# How many satellites can stay in a Lagrange point?

Lagrange points as I understand it are points in space between 2 objects where the gravitational pull between them is effectively equal. That makes station keeping at these points relatively easy.

But how many satellites could stay in one Lagrange point? How big is the risk of congestion/collision in these areas?

• You can’t put two of anything at a point Commented Jun 23, 2019 at 5:53

Lagrange points as I understand it are points in space between 2 objects where the gravitational pull between them is effectively equal.

A quick check of Wikipedia's Lagrangian point or any article will show that only one of the five Lagrange points are "between (the) two objects". The pulls are not equal, they balance in such a way as to allow for an orbit with the same period as the other two objects, so in a frame rotating with them the point appears to be stationary.

...how many satellites could stay in one Lagrange point?

Satellites are never placed at the Lagrange points themselves, but instead they are in Lissajous or Halo orbits associated with the Lagrange points. In the rotating frame it looks like they are orbiting around the Lagrange point.

How big is the risk of congestion/collision in these areas?

You could put thousands of satellites in halo orbits around a Lagrange point, but depending on which Lagrange point in which system, they may have to do some small propulsive orbital corrections to stay there long term. These orbits have sizes of hundreds of thousands of kilometers (in the case of Sun-Earth Lagrange points) and so the chances that they would bump into each other are extremely small.

@Sean's comment and @dmckee's comment remind us that in the Circular Restricted Three-body approximation orbits near L4 and L5 tend to be stable. It turns out that some halo orbits associated with L1 and L2 are also stable in the CR3BP approximation as well, see answers to Are some Halo Orbits actually Stable? but real spacecraft don't live in the CR3BP approximation. All halo orbits in the Earth-Moon system will probably need some station-keeping sue to effects from the Sun, as would all halo orbits associated with Sun-Earth L1, L2 and L3 that needed to last for decades. But the comment is right, you can place objects in certain orbits near Sun-Earth's L4 and L5 and they should stay there for decades or centuries.

• Q: How many satellites can I have at L5? A: How good is your traffic control? Commented Jun 22, 2019 at 15:05
• @Saiboogu - And how much of your military communications do you want to put at the mercy of Chinese ASat weapons? Commented Jun 22, 2019 at 17:51
• Note that only the stable points (4 and 5) have stable halo orbits. Put your satellite near-but-not-at L1-L3 and it tends to wander off without active station-keeping. This may still be useful for some purposes. Commented Jun 22, 2019 at 21:52
• "You could put thousands of satellites in halo orbits around a Lagrange point, but they would all have to do some small propulsive orbital corrections to stay there long term." Only for L-1 through L-3; orbits at or around L-4 and L-5 are stable indefinitely (barring the destruction or expulsion from orbit of one of the bodies producing the set of Lagrangian points under discussion), as long as the mass of the object(s) at or orbiting around the point(s) does not approach that of either of the two Lagrangian-point-set-producing objects. Commented Jun 22, 2019 at 22:02
• @Sean thanks for that! I've made an edit, how does it look?
– uhoh
Commented Jun 23, 2019 at 1:11