: You have two asteroids in a vacuum. Each is large enough to be round by gravity. They are separated by roughly the distance from the Earth to the moon. Relative to each other, they are moving at 0 in all directions (aka, they are immobile). Time starts. Gravity causes the two objects to begin to move toward each other. Time stops when they have traversed half the gap between them. The distance is now 1/2 Earth to Moon.

In this situation, the "action" is the two bodies moving toward each other. What is the equal and opposite reaction?

[Mentor's note: Some speculation not allowed under the forum rules has been removed]
Thank you for your replies.

 

[rumborak]

There are two forces: the one tugging on asteroid 1 towards asteroid 2, and the exact equal but opposite-direction force that tugs asteroid 2 towards asteroid 1. That's all there is to it.

 

[brand1130x]

I just feel like that's two separate actions caused by the curvature of space time from the masses. I don't see the "reactions" there. (I realize I'm wrong. I'm just saying I don't see it).

 

[rumborak]

You're entirely overthinking this. For the purposes of force analysis (i.e. action and reaction), just stick with the regular gravitational force. No spacetime curvatures necessary.

 

[Nugatory]

In this situation, the "action" is the two bodies moving toward each other. What is the equal and opposite reaction?

If the masses of the two bodies A and B are $m_A$ and $m_B$, then body A will exert a gravitational force of $Gm_Am_B/r^2$ on body B. Body B will exert an equal and opposite force on body A, and that's the equal and opposite reaction that you're looking for.

Of course they will tend to drift towards one another under the influence of these forces, because there's no such thing as "time stops". If you want to hold them apart, you'll need to a rigid rod to resist the gravitational forces. In this case, body A will exert a force on its end of the rod, and the end of the rod will exert an equal and opposite force on body A; and likewise at the other end with body B. In this case there are two action-reaction pairs.

 

[rcgldr]

In the case of gravity, there is no "reaction" force. There is a Newton third law pair of equal and opposing forces exerted on each object by the gravitational field from the other object.

As an example of a reaction force, assume a string is used to accelerate a box (and that there are no other forces involved). The string exerts a force on the box to accelerate the box, and the box exerts an opposing reactive force on the string due to the acceleration.

 

[Dale]

I just feel like that's two separate actions ... I don't see the "reactions" there

The gravitational force of one is the "action" and the gravitational force of the other is the "reaction". Which is designated as "action" and which is designated as "reaction" is completely arbitrary. The important part is that they form a third law pair.

 

[Nugatory]

I just feel like that's two separate actions caused by the curvature of space time from the masses. I don't see the "reactions" there. (I realize I'm wrong. I'm just saying I don't see it).

As @rumborak said... You're overthinking this. You don't have to learn general relativity to understand this problem.

But if you are going to insist on trying to understand the gravitational attraction between two bodies in terms of curved spacetime, then there no forces involved at so no action/reaction pairs at all. We just have two objects moving in a straight line at a constant speed just like inertial says they should when there are no forces at work. It just so happens that spacetime is curved in such a way that those straight lines are moving closer to one another.

 

[brand1130x]

In the case of gravity, there is no "reaction" force. There is a Newton third law pair of equal and opposing forces exerted on each object by the gravitational field from the other object.

As an example of a reaction force, assume a string is used to accelerate a box (and that there are no other forces involved). The string exerts a force on the box to accelerate the box, and the box exerts an opposing reactive force on the string due to the acceleration.

I think I see. So would the "reaction" be the inertia of the bodies?

 

[rumborak]

Action/reaction is only relevant when considering forces. When you switch to the spacetime curvatures view of it, it no longer applies.

 

[Nugatory]

Interesting though, in order to be equivalent to the "force view" of the experiment, the curvature can't just be an addition of the two objects' gravity wells, right? Does curvature "multiply" in order to be equivalent to the m1*m2 of the gravitational force?

It's even worse... The Einstein field equations are non-linear and so brutally complex that there are no exact general-relativistic solutions to the two-body problem. However, we're about to hijack the thread, so we better stop.

 

[FactChecker]

The mass of each body would distort space-time in a way that would effect the other one. The effects would be "equal and opposite" when the different masses and different amounts of distortion are considered. Newton's "equal and opposite" does not refer to an "action" of a complicated machine or to a combination of things that occur. It refers to an individual force of one object on another object. Given an individual force of one object on another object, there is an opposite force from the second object on the first.
Newton says it is done by each object applying a force on the other. In GR it is done by each object distorting space-time in a way that effects the other. The results are very similar -- only tiny differences.

 

[sophiecentaur]

I just feel like that's two separate actions caused by the curvature of space time from the masses.

You were trying to bring Newtonian Physics up against GR. Not surprising that you found some inadequacies. If there weren't, we would not have needed to develop GR.

 

[A.T.]

I think I see. So would the "reaction" be the inertia of the bodies?

There are two equal but opposite forces in Newtons 3rd Law. And it's completely irrelevant which of them you call "action" and which "reaction". Naming conventions don't change the results of calculations.

 

[sophiecentaur]

There are two equal but opposite forces in Newtons 3rd Law. And it's completely irrelevant which of them you call "action" and which "reaction". Naming conventions don't change the results of calculations.

But people do like to categorise. It avoids thinking too much.

 

[A.T.]

But people do like to categorise. It avoids thinking too much.

In this case it leads to too much thinking about irrelevant stuff, as this and similar threads demonstrate.