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Every Action Has An Equal and Opposite Reaction (Newton's Third Law.)

If this is the case, does gravity have an equal-opposing force?

From asking around I still haven't got a very clear answer; those who I've talked to seem to believe there isn't one - that gravity is actually a singularity [a one way force] which somehow "just works", others think it differently - believing there is an opposing force of which prevents gravity from compressing masses more than it already does.

So which one is the right answer? (if either!)

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Both the posts of Emilio and John provide excellent descriptions, so I am just going to leave a short comment. The important point is that when you observe say mechanical objects in nature, you cannot even say there was a force acting "there and there" - you always have a force in between two objects and it is nonsensical to event talk about an unreciprocated force. – Void Aug 27 '14 at 20:32
Consider a spring you hook up to a wall and pull it towards yourself with a force $10N$. We would say the wall reciprocates $10N$ back. So what force will the spring feel? $20N$? No, $10N$, because there is really just a $10N$ between them. You can verify this with a spring scale, it makes total sense. Decomposing the force "in between" into two opposite forces is actually just a useful tool to analyse effects on separate bodies under it's influence. – Void Aug 27 '14 at 20:34
You seem to be asking two different questions here. The first question is what gravity's "equal and opposite" force is, and the second question is which force prevents gravity from compressing masses more than it already does. These questions have two different answers. – Tanner Swett Aug 28 '14 at 0:48
I guess so, I thought prior that the same force which is preventing further compression of objects by gravity may have been the same force which opposed it, anyway thanks for telling me. – Harry David Aug 28 '14 at 9:51
@HarryDavid perhaps you could accept an answer, if you feel your question has been sufficiently addressed? Click the green checkmark next to any answer to accept that one. – David Z Oct 25 '14 at 3:24

5 Answers 5

up vote 29 down vote accepted

Yes, every gravitational force in Newtonian mechanics has an equal and opposing force, and it usually acts on other mass.

More specifically, every two pairs of masses feel a gravitational force that's proportional to the product of their masses and inversely proportional to the square of their relative distance, but more important is the fact that both masses feel the attraction to each other.

Thus, when you throw a ball of ~100g in the air, it experiences a gravitational force of 1N downwards, and in doing so it exerts a force of 1N upwards on the Earth. The reason you don't observe the Earth moving is that its acceleration is so small (on the order of 10-25 m s-2) that it gets swamped in everything else, but it does happen.

Now, it's important to note that gravity is not usually the only force acting on any object at a given time. If it is, then the total force will be nonzero and the object will accelerate (as per Newton's Second Law). Conversely, if an object is not accelerating, then the net force on it is zero, and there must be additional forces that cancel out the gravitational one.

For a book lying on a table, for example, the weight is cancelled by the upwards reaction force from the table. (And, of course, this gives an added reaction force downwards from the book on the table, which gets cancelled by a correspondingly larger reaction force from the floor on the table.)

Similarly, the reason that masses (like, say, the interior of the Earth) don't get compressed any further is that any given volume of rock will be acted on by the downwards gravitational force and by the upwards pressure from the rocks below it.

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Very helpful, thanks; that does indeed answer my question, and very well too! – Harry David Aug 27 '14 at 11:48
I always liked the fact that I am exerting exactly the same gravitational pull on the Earth than it does on me. Kind of makes me feel powerful. – Davidmh Aug 27 '14 at 20:34
@Davidmh yes. also this. – Emilio Pisanty Aug 27 '14 at 20:41
"and it usually acts on other mass." Usually? Is there any cases where it does not act on the other mass. – Taemyr Aug 28 '14 at 7:32
@Taemyr not really, but if there are many masses then it becomes tedious to keep track of all the pairs of forces, and often there exist simpler ways of accounting for them. – Emilio Pisanty Aug 28 '14 at 9:46

Suppose you're standing on a box as shown in (a) below:

Third Law

There are four forces acting. You apply a downward force $mg$ on the top of the box, and by Newton's third law the box applies an upwards force $-mg$ on you. The box transmits your force to the ground, so the box applies a downwards force $mg$ on the ground and the ground applies an upwards force $-mg$ on the base of the box.

So far so good. But how suppose we suddenly pull the box away as in (b). There is still a downwards force $mg$ on you, and indeed that force is going to make you fall downwards. The question is whether there is an equal and opposite force upwards.

The answer is that yes, there is indeed an equal and opposite force of $-mg$ on the Earth, so Newton's third law still applies. The confusion arises because we normally think of the action and reaction force as operating at the same point. So in (a) there is an equal and opposite pair of forces at the top of the box and another equal and opposite pair of forces at the base of the box. But now we seem to have the action and the reaction separated in space.

With Newtonian gravity you just have to accept that there is a gravitational field in between you and the Earth, and this field transmits the force on you to the ground and the force on the ground to you. To really understand what's going on you need to understand general relativity. This tells us that the Earth curves spacetime and this creates the downwards force on you, however your mass also curves spacetime and this creates an upwards force on the Earth.

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Thank you for the answer,very helpful! :) – Harry David Aug 27 '14 at 11:53
And also grat for the 100k :) – peterh Aug 27 '14 at 12:22
@PeterHorvath: Thanks :-) – John Rennie Aug 27 '14 at 14:33
IMO the figures are a bit confusing: in a) "the force applied by you to the box" is drawn in the same place where in b) there is "the force applied by earth to you". – JiK Aug 27 '14 at 17:32
@JohnRennie: If Einstein was still alive, he might sue you for using his figure while explaining gravity through the concept of force. :) – bright magus Oct 24 '14 at 9:54

My knowledge is limited on the subject but matter is typically prevented from collapsing under the weight of extreme gravity by particle degeneracy. This is what keeps neutron stars from collapsing into black holes and is the result of particles resisting occupying the same quantum states.

There are also some recent observations that indicate that there is a repulsive force that acts only over large distances (almost the inverse of gravity) causing the universe to expand at an accelerating rate. Why this occurs is still a matter of debate and there are various theories from the topography of space itself causing gravity to act repulsively to an as yet undiscovered force causing this.

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For a book lying on a table, for example, the weight is cancelled by the upwards reaction force from the table.

That's not quite true -- unless the table in a vacuum chamber at the south pole. The upward normal force exerted by the table and the downward gravitational force exerted by the Earth don't quite cancel. The book rotates with the Earth, and except at the north or south pole, this rotation means the book is accelerating. It's a rather small acceleration, about 0.35% g at the equator, but it's not zero. This means the net force on the book is not zero, and that in turn means the weight of the book is not quite cancelled by the table. What about the vacuum chamber? The buoyant force of the air on the book is about 0.15% g. This means the upward normal force on the book by the table is about 0.5% less than the book's weight (at the equator).

Newton's third law says the forces in an action-reaction pair are equal but opposite. Forces that are only approximately equal and approximately opposite do not qualify as a third law action-reaction pair.

... others think it differently - believing there is an opposing force of which prevents gravity from compressing masses more than it already does.

Gravity can compress masses quite a bit. The density of the stuff (mostly hydrogen) at the center of our Sun is about 150 times the density of water. Closer to home, the density of the stuff (mostly iron) at the center of the Earth is about 13 times the density of water. That's about 2/3 greater than the density of iron at the surface of the Earth. That increased density is because the iron in the Earth's inner core has been compressed by quite a bit. The rock at the core/mantle boundary similarly is considerably denser than is the same rock at the Earth's surface.

The pressure from below is not what counteracts gravity inside the Earth. What counteracts gravity is buoyancy. Imagine a chunk of rock deep inside the Earth. The pressure at the top of the rock is slightly less than is the pressure at the bottom of the rock because of hydrostatic equilibrium. This pressure gradient results in a buoyant force that keeps the chunk of rock where it is.

What stops pressure from compressing a chunk of iron or rock inside the Earth into nothingness is a quantum mechanical effect. The electrons get pushed ever closer together with increased pressure. Those electrons can't share space thanks to the Pauli exclusion principle. The material does compress with increased pressure, but this compression stops at the point where the quantum mechanical pressure balances the external pressure.

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Cool, thanks for that. – Harry David Aug 28 '14 at 9:46
When the book is lying on the table, there is no air underneath, so the air pressure should be pushing down on it from the top (the sides cancel out). As such, I think that adds to the nominal weight, but you subtracted it. – Jester Aug 28 '14 at 15:02
But surly, even though the book is flat against the tabletop there will be some air under it- seeing as it was simply placed there and not forming a vacuum seal. – Harry David Aug 29 '14 at 11:17
@HarryDavid in practice, sure. But I guess that should exert negligible force compared to the top side. – Jester Aug 30 '14 at 0:12
True, I guess so. – Harry David Aug 30 '14 at 3:23

Assume a person is falling towards the earth. We know that there is a force and thus an acceleration acting on the person. The opposing force is the gravitational force exerted by the person onto the earth equal in magnitude (Newton's Law of Gravity). This force produces an acceleration (Newton's Second Law) but because the mass of the earth is massive as compared to the human body, it is relatively small and can be taken as zero . Adding these two forces gives a net resultant of zero, (Newton's Third Law).

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