4

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
  • 1,859
  • 3
  • 22
  • 42

1 Answers1

1

@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
  • 14,246