How (un)stable are the Lagrangian points 1, 2 and 3?

[xpell]

A couple questions, please: I know that the Lagrangian points 1, 2 and 3 are unstable and special Lissajous orbits plus some station-keeping are required to place a spacecraft around them. But I was wondering if they are so totally unstable that they can't temporarily "capture" a passing natural object (let's say an asteroid or a cloud of cosmic dust, in a stationary way or entering some kind of not-very-stable orbit around them)? Or could they?

And if they were able to, how much time would (approximately) be required for this/these object(s) to go "off-orbit" and abandon the L(1,2,3) area? In the case of the cloud of cosmic dust, would it just slowly (or quickly) drift away, or would they be "launched" towards another direction or orbit?

Thanks in advance!

PS. NASA says that L(1,2) are unstable "on a time scale of approximately 23 days" and this book talks about 23 days too. But I'm not sure if I can understand this as L(1,2) being naturally able to capture an object during approximately 23 days before "losing it"...

 

[Orodruin]

Capturing an object moving from far away will always require that the object loses energy by some means. Regardless of how stable the potential is at that point. The sun could not capture a spec of dust unless that spec of dust hit something else while in the solar system.

 

[xpell]

Capturing an object moving from far away will always require that the object loses energy by some means. Regardless of how stable the potential is at that point. The sun could not capture a spec of dust unless that spec of dust hit something else while in the solar system.

Thank you, Orodruin. Actually I was thinking in a cloud of dust just "wandering" out there. But if so, how did the Trojans end up in so many (more stable but not totally stable) points L(4,5) of the Solar System, please? Or, how could a wandering planet be captured into a solar system? Does it need some kind of collision? (I thought those were fully gravitational / orbital mechanics phenomena...)

 

[Orodruin]

You do not need an actual collision. It is sufficient with some gravitational deflection. Anything which changes the velocity of the object other than the background potential itself.

In a rotating coordinate system such as the one where the Lagrange points appear also makes it a bit more difficult to analyse due to the implied inertial forces.

 

[xpell]

You do not need an actual collision. It is sufficient with some gravitational deflection. Anything which changes the velocity of the object other than the background potential itself.

In a rotating coordinate system such as the one where the Lagrange points appear also makes it a bit more difficult to analyse due to the implied inertial forces.

Thank you again, Orodruin. :-) Unfortunately I'm still unsure about my original question. :-( Could an L(1,2,3) point capture some small asteroid or cloud of dust or gas and keep it there for some time? Is that what NASA is talking about when they mention the "23-day stability"?

 

[Orodruin]

They are talking about a typical time-scale on which the Lagrange points are unstable so that if you have an object placed there, the typical time taken to leave the Lagrange point would be of the order of that time.