What Is a Lagrange Point? Five Places Where Gravity Balances Out

An object orbiting the sun closer than the Earth normally moves faster and one further out moves slower, so nothing can stay lined up with the Earth for long. At certain distances, though, the Earth's own gravity modifies the balance. A little closer to the sun than the Earth, the Earth pulls outward against the sun's pull, reducing the net inward force, which slows the orbital speed required to that of the Earth itself, and an object placed there keeps pace. A little further out, the Earth pulls inward and adds to the sun's pull, which speeds up the required orbit to match. Those are the first two of the five positions. A third sits on the far side of the sun, and the remaining two lie sixty degrees ahead of and behind the smaller body in its orbit, where the geometry of the two gravitational pulls produces a net force directed at the common centre of mass. The mathematics was worked out by Euler and Lagrange in the eighteenth century as a special case of the three-body problem.

The five positions differ fundamentally in whether an object placed there stays put:

• •The first three are unstable, like a ball balanced on a saddle, so an object drifts away and must correct its position periodically using thrusters
• •That instability is manageable rather than fatal, since station-keeping costs only a small amount of fuel per year, and it does set a lifetime for a mission
• •The fourth and fifth are stable for mass ratios above a threshold, which the sun and planets comfortably exceed, so objects placed there stay and objects drifting nearby accumulate
• •Spacecraft at unstable points do not sit exactly at them but orbit around them in halo or Lissajous paths, which avoids the sun being directly behind the point and interfering with communications
• •Each pair of orbiting bodies has its own set, so there are Earth and moon points as well as sun and Earth points
• •The stable points collect material naturally, which is why they hold asteroid populations and why they are of interest for future infrastructure

The second sun-Earth point, roughly one and a half million kilometres beyond the Earth away from the sun, has become the preferred location for infrared and cosmological observatories for a specific set of reasons. The sun, Earth and moon all lie in the same direction from that position, so a single sunshield blocks all of them at once, allowing an instrument to cool passively to very low temperatures, which is essential for infrared observation because a warm telescope glows in exactly the wavelengths it is trying to detect. The thermal environment is stable, with no repeated heating and cooling from passing in and out of Earth's shadow every ninety minutes as a low orbit would impose. The whole sky becomes observable over the course of a year. Communication is straightforward since the spacecraft stays in a fixed direction. The cost is that repair is not practical, which is why the James Webb Space Telescope had to work first time, and the first point is used instead for solar observatories, which want an uninterrupted view of the sun.

The stable fourth and fifth points of the sun and Jupiter hold large populations of asteroids, conventionally named after figures from the Trojan war and divided into two camps accordingly, and over ten thousand are known with estimates of many more. Neptune has its own substantial population, Mars and Uranus have a few, and one Earth companion was confirmed in 2010 with another since. The moon's points are thought to hold faint concentrations of dust, reported repeatedly and difficult to confirm. Studying these objects matters because they have been in place for a very long time and may preserve material from the early solar system, and a dedicated mission is visiting several Jupiter companions to sample the diversity. Beyond observation, the points have long featured in proposals for infrastructure including relay satellites for communication with the far side of the moon, staging points for deep space missions and sites for future habitats, on the reasoning that a stable location requiring no fuel to hold is a genuinely scarce resource.

The Earth's gravity adds to or subtracts from the sun's at particular distances, changing the orbital speed required so that a small object can keep pace with the Earth. Three of the five positions are unstable and need occasional thruster corrections, while two are stable and collect asteroids. Telescopes use the outer point because the sun, Earth and moon all lie one way, so one shield blocks them and the instrument cools passively.