Is it possible for astroids to be captured by a Lagrangian point?
Yes. See Trojan asteroid.
Yes, they are called Trojans.
The Lagrange points aren’t all that stable (wiki).
So if you’re imagining an asteroid whizzing past an L point at high speed & getting snagged in a deep gravity well centered on the L point, that’s not it at all.
But if something passed an L4 or L5 point going slowly enough, it can get stably captured long term.
Sounds like a good Twilight Zone episode setup.
This is what I was envisioning: That there is an orbital speed at which an object could be captured by a Lagrange point. We have seen it in Sci Fi, but I was wondering if it could happen naturally.
It should be understood that libration or Lagrange (not Lagrangian) “points” are actually regions in the gravitational field in a system of two major bodies (m[SUB]1[/SUB] is the primary body and m[SUB]2[/SUB] is the secondary body) where the gravity potential is sufficiently near zero that the objects in this region are effectively weightless with respect to the rotating coordinate system at the epicenter with an axis drawn through m[SUB]1[/SUB] and m[SUB]2[/SUB].
The L1 and L2 (conjunctional) and L3 (oppositional) regions are very small and relatively unstable; small perturbations, including tidal drag, will cause objects to fall outside of the equilibrium zone quickly. However, it is possible to find relatively stable orbits around the “points” in which a spacecraft can orbit with only minor stationkeeping effort. For a system with a sufficiently large mass ratio (m[SUB]1[/SUB]>m[SUB]2[/SUB] x 24.96 >> m[SUB]trojans[/SUB]) the L4 (leading) and L5 (trailing) regions are relatively stable and also drawn along the orbit of m[SUB]2[/SUB]. That stability can be evaluated in terms of the three body constant, μ*, where μ* = m[SUB]2[/SUB]/(m[SUB]1[/SUB]+m[SUB]2[/SUB]); the smaller the constant, the more stable the system. For systems the size of the Earth-Luna system (μ* ~ 0.012) the regions will collect dust and small asteroids (<500 m diameter) called trojans. For systems the size of the Sun-Jupiter (μ* ~ 0.000 95) can collect asteroids many tens of kilometers in diameter; the largest Jovian trojans are 624 Hector (225 km), 911 Agamemnon (167 km), and 1437 Diomedes (164 km).
LSLGuy is correct that libration points don’t drag a passing object into them; they have to have a relatively small relative motion which is altered by the local gravity gradients to fall into the region and not exit. In fact, many supposed trojans are actually in quasi-stable orbits where they will enter and leave the libration region periodically, returning to an orbit directly around the m[SUB]1[/SUB] body. However, because these regions collect a lot of dust and small objects, they may have their own local gravitational field that can drag on other objects, both causing those objects to slow and enter the region or objects within the region to be ejected. Note that this also means there is a lot more debris in these regions, which would make it a place ill-suited for a conventional space station or habitat without some protection against the charged dust and debris (unless, of course, the station were intended for collecting material, although it is probably poor in dense metals). It is also outside of the Earth’s protective magnetosphere and would require either a very slow logarithmic spiral trajectory or a lot of reverse impulse to achieve (from Earth orbit), so despite the oft-mentioned claim in science fiction and by space habitation enthusiasts, the L4 and L5 points would not be very desirable places to put a conventional space habitat.
It just occurred to me: looking at the display
The Central Body, the Orbiting Body, and the L4 and L5 points are 60 deg. +or- from the Orbiting body.
If we assume the Orbit is circular and place a body of equal mass to the Orbiting Body at the L4 and L5 points…now assign a Point and Body to the L4 and L5 Points, and finally a Body at the L3 point.
Thus, you have a system with 6 equidistant, equimass bodies in orbit.
Would such a system be stable?
The stability of the L4 and L5 points is based on the presumption that m[SUB]1[/SUB]/24.96 > m[SUB]2[/SUB] >> m[SUB]3[/SUB] … m[SUB]n[/SUB]; in essence, it is a restricted three-body simulation with the assumption that there is no coupling between the smaller masses and the two primary masses. With equal mass bodies the coupled influence of each body has to be considered. In a perfectly symmetric circular orbit the configuration would be theoretically stable, but any perturbation (including even a slight eccentricity in the orbit) will result in oscillatory motions between the bodies that will result in orbital instability, with bodies falling in to doublets or more exotic orbits. Depending on orbital energy they could eventually be thrown into separate higher and lower orbits entirely.
Klemperer rosettes (polygonal configurations with no dominant central body) are even worse; the slightest perturbation will rapidly cause the bodies to fall out of dynamic equilibrium and will eject one another from the system.
It has to be safe. The puppeteers would never build something so unstable, especially when their homeworld is at stake.