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I know that we already have satellites in position at our Lagrange points, but what if we want to use them to park spacecraft sections for assembly reasons, or possibly even a meteorite for mining.

Are the 10 points big/stable enough to have multiple objects stationed there without causing collisions? If not for all 10, which ones?

Do we already have points that have more than one objects?

Rickest Rick
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    Which Earth's Lagrange points? There's the Sun-Earth L-points (SEL), or the Earth-Moon L-points (EML). Wikipedia maintains a List of objects at Lagrangian points – TildalWave Feb 05 '16 at 23:18
  • The most practical point for vehicle assembly would be EML2 I believe. Lets pick that one! – Rickest Rick Feb 05 '16 at 23:30
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    Actually it's fine to ask about all five of Earth's Lagrange points - it would make for a more informative question and answer in the long run, which is one of the, and probably the main mission of Stackexchange. Much better than asking five identical questions about each point separately. – uhoh Feb 06 '16 at 01:03
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    As a starter, this image from this article shows a satellite in orbit around earth L2, which is almost as large as the moon's orbit! I could't immediately find a pic of a Halo orbit though. A good answer would summarize all five, including caveats about stability and station keeping. – uhoh Feb 06 '16 at 01:06
  • And the "Lagrange Points" proper are theoretical points for a simplified mathematical system of two bodies. In the real solar system with perturbations and elliptical orbits, they are more like areas than single points in space. the link from @jcaron has a table, maybe the fact that there exists a list of objects answers your question? – uhoh Feb 06 '16 at 11:55
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    @uhoh There's 10 L-points bound to Earth, not 5! All with different stability timescale and magnitude of perturbations, and each set of 5 has two types of manifolds. – TildalWave Feb 06 '16 at 14:52
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    Related: Do we sufficiently understand mechanics of Lagrange point stationkeeping for EML2 rendezvous and assembly?, and Halo vs Lissajous orbit: Which station-keeping strategy to select and when? – TildalWave Feb 06 '16 at 15:19
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    OK that's excellent @TildalWave! This will keep me busy over the holiday :) Are the 'other five' the earth-moon points, or are there L6 through L10 that nobody told me about? – uhoh Feb 06 '16 at 15:39
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    Slightly related question (earth L3) – uhoh Feb 06 '16 at 16:13
  • @uhoh The other five are for the Earth-Sun system. – SE - stop firing the good guys Feb 06 '16 at 18:46
  • Hi All, I just updated the question to specifically ask about all 10 points (5 Earth-Sun, and 5 Earth-Moon) to make this question a one stop shop for all the points. Also changed question language from just size to size/stability. – Rickest Rick Feb 08 '16 at 15:21
  • Great! Stay tuned... – uhoh Feb 08 '16 at 18:30
  • @uhoh still staying tuned. Are you finding anything useful out there? – Rickest Rick Feb 09 '16 at 17:13
  • There is lunar new year where I am right now - everything is shut down hard @@ - lock the doors and turn off the servers. There's a review that has a nice, concise summary I'm trying to locate for you. – uhoh Feb 10 '16 at 03:45
  • @uhoh I understand, get back to us when you can, Happy New year! – Rickest Rick Feb 10 '16 at 17:32
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    Just give them docking ports and start constructing a base, dammit! – SF. Feb 12 '16 at 18:34
  • Bah, Humbug @RickestRick! Locking up millions of books for almost week is nothing to celebrate. It's just... "counterintuitive" - I'm trying to be more delicate than SF :) Everything opens tomorrow morning - yay! – uhoh Feb 12 '16 at 19:58
  • @uhoh Wow, a whole week?? No worries, I'm not going to award the bounty until the very end. I would rather have a well structured and sound answer than a half-hearted with no references. Cheers! – Rickest Rick Feb 12 '16 at 20:07
  • While you are waiting, take a look at the GIF on this page I stumbled-upon. Those are Jupiter's L3 (at the bottom) L4 and L5 "points". (jupiter at top, earth orbiting near the center). Bigger here So one might define the size differently depending on the application, but there's a lot of room even in this little 2D simulation GIF! – uhoh Feb 13 '16 at 13:50
  • @TildalWave has some goodies here as well. Also, a giant GIF can be found at that site. Ignore the green - look at the tiny blue dots to the left and right of Jupiter, hanging out at the Sun-Jupiter L4, and L5 Lagrange "points." – uhoh Feb 13 '16 at 15:34
  • This question has not received enough attention. Not True! I won't post in time for your bounty but wow this is fascinating! The short answer is L1, L2, L3 unstable, L4, L5 stable for both SE and EL, but L1, L2 are used "often" via active station keeping. L3's are more mathematical curiosities - weak and subject to perturbations. In the real solar system (many bodies, elliptical orbits) the L's are really regions, not points, and things are put in a zoo of cool-looking orbits around the "points." Trying to get vertical & planar Lyapunov, halo, and Lissajous orbits in one plot now. – uhoh Feb 19 '16 at 14:07
  • @uhoh Yes it's true that now there is a lot of chatter going on here, I guess I'm used to the kind of volume that Stack Overflow would generate! Get an answer in within the next few hours, it's not too late, ..yet! – Rickest Rick Feb 19 '16 at 15:03

2 Answers2

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When the media talks about spacecraft at the Lagrange point, what they really are saying is that the spacecraft will be somewhere in the general area of the Lagrange point, not at the point itself which is infinitely small.

The gravitational pull of one of the bodies will be a bit higher, but in practical term it does not make any difference, so yes, the Lagrange "points" are big enough.

Are they stable? Again, for practical purposes they are i.e. with some modest station keeping you can keep a spacecraft there.

More details can be found here:

Lagrangian points article [astronomy.com]
Lagrangian points - stability [wikipedia]

James C
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ventsyv
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  • That's right - it's better to think of them as "areas" from a practical point of view. Orbits in the areas near L4 and L5 have at least a chance of being stable, but L1, L2 L3 don't. An object at those points needs some kind of propulsion system to provide regular but small "nudges" to stay there, otherwise they will soon drift completely away. There must also be some kind of position measurement (on the object, or remote) to signal the direction and strength of the nudges. – uhoh Feb 12 '16 at 19:52
  • Awarded Bounty for including credible references. Thanks for your answer! – Rickest Rick Feb 19 '16 at 17:58
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I presume you are referring to the five Lagrange points for the earth and the sun (SE) and the five points for the earth and the moon (EM), to get to your tally of ten points.

Broadly speaking for systems like SE and EM, L1-3 lie in a straight line between the bodies and are unstable. L4 and L5 are pretty stable when the larger body is ~>25 times the size of the smaller one. This is just about true for EM and is obviously true for the earth and sun. Practically speaking l4 and l5 are generally not as useful as the other Lagrange points in terms of sun earth observation, getting shielding from the sun or as a staging point for BEO exploration.

You may have heard of the three body problem, and this is the reason why there is no definitive long term stable orbit at L1-3.

There are some relatively predictable associated orbits called Lissajous orbits which don't solve the three body problem but can let you park a spacecraft in an orbit around any of the L1-3 points with some very minimal station keeping. These are the orbits that have been used to date for satellites, but are not very useful for storing a large asteroid unless we also add a large enough propulsion system to keep it in the Lissajous orbit.

Bubs
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