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Wikipedia says:

The Lagrange points mark positions where the combined gravitational pull of the two large masses provides precisely the centripetal force required to orbit with them

The major bulk of the Solar System is concentrated in Sol with planets gravitationally bound to Sol. Sol orbits the galactic centre over a distance of some thousand light-years. The galactic centre is therefore massive enough to exert it's influence over such large separation.

  • Can Lagrangian points exist for a whole planetary system/star-system? E.g. Between Sol, and the Galactic Hole. Similarly between any other Star in the galaxy, and the Galactic Hole.
  • How much must a star/planetary system mass for such libration points to exist?
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  • $\begingroup$ I'm a little unclear on what you're asking. The solar system Lagrange points are between two gravitationally bound bodies. So the Earth-moon has them, Sol-Earth has them, but Earth-Venus doesn't have them. There is some mathematics necessary for justification of this. But the idea of a "whole" system Lagrange point is lacking definition, so I don't see how it could be answered. $\endgroup$ – AlanSE Sep 9 '13 at 13:28
  • $\begingroup$ @AlanSE: The bulk of the Solar System's mass lies in the Sun. The question stems from the knowledge that Sol carries the Solar System in it's orbit around the Galactic Hole. $\endgroup$ – Everyone Sep 9 '13 at 13:41
  • $\begingroup$ I was under the impression that the "three body problem" was difficult enough. I'm not sure that I see the value in asking questions about the "n body problem". $\endgroup$ – Donald.McLean Sep 10 '13 at 14:45
  • $\begingroup$ @Donald.McLean: Sol forms over 99.5% of the Solar System mass. Admitted that difference from 100% is a huge number; could the Solar System be considered a uniform entity here? $\endgroup$ – Everyone Sep 10 '13 at 17:45
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    $\begingroup$ @BenCrowell Sagittarius A* may be relatively small (in mass) compared to the Milky Way, but the two parsecs around the Galactic Center have thousands and thousands of stars, with a high concentration of massive stars. $\endgroup$ – called2voyage Sep 11 '13 at 13:20
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Lagrangian points would work for any system where the third object is "small" relative to the other two bodies. Since, in your question, the first two bodies are the galactic center and the Solar System, even a fairly large object, such as an M class red dwarf star could be used as the third body.

Unfortunately, the nature of this specific case could create two problem situations:

  1. Unlike the area immediately around the Earth, the area around the Sun has lots of stuff in it: planets, asteroids, comets and the Oort Cloud. The placement for the third body could be close enough to Sol that it could be pelted by material from, say, the Oort Cloud.

  2. Again, unlike the Solar System, where there are a moderate number of large objects (planets), the Milky Way is home to something like 100 billion stars and the area around Sol is relatively clear only in absolute terms, not in relative terms and this condition is not guaranteed to continue indefinitely. The placement for the third body could be far enough away from Sol that another passing star could yank it out of the Lagrangian point (in a few million years, say).

The exact circumstances would depend on the size of the object to be used. Do the math and see where it would have to be to satisfy the conditions of the Lagrangian point.

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Any two gravitational systems will have Lagrange points where the fields cancel each other out or compliment each other in a way that produces a stable "parking place". In fact it is a bit more complex that that in that the gravitational field at any point in space is affected by the gravity of every subatomic particle in the entire universe. There is are earth moon Lagrange points, earth sun Lagrange points and earth Milky Way Lagrange points. Most objects are distant enough to disregard including our local star system and our proposed binary partner the invisible red dwarf star Nemesis. For the most part the gravity of the universe behaves as if it is concentrated an the galactic center of mass but at galactic distances the laws of gravity break down slightly which is the reason for the proposed "dark matter".

Any references to the three body problem or the N-body problem are mathematical simplifications which for purposes of having a solution disregard less significant gravitational systems. Even in the earth moon sun three body problem all other gravitational systems in the solar system and even beyond must be disregarded but that does not mean their influence does not exist. There is math and there is the "big picture" which is reality. If you think you have a grasp on reality you need a reality check. The universe is not only stranger than you imagine it is stranger than you can imagine.

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