What Are Lagrange Points?
Take two large bodies orbiting each other, such as the Sun and Earth. There are five points where a small object, like a spacecraft, can stay in the same position relative to both. At these points, the gravity of the two bodies and the centrifugal effect of the rotating system balance exactly.
They are named after Joseph-Louis Lagrange, who described them in 1772. Leonhard Euler had already found L1 to L3 a few years earlier.
The Five Points
| Point | Position (Sun–Earth system) | Stable? | Used for |
|---|---|---|---|
| L1 | Between the Sun and Earth, about 1.5 million km from Earth | No | Watching the Sun without interruption (SOHO, DSCOVR) |
| L2 | Beyond Earth, on the side away from the Sun, about 1.5 million km away | No | Space telescopes (JWST, Gaia, Euclid) |
| L3 | On the opposite side of the Sun, behind it as seen from Earth | No | Nothing so far; a classic location in science fiction |
| L4 | 60° ahead of Earth in its orbit | Yes | Natural collection point for asteroids |
| L5 | 60° behind Earth in its orbit | Yes | Natural collection point for asteroids |
L1, L2 and L3 lie on the line through both bodies. L4 and L5 each form an equilateral triangle with the two bodies.
Stable or Unstable?
- L1, L2, L3 are unstable, like a ball balanced on top of a hill. Any small push grows over time. Spacecraft fly halo orbits around these points and need small correction burns every few weeks.
- L4 and L5 are stable, like a ball in a bowl, as long as the larger body is at least about 25 times heavier than the smaller one. This holds for Sun–Earth, Sun–Jupiter and Earth–Moon.
Where L1 and L2 Lie
The distance from the smaller body (mass m) to L1 or L2 is roughly:
r ≈ R · ∛( m / (3M) )R is the distance between the two bodies and M is the mass of the larger one.
For Sun–Earth: r ≈ 149.6 million km × ∛(3.0 × 10⁻⁶ / 3) ≈ 1.5 million km. That is about four times the distance to the Moon.
Why L2 Is Perfect for Telescopes
- The Sun, Earth and Moon are all on the same side, so a single sunshield can block all three.
- The temperature stays steadily cold, which is important for infrared telescopes.
- It is close enough to Earth for fast data links.
- There are no day–night cycles like the ones in low Earth orbit.
The James Webb Space Telescope has been in a halo orbit around Sun–Earth L2 since January 2022.
Natural Examples: Trojan Asteroids
Over billions of years, asteroids have gathered at the stable points:
- Jupiter's Trojans: more than 10,000 known asteroids at Jupiter's L4 and L5. NASA's Lucy mission is on its way to visit several of them.
- Earth Trojans: a few have been found so far, for example 2010 TK7 and 2020 XL5.
Other Systems
Every pair of bodies has its own Lagrange points. Earth–Moon L2, for example, is the planned region for orbits used in Moon missions such as the Lunar Gateway station (it will use a "near-rectilinear halo orbit").
See also: Orbital Mechanics: Key Equations