# How many objects could you fit around a Lagrange point?

Specifically, how many 5 to 10 kilometer asteroids could you fit around the Earth-Moon Lagrangian points? Does the number change depending on which Lagrange point it is?

• You can fit however many objects you feel like fitting. Obviously the further you get away from the exact Lagrange point, the more station keeping you're going to need. – Cort Ammon - Reinstate Monica Mar 7 '17 at 17:17
• I asked something similar, a few years before WB existed, but I don’t recall where. I learned that hundreds or even thousands of habitats would be able to occupy the L4 and L5 points, in “halo orbits”. Beyond that you get into “horseshoe orbits” strung out over the circomference of the orbit, which is very very large. – JDługosz Mar 8 '17 at 10:23
• @JDługosz I suspect astronomy SE, space SE or physics SE. – Gray Sheep Mar 8 '17 at 22:11
• I think it was before that, too. But, I do think if you ask there, now, you’ll get a more authoratative real-world answer. – JDługosz Mar 8 '17 at 23:50
• Lagrange points 4 and 5 have their own gravitational fields by themselves, but all other Lagrange points you would need fuel to maintain that position. – Pyrania Aug 31 '18 at 16:55

From Wikipedia:

# Stability

Although the L1, L2, and L3 points are nominally unstable, it turns out that it is possible to find (unstable) periodic orbits around these points, at least in the restricted three-body problem. These periodic orbits, referred to as "halo" orbits, do not exist in a full n-body dynamical system such as the Solar System. However, quasi-periodic (i.e. bounded but not precisely repeating) orbits following Lissajous-curve trajectories do exist in the n-body system. These quasi-periodic Lissajous orbits are what most of Lagrangian-point missions to date have used. Although they are not perfectly stable, a relatively modest effort at station keeping can allow a spacecraft to stay in a desired Lissajous orbit for an extended period of time. It also turns out that, at least in the case of Sun–Earth-L1 missions, it is actually preferable to place the spacecraft in a large-amplitude (100,000–200,000 km or 62,000–124,000 mi) Lissajous orbit, instead of having it sit at the Lagrangian point, because this keeps the spacecraft off the direct line between Sun and Earth, thereby reducing the impact of solar interference on Earth–spacecraft communications. Similarly, a large-amplitude Lissajous orbit around L2 can keep a probe out of Earth's shadow and therefore ensures a better illumination of its solar panels.

Emphasis mine.

Example is about Earth-Sun, but for Moon-Earth it's the same, only proportionally smaller. This means that around these points you can have a semi-stable orbits far larger than your intended spacecrafts. As long as you keep masses irrelevant in comparison to the mass of Earth and Moon, and not enough to create measurable gravity or other forces between them, there is no practical limit on how many you can fit.

Just note that the more of them, the more fuel you would use to stay away, avoid shadowing each other, and keeping "in orbit" - but the difference shouldn't be dramatic.

For L4 and L5, as far as I understand, such orbits are not so easy, impossible even, and you would need to have all your vessels actively track each other and use fuel almost constantly. Still, it is possible there already are clouds of interplanetary matter there. If cloud can be relatively stable long term, anything you can fit into that cloud could, too. Practical limits are a bit too hard for me to calculate - the less fuel you are willing to spend, the closer to the point you have to be and / or the higher drift and less stability you have to accept.

• Jupiter, at least, does have a million or so 1km objects in its L4 and L5 spots, the Jupiter Trojans. I can't do the math to see if this is viable for the Earth-moon system but since there are lots of existing, natural L4/L5 satellites, these might prove more practical than L1/L2/L3. – kingledion Mar 7 '17 at 15:13
• @kingledion Nice to know and I'll try to add this info to my answer. Sadly, neither me nor you can do the math for Earth-Moon, but glad to know it seems reasonable. With just one little note - Sun-Jupiter is far heavier than Earth-Moon, so it can probably support larger objects realistically. – Mołot Mar 7 '17 at 15:23
• Yeah, the size difference is the thing. I could see Sun-Earth having L4/L5 objects, but I think that for Earth-Moon, the variable gravity of the sun due to the slight eccentricity of Earth's orbit would mean that the objects are unstable. I just can't prove it. – kingledion Mar 7 '17 at 15:53
• According to WORLD-BUILDING (SCIENCE FICTION WRITING SERIES) (it's a book), the mass of the secondary body has to be under 4% of the primary's body to have effective Lagrange points. – Pyrania Aug 31 '18 at 16:58