What Are Lagrange Points? L1

📘 Definition

Lagrange points are five equilibrium positions in the orbital plane of two co-orbiting bodies — most often the Sun and Earth — where the combined gravity of the two masses and the centrifugal effect of the orbit cancel out, letting a much smaller object hold a fixed configuration relative to both. Three of them (L1, L2 and L3) lie on the straight line through the two bodies and are unstable, so a spacecraft parked there needs occasional station-keeping burns costing only a few metres per second of delta-v each year. The other two (L4 and L5) sit 60° ahead of and behind the smaller body, forming equilateral triangles; these are genuinely stable and naturally gather dust and Trojan asteroids. Their low fuel demand and steady thermal environment make them prized real estate for deep-space missions — most famously the James Webb Space Telescope, which orbits the Sun-Earth L2 point about 1.5 million km from Earth.

5 per two-body system

Number of Points

~1.5 million km from Earth

L1 & L2 Distance

L4 & L5 (60° triangular)

Stable Points

L1, L2, L3 (collinear)

Unstable Points

Understanding L-Points

The five Lagrange points at a glance

Every pair of co-orbiting bodies generates five Lagrange points. The three collinear points (L1, L2, L3) lie along the line joining the two masses and are unstable saddle points, so anything placed there drifts away within a few weeks. The two triangular points (L4, L5) share the smaller body's orbit, 60° ahead and behind, and are stable whenever the larger body is at least about 25 times more massive than the smaller one — easily satisfied by the Sun-Earth and Earth-Moon systems.

Point	Location (Sun-Earth)	Stability	Typical use / occupants
L1	~1.5M km sunward of Earth	Unstable	Solar monitors: SOHO, ACE, DSCOVR
L2	~1.5M km anti-sunward (night side)	Unstable	Space telescopes: Webb, Gaia, Euclid
L3	Opposite side of the Sun from Earth	Unstable	None — permanently hidden by the Sun
L4	60° ahead of Earth in its orbit	Stable	Earth Trojans 2010 TK7, 2020 XL5
L5	60° behind Earth in its orbit	Stable	Proposed space-weather sentinel

Why solar monitors and telescopes cluster at L1 and L2

L1 and L2 are the two most useful Lagrange points, and both sit about 1.5 million km from Earth. From L1, on the sunward side, a spacecraft has an unbroken view of the Sun; missions such as SOHO and DSCOVR exploit this to watch for coronal mass ejections and give up to about an hour's warning before the solar wind reaches Earth. L2, on the night side, lets a telescope face deep space while keeping the Sun, Earth and Moon all behind it — ideal for the infrared eyes of Webb, which must stay extremely cold. Because these points are unstable, spacecraft do not sit exactly on them; instead they trace wide 'halo' orbits around the point, which also keeps them out of Earth's shadow and preserves a clear radio link to the Deep Space Network.

L4 and L5: stable points that trap asteroids

Unlike the collinear points, L4 and L5 are genuinely stable: an object nudged away is gently herded back by the Coriolis effect, tracing a looping 'tadpole' path around the point. Over billions of years this sweeps up dust and asteroids. The best-known examples are the Trojan asteroids sharing Jupiter's orbit, thought to number close to a million larger than a kilometre, but Earth has its own confirmed pair — 2010 TK7 and 2020 XL5 — both leading the planet at L4. The mirror-image L5 point is a favoured site for a proposed space-weather sentinel: from 60° behind Earth it could spot solar active regions rotating into view days before they line up with our planet. You can follow other near-Earth objects on our live tracker.

A note on the name

The points are named after the Italian-French mathematician Joseph-Louis Lagrange, who described the two triangular solutions in a 1772 essay on the three-body problem. The three collinear points had already been found by Leonhard Euler a few years earlier, which is why some texts call the whole family 'libration points' instead. Whatever the label, they are among the handful of exact solutions to the notoriously unsolvable three-body problem — precisely what makes them so convenient for parking spacecraft.

Frequently Asked Questions

How many Lagrange points are there? ▼

Every two-body orbital system has exactly five Lagrange points, labelled L1 to L5. Three of them — L1, L2 and L3 — lie in a straight line through the two bodies and are unstable. The other two, L4 and L5, sit 60° ahead of and behind the smaller body, forming equilateral triangles, and are stable. So the Sun-Earth, Earth-Moon and Sun-Jupiter systems each have their own set of five.

Why is the James Webb Space Telescope at L2? ▼

L2 lets Webb keep the Sun, Earth and Moon all on one side of the spacecraft, so a single tennis-court-sized sunshield can block their light and heat at once. This keeps the telescope's cold side near -230°C, essential for infrared astronomy. L2 also sits about 1.5 million km from Earth in a fuel-efficient spot, and Webb loops around it in a roughly six-month halo orbit rather than sitting exactly on the point.

What is the difference between L1 and L2? ▼

L1 sits between the Sun and Earth, about 1.5 million km sunward, giving an uninterrupted view of the Sun; solar observatories like SOHO and DSCOVR use it to watch for incoming solar storms up to about an hour before they reach Earth. L2 lies the same distance the other way, on Earth's night side, which is ideal for space telescopes such as Webb and Gaia that need to look away from the Sun's glare.

Are Lagrange points stable? ▼

Only two of the five are truly stable. L4 and L5 act like shallow valleys — objects nudged away tend to drift back, which is why they collect dust and Trojan asteroids. L1, L2 and L3 are unstable, like balancing on a ridge: a spacecraft there slowly slides off within a few weeks and must make small station-keeping burns, typically only a few metres per second of delta-v per year.

What are Trojan asteroids? ▼

Trojan asteroids are small bodies trapped at a planet's stable L4 or L5 points, sharing its orbit 60° ahead of or behind it. Jupiter hosts by far the largest population — estimated at around a million objects larger than a kilometre, comparable to the main asteroid belt. Earth has two confirmed Trojans, 2010 TK7 and 2020 XL5, both leading the planet at L4, and NASA's Lucy mission is on its way to survey several of Jupiter's, with its first Trojan flyby due in 2027.

Do spacecraft use fuel at Lagrange points? ▼

Yes, but very little. Because L1, L2 and L3 are unstable, spacecraft stationed there fire their thrusters occasionally to stay put — Webb, for example, uses only about 2 to 3 metres per second of delta-v per year and manoeuvres roughly every 21 days. The stable L4 and L5 points need no fuel at all, which is why natural objects can linger there for thousands or even billions of years.

Sources & References

Definitions are reviewed against primary sources. Last reviewed: 2026-08-25.