What Are Lagrange Points? L1, L2, L3, L4, L5 Explained

📘 Definition

In celestial mechanics, Lagrange points (also called Lagrangian points or libration points) are five equilibrium positions in the gravitational field of two massive co-orbiting bodies — for example, the Sun and Earth. At these positions, a small object such as a spacecraft experiences a net gravitational force that allows it to orbit in a fixed configuration with the two larger bodies. Three of the points (L1, L2, L3) are collinear — lying along the line connecting the two bodies — and are unstable, requiring station-keeping manoeuvres. Two points (L4 and L5) form equilateral triangles with the two bodies and are semi-stable, naturally trapping dust and minor asteroids.

5 per two-body system

Number of Points

1.5 million km sunward

L1 Distance

1.5 million km anti-sunward

L2 Distance

L4 and L5 (semi-stable)

Stable Points

Understanding L-Points

The Five Points Explained

L1 sits between the Sun and Earth, about 1.5 million km sunward. Spacecraft here (like SOHO and DSCOVR) enjoy an uninterrupted view of the Sun. L2 is the same distance but on the opposite side, away from the Sun — ideal for space telescopes like JWST and Gaia because the Sun, Earth, and Moon are all behind the spacecraft, providing a thermally stable, dark sky. L3 is on the far side of the Sun, opposite Earth — currently unused but a favourite of science fiction. L4 and L5 lead and trail Earth by 60° in its orbit. Jupiter's L4 and L5 points trap thousands of Trojan asteroids.

Why L1 and L2 Aren't Truly Stable

The three collinear points (L1, L2, L3) are saddle points in the gravitational potential — a spacecraft at these locations will drift away if perturbed. JWST, for example, orbits in a halo orbit around L2 and performs station-keeping burns roughly once every 21 days to maintain its position. The total delta-v budget for this is remarkably small — only about 2–4 m/s per year.

Key Spacecraft at L-Points

Point	Spacecraft	Agency	Mission
L1	SOHO	ESA/NASA	Solar observation
L1	DSCOVR	NOAA	Solar wind monitoring
L2	JWST	NASA/ESA/CSA	Infrared space telescope
L2	Gaia	ESA	Stellar mapping (2B stars)
L2	Euclid	ESA	Dark energy survey
L4/L5	Trojans (natural)	—	Asteroid populations

Frequently Asked Questions

Why is L2 the best location for space telescopes? ▼

At L2, the Sun, Earth, and Moon are all on the same side — behind the spacecraft. This provides a thermally stable environment and an unobstructed view of the deep universe in all other directions. The position also allows a single sunshield to block light and heat from all three bodies simultaneously, which is critical for infrared telescopes like JWST.

Do spacecraft actually sit at the Lagrange point? ▼

Not exactly. L1 and L2 are unstable, so spacecraft orbit around them in large halo or Lissajous orbits rather than sitting precisely at the mathematical point. JWST's halo orbit around L2 has an amplitude of about 250,000–800,000 km, completing one orbit roughly every six months.

Are there Lagrange points for other planet pairs? ▼

Yes — every two-body gravitational system has five Lagrange points. The Jupiter-Sun system's L4 and L5 points are famous for harbouring thousands of Trojan asteroids. NASA's Lucy mission is currently en route to explore several of these Trojans. Even the Earth-Moon system has Lagrange points, though they are less commonly used.