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While teaching us about Gravitation, our Physics teacher told us that in the universe there exist a point where the gravitational force of all the mass bodies cancel out and that point experience no net gravitational force. He called that point null point.

When I tried to get the information on internet, I got that

A null is a point in a field where the field quantity is zero as the result of two or more opposing quantities completely cancelling each other.

On further research (on gravitation) I got that we can find a point where the gravitational force of two bodies on a single body cancel out. Nowhere is defined the gravitational null point for the whole universe, even the questions on this site do not talk of the whole universe (though some of them ask for such point when a body is experiencing gravitational force of two bodies).

So the question I m asking is that Is there a point in the universe where the gravitational force of all the mass bodies will cancel out each other and the body present at that point will experience no gravitational force??

Further If there exist such a point then will it be stationary??( I don't think that it will be stationary because all the mass bodies are somewhat moving about other body).

I shall be highly thankful to have information from you guys about this topic.

Vidyanshu Mishra
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    I am sorry but either you misunderstood your teacher or he is following some esoteric metaphysical proposals. The mainstream view of the universe has not null point for it in the sense you describe. The current model has an undefined region in the beginning of the universe but that has nothing to do with balances of forces. see https://en.wikipedia.org/wiki/Big_Bang – anna v Nov 20 '16 at 08:03
  • I agree with @claudechuber, here I m trying to find centre of gravity of whole thee universe (my question resemble to this to a small extent) – Vidyanshu Mishra Nov 20 '16 at 08:29
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    It seems this question has already been answered here –  Nov 20 '16 at 08:57
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    The centre of mass is not the point where there is no net force. I think this question is interesting, both in the Newtonian and in the relativistic case. For example on a 2-sphere it would be implied by the hairy ball theorem: https://en.wikipedia.org/wiki/Hairy_ball_theorem (under some mild assumptions). In the general Newtonian case or the general relativistic case there may also be some general geometric conditions. – doetoe Nov 20 '16 at 16:49
  • At least I have got someone's company here :) :) – Vidyanshu Mishra Nov 20 '16 at 17:09
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    People are giving the argument that this question is of Newtonian gravity and we have already got knowledge of special relativity and big bang. But I m just trying to get the knowledge of a point which do not experience net gravitational attraction, or vector sum of all the gravitational force is zero on the point. What is the significance of expansion of universe here?? – Vidyanshu Mishra Nov 20 '16 at 17:14
  • doetoe is right regarding the difference between barycenter and Lagrange points, these are usually different points. Your question seems to be about Lagrange points (no net force). Regarding existence of such points, and in the context of Newtonian gravity you seem to want to consider, then my answer to this question may interest you. Of course there is in general no reason for such a point to be stationary. –  Nov 20 '16 at 17:44

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@Anna is right. There is no such thing. The universe cannot be treated with Newtonian gravity, it's General Relativity, and it's all expanding. Anywhere you are the universe will expand around you, like an expanding balloon around its center. At no point is there no such thing. Your teacher must have been thinking of Newtonian gravity. For the earth sun moon there are three such points (or maybe 5, I forget), called Lagrangian points. I forget whether they are stable, but of course they are stationary (i.e. No motion or force if you are exactly there). Not sure about n bodies for n very large, I think it's not known because no known solution since bodies move, and it's a very nonlinear nonlinear problem. In physics and astronomy/astrophysics those kinds of numbers of objects gravitating all with each other is treated statistically or through hydrodynamic or kinetic theory flow models.

I suggest asking your teacher and expanding the question with:

1)is he talking Newtonian Gravity? If he says yes ask him if it's taking into account the expansion of the universe as General Relativity predicts and has been observed in supernova and the cosmic background radiation?

2)ask him if the n body problem for n greater than $10^{11}$ for Newtonian gravity has been solved and if he can give you the reference?

You could even go read the Wikipedia articles and surprise him/her.

EDIT after comment below by @claude chuber.

Claude assures us that one can prove the existence of Lagrange points (this is for Newtonian gravity) even for large n, without solving the no body problem for it. I'm thinking he's probably right, and asked him a couple follow up questions in a comment, including if the actual n body problem for large n has been solved - from what I remember having read it is no igeneral but plenty of approximate methods.

It is still true that for the universe it requires General Relativity, you have to account for expansion and relativistic as well as super-luminal expansion. If you ignore these effects, and are purely Newtonian, look at Claude's other comment, center of mass and Lagrange points are different.

CORRECTION: the 5 Lagrange point are for the 2 body problem, and it is where you can park a third small body and have it stay. It turns out that 3 of those are not stable, but are stable to certain nearby orbits, while two are stable. By the way, Euler discovered first 3 and Lagrange later 2 of them

And the n body problem in general even for n =3 or greater is not solvable, but plenty approximations.

See the two articles:

https://en.m.wikipedia.org/wiki/Lagrangian_point#Lagrange_points

And for more details

http://hyperphysics.phy-astr.gsu.edu/hbase/Mechanics/lagpt.html

So yes, @lonewolf, you'd be hanged there. I still don't know about larger n, if stable points or not.

Bob Bee
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    Would the answer be still no if I edit the question and ask for such a point not for universe but for a large number of bodies.without taking expansion of universe in account – Vidyanshu Mishra Nov 20 '16 at 09:10
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    @THELONEWOLF. It should be clear from the answer that in newtonian gravity in principle you could always find the center of mass, though as Bob Bee says it is a complicated solution. It is talking about "universe" that needs space expansion and general relativity. – anna v Nov 20 '16 at 11:59
  • @Bob Bee "Anywhere you are the universe will expand around you, like an expanding balloon around its center": this is yet an hypothesis, not a certitude (it hasn't been proved). As far as I know, we have not yet written the word "end" in the cosmology theory. Other comment: you don't need to solve the $n$ body problem for $n$ greater than $10^{11}$ for proving the existence of Lagrange points (BTW, there are 5 of them for the earth sun moon system.) PS: FWIW, I didn't vote down your answer. –  Nov 20 '16 at 18:51
  • Thanks Claude. I could understand it should be possible to prove it. Calculating where, is that a solved problem for n large? And is there a closed formula for how many for n large? – Bob Bee Nov 20 '16 at 19:21
  • @Bob Bee Calculation of where or how many with a closed formula: I guess the answer is no (it is likely as difficult as the $n$ body problem itself). Only proving existence is easy, see for example my answer to this question. –  Nov 20 '16 at 19:37
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    Even in Newtonian theory, a "stationary point" depends on the frame of reference. And most of the Lagrangian points *aren't* stationary with respect to the universe, so even for a two-body system they don't answer the question. – Peter Shor Nov 21 '16 at 16:59
  • @Peter Shor I agree with you. Maybe the choice of a reference frame (or the existence of an appropriate reference frame) should be included in the question. –  Nov 21 '16 at 18:04
  • I don't believe that the expansion of the universe has anything to do with this. The OP is asking fo ra comoving coordinate where the comoving acceleration is zero. – ProfRob Apr 19 '17 at 08:01
  • No, he was not asking that. He said a single point. If he asked it, answer is that all galaxies with zero peculiar velocity have a fixed comoving distance r, which never changes. Same is true between two galaxies. But the proper distance expands with expansion. Comoving velocity is zero and so is acceleration. If the density is uniform spatially and really isotropic then that's it, everywhere. Not just at some point. If you want to take real matter densities into account, peculiar velocities could be done with a psotnewtonian or perturbation approach. That's harder than the 3 body problem – Bob Bee Apr 20 '17 at 01:28
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    His prof was clueless – Bob Bee Apr 20 '17 at 01:28