The Loveliness of Lagrange Points

Article November 22, 2025

What’s this? The long-promised Lagrange point post? At last?? Well, I did tell you I’d get around to it eventually.

If you’re a space nut (guilty) it’s hard not to have a solid appreciation for gravity. After all, it more or less rules things out in the cosmos. And one thing I love about gravity is that it can be undeniably quirky. You have gravitational waves casually warping space-time. You have dark matter hiding from us in every feasible way except for its gravity. And you have Lagrange points.

Lagrange points are places where gravity behaves juuuuuust a little differently than otherwise. And it can be a surprisingly useful quirk. So let’s get gravitational and talk about Lagrange points and what they’re good for.

 

Lagrange Who?

This diagram shows where the five Lagrange points of the Sun-Earth system are. Credit: ESA
This diagram shows where the five Lagrange points of the Sun-Earth system are. Credit: ESA

Lagrange points are gravitationally stable points in space caused by the combined gravitational effects of two large objects. They come in sets of five. So, for instance, there are five Sun-Earth Lagrange points caused by the interaction of the Sun’s gravity and Earth’s gravity as Earth goes around the Sun. There are also five Earth-Moon Lagrange points due to a similar interaction between the gravity fields of the Earth and Moon. These sets of five points in space are generally (conveniently) labeled L1-L5. 

If history were being just, they’d probably be called Euler points, or at least Euler-Lagrange points. It was Leonhard Euler who puzzled out the existence of L1, L2, and L3 sometime around 1750. It wasn’t until 1772 that Joseph-Louis Lagrange published an essay outlining the existences of L4 and L5. But then if I went on a tear about history not being just this would become a whole different blog.

Since we’re sticking to the space science, for the purposes of this post we’ll mostly be considering the Sun-Earth Lagrange points—they’re the ones we make the most use of. We will, however, mention points from a few other celestial combos along the way

 

L1

The Solar and Heliospheric Observatory (SOHO) has been stationed at the Sun-Earth L1 point since starting its mission in 1996. Credit: NASA
The Solar and Heliospheric Observatory (SOHO) has been stationed at the Sun-Earth L1 point since starting its mission in 1996. Credit: NASA

If you have two objects in space with one orbiting the other—say the Earth going around the Sun—then the first Lagrange point, L1, will be between the two and closer to the smaller object. In the case of the Sun-Earth system, L1 is a little over 900,000 miles Sunward from Earth.

Normally an object that is closer to the Sun than Earth would move faster around the Sun than Earth does. This is why Venus and Mercury have shorter years than the Earth. But that’s the gravitational magic of a Lagrange point—at L1 Earth’s gravity counteracts the Sun’s enough that an object placed at there will orbit the Sun in 365 days, the same as Earth.

This image of the Earth with the Moon in front of it was taken by the DSCOVR spacecraft from its position at the Sun-Earth L1 point. Credit: NASA/NOAA
This image of the Earth with the Moon in front of it was taken by the DSCOVR spacecraft from its position at the Sun-Earth L1 point. Credit: NASA/NOAA

So why does that matter? Imagine for a moment that you are at the L1 point, looking back towards Earth. What would you see? What would you always see?

You’d see a full Earth, the entire daytime side of Earth at all times, 24/7/365. Earth would, of course, rotate, but you’d have a constant, completely unobstructed view of its daytime side. And you’d be far enough away to be able to see the whole planet at a glance.

And if you looked in the other direction, back towards the Sun, you’d have a constant, unobstructed view of the entire Sun. And you’d keep even with the Earth in its orbit, which means you’d never be out of communications range.

As a result, the Sun-Earth L1 point is a fantastic place to park Earth-observing and solar telescopes. It’s the home of DSCOVR, the Deep Space Climate Observatory, and its dual mission to monitor Earth’s climate and provide warning of major solar storms. For decades L1 has been the home of SOHO, the Solar and Heliospheric Observatory, one of our premier Sun-watching telescopes. It’s slated to be the future home of NEO Surveyor, the first mission to hunt for potentially hazardous asteroids inside Earth’s orbit, where the Sun’s glare can make them difficult to see.

That’s how we make use of L1. It’s a very handy spot. But it’s not quite so useful as L2.

 

L2

The L2 point between two objects in space is kind of like the opposite of L1. L2 is beyond both objects, though again closer to the smaller one. The Sun-Earth L2 point is a little over 900,000 miles farther out from the Sun than Earth is. Yes, that’s the same distance that L1 is in the opposite direction. What a coincidence! (It’s not a coincidence.)

Normally something farther from the Sun than Earth would take longer to orbit the Sun than Earth does. But I bet you’ve guessed the punch line here—the combined pull of Earth’s gravity and the Sun’s gravity at L2 means an object placed there keeps pace with Earth as it orbits the Sun.

The James Webb Space Telescope orbits the Sun-Earth L2 point to help it get its unprecedented ability to observe the universe. Credit: NASA
The James Webb Space Telescope orbits the Sun-Earth L2 point to help it get its unprecedented ability to observe the universe. Credit: NASA

So what would you see if you were at L2? If you looked towards the Earth, you’d see the entire nighttime side of the planet. Good for a pretty picture, maybe, but not an especially useful view. But if you turned away from the Earth, what would you see? Oh nothing, only the entire rest of the universe.

L2 is a fantastic place to put a telescope. It’s close enough to Earth to stay in constant contact, but far enough away that Earth will never block the telescope’s view (a problem for Hubble, which is in low Earth orbit).

The list of observatories that have and are making use of L2 as a parking spot is lengthy. WMAP and Planck observed the cosmic microwave background from there. Herschel revealed the infrared sky from there. In recent years, Gaia, James Webb, and Euclid have taken up residence as they casually change the way we view the universe (*sob* RIP Gaia). Many other observatories under construction will head for L2 when they’re done, including the next big one, the Nancy Grace Roman Space Telescope. And of course it’s where the ESCAPADE Mars spacecraft are (until late 2026) going to wait for Mars to get itself into a good position to head out on their mission. It’s a most useful spot in space!

 

L3

In our two-object system, L3 sits opposite the larger object from the smaller object. This means for the Sun-Earth Lagrange points, L3 sits on the other side of the Sun from Earth, just outside Earth’s orbit (due to the way the gravities combine). An object placed there would (you guessed it) orbit the Sun at the exact same rate as the Earth.

This means that if we put a spacecraft at L3, the Sun would always be exactly between it and Earth, blocking all communications. So L3 is pretty much useless. Let’s move on.

 

This diagram shows the collections of asteroids found at the Sun-Jupiter L4 and L5 points. Although all asteroids found in such places are known collectively as “trojans”, the ones at Jupiter’s L4 point are colloquially known as “Greeks” because they mostly draw their names from Greek figures of the Trojan War story, while the ones at the Sun-Jupiter L5 point are mostly named for Trojan heroes. Credit: Wikipedia Commons
This diagram shows the collections of asteroids found at the Sun-Jupiter L4 and L5 points. Although all asteroids found in such places are known collectively as “trojans”, the ones at Jupiter’s L4 point are colloquially known as “Greeks” because they mostly draw their names from Greek figures of the Trojan War story, while the ones at the Sun-Jupiter L5 point are mostly named for Trojan heroes. Credit: Wikipedia Commons

L4 and L5

In our two-body system, L4 and L5 share the orbit of the smaller object. If you picture the smaller object’s orbit as being about 360 degrees around, L4 is about 60 degrees ahead of the smaller object in its orbit, while L5 is about 60 degrees behind. In our Sun-Earth system, the direct distance to L4 or L5 is roughly the same as the distance from the Earth to the Sun, or about 93 million miles. 

There isn’t a particular advantage to putting a spacecraft in either of these locations—they’re much farther from Earth than, say, L2 without having a particularly better view of anything. They’ve been proposed as spots for far-future space stations, but that remains the realm of science fiction.

The Lucy spacecraft is on its way to Jupiter’s trojan asteroids and will visit both the “Greek” and “Trojan” camps during its mission. Credit: GSFC Conceptual Image Lab/Adriana Gutierrez
The Lucy spacecraft is on its way to Jupiter’s trojan asteroids and will visit both the “Greek” and “Trojan” camps during its mission. Credit: GSFC Conceptual Image Lab/Adriana Gutierrez

What is fact is that the L4 and L5 points of any two-body system are stable. Like…very stable. I know I said that all five of these points are points of equilibrium, and they are. But L1, L2, and L3 are points of what we call unstable equilibrium. It means if you park a spacecraft there, it will periodically need to give itself a push to stay there. So our spacecraft at L1 and L2 give themselves periodic thrusts with their engines, and any natural object, like an asteroid, that drifts into these points will eventually drift back out.

Not so with L4 and L5. Anything that drifts into an L4 or L5 point will stay there unless given a solid push to get out. Over the last 4.5 billion years, many asteroids have drifted into these stable points. Jupiter, with the might of its gravity combined with the Sun, has thousands of them. These are the Trojan asteroids that the Lucy mission is traveling to study. We’ve seen such Lagrange point asteroids associated with most of the planets. Even Earth is known to have a couple!

 

Points in Space

If there’s one thing I have learned to love about the universe, it’s when it throws us curveballs. I can only imagine Euler and Lagrange staring down at their sheets of equations and scratching their heads at the weird effects of combined gravities (and trying to tell their colleagues about them: “no, I swear, gravity actually does this! Look at my math and tell me I’m not crazy!”)

The particular quirks of gravity that are Lagrange points is something we’ve learned to make work for us in the best ways possible. No infrared telescope with the sensitivity of Webb would be able to function near Earth—Earth and the Moon are beacons of infrared light—but it functions perfectly well at L2. DSCOVR needs to have the unobstructed view of Earth provided at L1 in order to do its job. And the highly ambitious Lucy mission is certainly only possible because of the huge asteroid collections at Jupiter’s L4 and L5 points.

It’s wonderful when you can find a way to utilize those little universal curveballs. And who knows, maybe we’ll even come up with a use for the L3 point someday. Maybe.