<p>All five Lagrange points are unstable </p>

<p><a href="https://i.sstatic.net/z2fw3.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/z2fw3.png" alt="enter image description here"></a></p>

<p>L1, 2, and 3 are "saddle points" in the effective potential formed from the combination of gravity and the centrifugal force of a rotating frame of reference. An object which is in front or behind in the orbit would tend to approach the Lagrange point, and then move away, either towards or away from the sun, following the lines in the picture.</p>

<p>However note that in the picture, the lines around the Lagrange points are not close together, this means that the motion towards, or away from the point is very slow (in the rotating frame) An object near the Lagrangian point would not be "ejected" at high speed. Any cosmic dust that was near the Lagrangian point would drift slowly away.</p>

<p>However although the L4 and L5 points are unstable, there are quite stable orbits that (in the rotating frame) orbit around the L4 and L5 point, allowing for <a href="https://i.sstatic.net/z2fw3.png" rel="nofollow noreferrer">Trojan</a> satellites.</p>

CC BY-SA 3.0
2015-11-28T16:37:24.557Z
2015-11-28T16:37:24.557Z
James K
<p>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?</p>

<p>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?</p>

<p>Thanks in advance! </p>

CC BY-SA 3.0
2015-11-28T05:20:52.113Z
Lagrange points can not *directly* capture anything, just like bodies can not capture objects without some help. Material will enter with at least some velocity and that kinetic energy will carry them right through the Lagrange point neighborhood. See http://astronomy.stackexchange.com/questions/8795/how-do-moons-get-captured . For an object to come to rest around a Lagrange point would require it to lose some kinetic energy by some other action. For a spacecraft, this would be done by propulsion. For an asteroid or meteoroid, a collision would have to happen at exactly the right place.
Eubie Drew
<orbit><lagrange-point>
How (un)stable are the Lagrangian points 1, 2 and 3?
xpell
# How (un)stable are the Lagrangian points 1, 2 and 3?

(Asked by: username_0 on 2015-11-28)

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!

**Tags:** orbit, lagrange-point

> **Comments:**
> **username_1**: Lagrange points can not *directly* capture anything, just like bodies can not capture objects without some help. Material will enter with at least some velocity and that kinetic energy will carry them right through the Lagrange point neighborhood. See http://astronomy.stackexchange.com/questions/8795/how-do-moons-get-captured . For an object to come to rest around a Lagrange point would require it to lose some kinetic energy by some other action. For a spacecraft, this would be done by propulsion. For an asteroid or meteoroid, a collision would have to happen at exactly the right place.  

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## 1 answers

### Answer by username_2 on 2015-11-28. Score: 2

All five Lagrange points are unstable

[![enter image description here](https://i.sstatic.net/z2fw3.png)](https://i.sstatic.net/z2fw3.png)

L1, 2, and 3 are "saddle points" in the effective potential formed from the combination of gravity and the centrifugal force of a rotating frame of reference. An object which is in front or behind in the orbit would tend to approach the Lagrange point, and then move away, either towards or away from the sun, following the lines in the picture.

However note that in the picture, the lines around the Lagrange points are not close together, this means that the motion towards, or away from the point is very slow (in the rotating frame) An object near the Lagrangian point would not be "ejected" at high speed. Any cosmic dust that was near the Lagrangian point would drift slowly away.

However although the L4 and L5 points are unstable, there are quite stable orbits that (in the rotating frame) orbit around the L4 and L5 point, allowing for [Trojan](https://i.sstatic.net/z2fw3.png) satellites.


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