What Are Lagrange Points, and Why Does JWST Sit at L2?

The James Webb Space Telescope (JWST) does not orbit Earth. It orbits the Sun, about 1.5 million kilometres beyond us, at a spot called L2, and it keeps pace with Earth all year. This post builds on our explainer Why Is the Speed of Light the Limit? in our relativity and cosmos series, though everything here is ordinary Newtonian gravity. It is drawn by Libratrix, our Lagrange-points character. You will find more orbit and gravity designs in our Classical Mechanics collection.

What is a Lagrange point?

NASA’s definition is short: “Lagrange points are positions in space where objects sent there tend to stay put.” At these points, “the gravitational pull of two large masses precisely equals the centripetal force required for a small object to move with them” (NASA^[1]). In plain terms, a small object there goes round the Sun in exactly one year, side by side with Earth, so the three bodies keep the same arrangement.

Joseph-Louis Lagrange studied this problem in his prize-winning 1772 paper, Essai sur le Problème des Trois Corps (NASA^[1]). Any two bodies in a circular orbit have five such points, L1 to L5:

• L1 lies between the two bodies, on the line joining them.
• L2 lies on the same line, beyond the smaller body. For the Sun and Earth, that is on the night side of Earth.
• L3 lies on the far side of the bigger body, opposite the smaller one.
• L4 and L5 sit 60° ahead of and behind the smaller body in its orbit, each at the tip of an equilateral triangle with the two bodies.

John Southworth describes the same thing mathematically: the Lagrangian points are “five stationary points in the Roche potential,” the combined gravitational and rotational potential felt by a small body moving with two big ones (Southworth 2023^[2]).

Why doesn’t an object at L2 just fall toward Earth or the Sun?

Normally, anything farther from the Sun than Earth orbits more slowly; Kepler’s third law says so. At L2 there is an extra pull: Earth’s gravity adds to the Sun’s, both pointing sunward. That bigger total pull is exactly what an object at that greater distance needs to circle the Sun in one year rather than a bit more. So it keeps pace with Earth.

The easiest way to see all five points is to sit in a frame that rotates with Earth. There, the Sun and Earth stand still, and a test object feels gravity plus an outward centrifugal effect. The figure in this post maps that “effective potential”: the Lagrange points are its flat spots, where the forces cancel.

How far away is L2, and can you work it out?

Yes, with a good approximation. For a small body orbiting a much bigger one, Southworth notes that the distance of L1 and L2 from the small body becomes approximately the size of its Hill sphere, the zone where its own gravity dominates (Southworth 2023^[2]). Written as a distance:

r ≈ a (q/3)^(1/3)

Here r is the Earth–L2 distance, a is the Earth–Sun distance and q is the mass ratio, Earth’s mass divided by the Sun’s. NASA’s fact sheets give Earth’s mass as 5.9722 × 10²⁴ kg (NASA Earth Fact Sheet^[3]) and the Sun’s as 1,988,400 × 10²⁴ kg (NASA Sun Fact Sheet^[4]), so

q = M⊕/M☉ ≈ 3.0 × 10⁻⁶

where M⊕ is Earth’s mass and M☉ the Sun’s. The cube root of q/3 is about 0.0100. With a = 149.598 million km (NASA Earth Fact Sheet^[3]):

r ≈ 0.0100 × 149.6 million km ≈ 1.50 million km

That matches ESA: L2 “is located 1.5 million kilometres directly ‘behind’ the Earth as viewed from the Sun” and is “about four times further away from the Earth than the Moon ever gets” (ESA^[5]). The Moon’s greatest distance, its apogee, is 405,500 km (NASA Moon Fact Sheet^[6]); 1.5 million km is about 3.7 times that. When we solved the full equations numerically for the Sun and Earth alone, ignoring the Moon, we got about 1.50 million km too.

Are Lagrange points stable?

Three are not. L1, L2 and L3 are balance points along a line, like a ball on top of a saddle: nudge an object and it drifts away. NASA says L1 and L2 “are unstable on a time scale of approximately 23 days, which requires satellites orbiting these positions to undergo regular course and altitude corrections” (NASA^[1]).

L4 and L5 can be stable. They are “home to stable orbits so long as the mass ratio between the two large masses exceeds 24.96,” which holds for the Sun and Earth and for Earth and the Moon (NASA^[1]). Nature uses them: the Trojan asteroids share Jupiter’s orbit at its L4 and L5 points, named after the asteroids Agamemnon, Achilles and Hector (NASA^[1]).

Why did NASA put JWST at L2?

Three reasons, all about keeping a telescope cold and steady.

The Sun, Earth and Moon stay on one side

Because L2 lies on the Sun–Earth line, the orbit “lets the telescope stay in line with the Earth as it moves around the Sun.” That “allows the satellite’s large sunshield to protect the telescope from the light and heat of the Sun and Earth (and Moon)” (NASA Webb^[7]). Behind the shield, the telescope works “at about 225 degrees below zero Celsius (minus 370 Fahrenheit).” The cold matters because “Webb primarily observes infrared light, which can sometimes be felt as heat,” and its targets send only “very faint infrared signals.” The sunshield works only if the Sun, Earth and Moon “all have to be located in the same direction,” which L2 provides (NASA Webb^[7]).

No day–night cycle

A telescope orbiting close to Earth passes in and out of Earth’s shadow, “causing it to heat up and cool down, distorting its view” (ESA^[5]). Hubble, which orbits 560 km above Earth (NASA Webb^[8]), “goes in and out of Earth shadow every 90 minutes,” while Webb has an unimpeded view that allows science operations 24/7 (NASA Webb^[7]).

It loops around L2 rather than sitting on it

“Webb orbits around L2; it does not sit stationary precisely at L2.” Its loop is similar in size to the Moon’s orbit around Earth and takes about six months to go round once, keeping it out of the shadows of both Earth and Moon (NASA Webb^[7]). Because L2 is unstable, the spacecraft still needs the regular course corrections NASA describes for L1 and L2.

Webb launched on 25 December 2021 and arrived at L2 on 24 January 2022 (NASA Webb^[8]). Getting there “took roughly 30 days,” yet it took only 3 days to reach the distance of the Moon’s orbit, which is “about a quarter of the way there” (NASA Webb^[7]). NASA compares it to cycling up a hill: pedal hard at the very beginning, then coast most of the way up.

Webb is not the first. NASA’s Lagrange-point page also lists L2 as home to WMAP and Planck, two missions which mapped the cosmic microwave background (NASA^[1]).

FAQ

How many Lagrange points are there?

Five for any pair of bodies in a circular orbit: L1, L2 and L3 on the line through the two bodies, and L4 and L5 at 60° ahead of and behind the smaller one.

Is JWST exactly at L2?

No. It follows a looping orbit around L2 about the size of the Moon’s orbit, and each loop takes about six months.

Why is L2 unstable?

It is a balance point on the line, like a ball on a saddle. A small push grows over roughly 23 days, so spacecraft make regular small corrections.

How far is L2 from Earth?

About 1.5 million km, roughly four times the Moon’s greatest distance. You can estimate it as r ≈ a (q/3)^(1/3) with the Earth–Sun distance and mass ratio.

References

1. NASA Science, “What is a Lagrange Point?” (27 March 2018). https://science.nasa.gov/resource/what-is-a-lagrange-point/
2. J. Southworth (2023), “Simple approximations to the positions of the Lagrangian points,” arXiv:2309.15661. https://arxiv.org/abs/2309.15661
3. NASA NSSDCA, Earth Fact Sheet (D. R. Williams). https://nssdc.gsfc.nasa.gov/planetary/factsheet/earthfact.html
4. NASA NSSDCA, Sun Fact Sheet (D. R. Williams). https://nssdc.gsfc.nasa.gov/planetary/factsheet/sunfact.html
5. ESA, “L2, the second Lagrangian Point”. https://www.esa.int/Science_Exploration/Space_Science/Herschel/L2_the_second_Lagrangian_Point
6. NASA NSSDCA, Moon Fact Sheet (D. R. Williams). https://nssdc.gsfc.nasa.gov/planetary/factsheet/moonfact.html
7. NASA Science, “Webb’s Orbit” (James Webb Space Telescope). https://science.nasa.gov/mission/webb/orbit/
8. NASA Science, James Webb Space Telescope mission page. https://science.nasa.gov/mission/webb/

Written by Pixelated Physics. Every factual claim is linked to the source we checked; points that are still debated are labelled open.