[modest]

CC,

Are there any examples or observations of something natural (not something human made) at a L1, L2, or L3 point? Has that ever been observed?

-modest

[Little Bang]

Wouldn't finding a natural object at a Le grange point be like balancing a pencil on it's point?

[coldcreation]

Originally Posted by modest

CC,

Are there any examples or observations of something natural (not something human made) at a L1, L2, or L3 point? Has that ever been observed?

Fair question. I've already answer it above. The answer, at least with respect to the L1 point, is yes. I've also provided images of a large variety systems where the L1 point is occupied. After all, this is observational evidence. It could of course be argued that this claim, or interpretation of empirical evidence is false, e.g., that these are chance alignments of objects that, on the surface, mimic the M1, L1, M2 line.

Terminology: By chance alignment it is meant that object known to be gravitationally associated appear lined up along the same axis (e.g., two massive clusters separated by, say, an active Seyfert galaxy or strong radio source located at the saddle point; between the two). It is not meant the chance alignment of background objects.

However, a close inspection of the local extrema, the maximum and minimum of potentials, along with saddle point positions and other critical points of a system, It is straight forward to show that orbits can be (and are) attained or maintained around saddle point (notably around L1). The motion consists of regular invariant curves, closed topological circles around one rotating about one singular invariant Lagrangian point: L1. (Caranicolas, N. D., 2002, Connecting Global to Local Parameters in Barred Galaxy Models). See the following illustration, from the above reference (enhanced by Coldcreation).

Caranicolas writes regarding this orbit in barred galaxy models:

The corresponding orbits are box-orbits. Those forming the outer invariant curves belong to elongated boxes that support the bar while, as we approach the “central” invariant point, the boxes become more rectangular.

3. Orbits in the local potential

Furthermore, the local potential can be found by expanding the effective potential (3) in a Mc-Laurin series near the stable Lagrange point L1, which coincides with the origin. [...]

4. Discussion

[...] Furthermore, we must note that in the global model [describing global motion in a barred galaxy and the corresponding parameters of the local potential] the resonant orbits of type b as well as the chaotic orbits of type d carry stars in the central parts of the galaxy. Therefore we have an increasing density near L1. It is interesting to observe that a large number of high energy stars passing near L1 are in chaotic orbits. The other two types of orbits a and b do not contribute in the central density.

Here the reader might respond: But this is only a model. What proof do we have that, in the real world, barred galaxies exhibit Lagrangian (and Hamiltonian) dynamics?

Good question. The answer: this is the only compelling solution that explains the formation, existence and longevity of the bar structure.

So, are there non-man-made objects observed to be located at, or orbiting around L1? Looking at the evidence (both quantitative and observational, some of which has been presented above), I would answer resoundingly yes.

I will come back to barred galaxy structure and the relation to Lagrange dynamics in my next few posts.


CC

[Little Bang]

An interesting question for NASA. " Could you put a satellite at the moon earth Le Grange point and have it stay there for a million years? " Myself I think their response would be no.

[Moontanman]

Originally Posted by Little Bang

An interesting question for NASA. " Could you put a satellite at the moon earth Le Grange point and have it stay there for a million years? " Myself I think their response would be no.

I don't see why not, I've read about plans to put objects in the Le Grange points of the Earth moon system. Jupiter has natural satalites in some of it's Le Grange points. Does it matter to this discussion that our Milky Way Galaxy has recently been shown to probably be a barred spiral?

[modest]

Originally Posted by Little Bang

An interesting question for NASA. " Could you put a satellite at the moon earth Le Grange point and have it stay there for a million years? " Myself I think their response would be no.

Originally Posted by Moontanman

I don't see why not, I've read about plans to put objects in the Le Grange points of the Earth moon system. Jupiter has natural satalites in some of it's Le Grange points. Does it matter to this discussion that our Milky Way Galaxy has recently been shown to probably be a barred spiral?

I had a good source on this, but can't at the moment find it... Maybe I posted it in the dynamic equilibrium thread.

In any case, the L4 and L5 points are stable and I think Jupiter has satellites there. L1, L2, and L3 are not stable and it takes a good amount of fuel to keep spacecraft there.

Here's a source, even if it's not the best:

If the heavy body is sufficiently massive compared with the light one, then L4 and L5 are stable positions, but L1, L2 and L3 are always unstable—a probe placed there will gradually wander away. However, the whole point of control engineering is to stabilise the unstable, and it turns out that regular, but relatively small, expenditures of fuel can keep a probe close to an unstable Lagrange point for decades.

-source

[modest]

Originally Posted by coldcreation

Fair question. I've already answer it above. The answer, at least with respect to the L1 point, is yes. I've also provided images of a large variety systems where the L1 point is occupied.

I don't really understand that. How could you find a Lagrange point in those pictures and what would they be relative to? For instance, how would a globular cluster have a Lagrange point? A particular star in the cluster with its orbit relative to the whole cluster I understand. But, just looking at the whole cluster and picking a spot for L1 - I don't get.

Originally Posted by coldcreation

Caranicolas writes regarding this orbit in barred galaxy models:

Looks good, it will take me a while to go over it.

Originally Posted by coldcreation

Here the reader might respond...What proof do we have that, in the real world, barred galaxies exhibit Lagrangian (and Hamiltonian) dynamics?... Good question. The answer:

complimenting your own question

-modest

[coldcreation]

Originally Posted by modest

I don't really understand that. How could you find a Lagrange point in those pictures and what would they be relative to? For instance, how would a globular cluster have a Lagrange point? A particular star in the cluster with its orbit relative to the whole cluster I understand. But, just looking at the whole cluster and picking a spot for L1 - I don't get.

I had not portrayed globular clusters above for that very reason.

In those systems, it is apparent, unlike many others, that there would be no global L1 point. Locally, between each star, there would inevitably not just L1 points but other L-points as well. And yet, globular clusters are some of the oldest structures in the universe.

Here is a beautiful example (a QuickTime simulation) of what could possibly be the dynamics of such systems. Note, however, at the end of the vid all the stars disperse into surrounding space: this may be a little whimsical, since so far, all of the evidence is that they are stable systems for time-scales exceeding the age of the universe.


EVOLUTION OF A STAR CLUSTER


There is an interesting feature, or two, about this simulation: The stars do not appear to be rotating about a central axis or point. They look as if they are orbiting, albeit chaotically or 'randomly,' around one another first (possibly for the reason I mentioned above, i.e., there is no central L1 point). In other words, there is no global rotational curve, as many galaxies would have (but I need to research this more before delving further). I'm sure some GC's rotate. What would be interesting to see is if in all such systems there is the type of intrinsic motion to all the components observed in the simulation. I would bet that some are quite static. More in line with this:

Million Star Cluster NGC 2808 Profile

In this video (below), stop the image at 20 seconds, you will notice the beginning of a structure that looks Lagrangian. Though this is only a simulation. We cannot see the central core of real globular cluster, as portrayed here. But I would think that the nucleus of these systems are indeed extremely tightly bounded binary stars or quadruple stars (neutron stars perhaps) with their respective L-points filled to the max. In that way at least the nucleus would be stable for Gyr time-scales.

NGC 104/47 Tucanae Globular Cluster, animation

Or this which looks similar even though it represents galaxies as opposed to stars:

100 Galaxy Simulation

Originally Posted by modest

complimenting your own question

You caught that.


PS. Isn't anyone going to give me any Rep Points for all the work I put into this thread?




CC

[Little Bang]

CC, I for one am astounded by the huge amount of work you have put forth and I do give you points.

Moon, I am unaware of these objects you say exist in Jupiter's Le Grange points, could you name them for me please.

[coldcreation]

Here is a nice document to find info about objects in L-points here in the solar system.

Lagrange Points, John Baez, December 19, 2005

Trojan asteroids

So far a total of 1691 asteroids called "Trojans" have been found orbiting the stable Lagrange points of Jupiter's orbit around the sun.

1691, wow.


CC