Space has no parking brakes, yet spacecraft routinely sit in fixed positions relative to Earth and the Sun for years at a time. They do it at Lagrange points, five special locations in any two-body system where gravitational forces and orbital motion balance out, letting a small object hold its position with minimal fuel. The James Webb Space Telescope lives at one of them, and understanding these points explains a surprising amount of modern spaceflight.

The points are named for Joseph-Louis Lagrange, who calculated them in the 18th century while studying the three-body problem. In the Sun-Earth system, three of the points, L1, L2 and L3, lie along the line joining the Sun and Earth. L1 sits between the Sun and Earth, L2 sits beyond Earth on the far side from the Sun, and L3 sits on the opposite side of the Sun from Earth. The other two, L4 and L5, sit 60 degrees ahead of and behind Earth in its orbit, forming equilateral triangles with the Sun and Earth.

Stability separates the points into two groups. L4 and L5 are stable, meaning an object nudged away tends to drift back, which is why they collect natural debris: the Trojan asteroids share Jupiter's orbit at its L4 and L5 points, and Earth has a few known Trojans too. L1, L2 and L3 are unstable, like balancing a ball on a hilltop, so spacecraft there need small, regular course corrections to stay in place. Webb, for example, fires its thrusters roughly every three weeks to maintain its halo orbit around L2.

L2 is ideal for an infrared observatory for a specific reason: geometry. At L2, the Sun, Earth and Moon all lie in roughly the same direction from the spacecraft, so a single sunshield can block heat and light from all three at once. That keeps Webb's instruments at cryogenic temperatures, near minus 233 degrees Celsius, which is essential for detecting faint infrared light from the early universe. No other nearby location offers that combination of a stable thermal environment and an unobstructed view of deep space.

L1 has a different job. Sitting between the Sun and Earth, it offers an uninterrupted view of the Sun, which is why solar observatories like SOHO and the Deep Space Climate Observatory operate there. A spacecraft at L1 sees solar storms and solar wind about an hour before they reach Earth, giving forecasters a crucial early warning for space weather that can disrupt satellites and power grids.

L4 and L5, meanwhile, are attractive for future missions precisely because of their stability. Proposals exist for observatories, fuel depots and even habitats at Earth-Sun L4 and L5, where station-keeping fuel costs would be minimal. The same stability that traps Trojan asteroids could one day hold human infrastructure, parked in gravitational eddies that need almost no maintenance.

Lagrange points are not magic anti-gravity zones, and spacecraft do not sit exactly at them. Most missions orbit around the point in a halo or Lissajous orbit, a looping path that keeps the spacecraft near the point while avoiding practical problems such as radio interference or eclipses. Webb's halo orbit around L2, for instance, is about 800,000 kilometres across, wide enough to keep it out of Earth's shadow so its solar panels stay lit.

The next time you read that a telescope is parked at L2 or a solar probe watches from L1, picture the balance behind it: gravity pulling one way, orbital motion pulling the other, and a spacecraft riding the equilibrium between them. Lagrange points are the solar system's free parking, and we are only beginning to use them.