Home on Lagrange

 In a big universe, where gravity makes the rules, finding stable locations is clearly an advantage. Here we take a look at Lagrange points, and their uses in science and SF.

[Note: while I'll mention Earth-Moon L-5 habitats briefly here, see my earlier blog on High Frontiers for more!]

In a static system with two large objects, the only point of gravitational balance lies on a line directly between them. However, nothing in our universe is static - conservation of angular momentum means that any two bodies in close proximity to one another are likely to be orbiting their centre of mass. In any system with orbital motion, the effect of centrifugal force is to balance the shared gravity of the two objects at not just one point but at five. The mathematics and physics of this was calculated by Joseph-Louis Lagrange in 1772 (building on earlier work by Leonhard Euler) and the five balance points share his name: Lagrange points.

• L-1 lies at the first balance point, between the two bodies.
• L-2 lies on the line between them, outside the smaller of the two.
• L-3 lies on the same line, outside the larger.
• L-4 lies sixty degrees ahead in the orbit of the smaller object, forming an equilateral triangle.
• L-5 lies sixty degrees behind the smaller object, also forming an equilateral triangle.

In theory, a comparatively small object (with negligible gravity of its own) can be sited at any of these points and will remain in place. However the first three points are unstable - any slight velocity mismatches or displacement from the point will result in forces which act away. L-4 and L-5 are relatively stable - any small displacement results in a force which returns objects to the point in question. In effect, L1-3 are hill summits. L-4 and L-5 are valleys into which objects can fall and come to rest. Anywhere in between, gravity acts like a hillside slope, preventing objects from coming to rest.

In practice, there are seldom precisely two significant bodies in a system - other planets (or stars, or other objects) will constantly perturb the orbits. The relative masses of the three objects will also affect how deep the valleys are, and how pointy the summits become. If the two large bodies are too similar in size (less than a factor of about 25), their tidal forces can destabilise the L-4 and L-5 regions. Stationkeeping at relevant Lagrange points (or more typically in orbits around them) is nonetheless typically easier than holding a fixed position anywhere else in a multi-body system.

Sun-Mercury and Venus

The Sun-Mercury Lagrange points are extremely unstable due to the significant perturbations from Earth and Venus. Unsurprisingly they seldom appear in science fiction. Robert L Forward’s Rocheworld (novel, 1984) nonetheless describes a significant possible use for them. Rocheworld begins with a crew leaving the Solar System to visit the planets orbiting Barnard’s Star. Their vessel is equipped with a lightsail and launched by a laser powered by a hundred collecting stations in Mercury orbit. The combiner for the laser is positioned in the Sun-Mercury L-2 point, protected from the worst solar flares (which could damage both equipment and personnel) and the most accessible local semi-stable point.

The Sun-Venus Lagrange points are similarly unstable, mostly due to the nearby influence of relatively-massive Earth. However Venus’s L-4 point has featured in a well known classic science fiction - George O Smith’s series of short stories collected under the title of Venus Equilateral. This follows a commercial venture of free-thinking scientists and engineers who occupy a space station on the lagrange point that forms an equilateral triangle with Venus and the Sun. This is a key location for their primary technological service: providing communications relays between the planets.

The nature and operations of the station are described in the first story QRM - Interplanetary (Galaxy, Oct 1942):

“Venus Equilateral Relay Station was a modern miracle of engineering if you liked to believe the books. Actually, Venus Equilateral was an asteroid that had been shoved into its orbit about the Sun, forming a practical demonstration of the equilateral triangle solution of the Three Moving Bodies. It was a long cylinder, about three miles in length by about a mile in diameter.”

After describing the contents, the logic behind its location at the Sun-Venus L-4 point is also explained:

“This was the Venus Equilateral Relay Station, sixty degrees ahead of the planet Venus, on Venus’ orbit. Often closer to Terra than Venus, the relay station offered a perfect place to relay messages through whenever Mars or Terra were on the other side of the Sun. It was seldom idle, for it was seldom that both Mars and Terra were in such position that direct communication between the three planets was possible.”

However the peace of the station is soon disrupted by an attempt to impose corporate ‘efficiency savings’ that soon put the whole station at risk.

While I’m not aware of any other major stories set at the Sun-Venus Lagrange points, an interesting example of their potential application can be found in Dawn Venus, a short story by G David Nordley, that appeared in Asimov’s in August 1995. This describes a man striving to obtain a land parcel on Venus in the hope of raising his son there. The background is a solar system in the advanced stages of colonisation, with Venus terraformed, settlements under construction on Mercury, and the beginnings of extrasolar colonisation, as well as effective immortality. Amongst the technologies which make this possible is one at the Sun-Venus L-1, as described from the perspective of the land-hunter.

“The sun was tiny by Bik’s Mercurian standards, and seemed to sparkle inside a broad, off-center ring of diffuse light. This, he realized, was the twenty-four-million-meter sunshield. His engineering imagination saw the vast structure balance gravity with constantly adjusted photon pressure the Lagrange point between Venus and the sun. A sun-sieve now, it let half the light get through to Venus and converted the other half to energy for starship ports and antimatter factories. His eyes saw a ghostly, sparkling disk, visibly larger and nearer than the sun, with edges that caught and reflected light in a grazing incidence that created the effect of the bright ring.”

Sun-Earth

Stories using the Sun-Earth Lagrange points are relatively rare, although becoming increasingly common now that the L-2 point (opposite Earth from the Sun) has become widely used for space telescopes studying the stars, and L-1 for studying the Sun.

An interesting example is Sunstorm by Arthur C Clarke and Stephen Baxter (novel, 2005). Here solar instability threatens Earth, and the solution adopted is to build a shield which is placed at the L-1 point to protect Earth against flares. This is not an easy task, and the sunshield is controlled by an AI to keep its light-weight mirrored fabric taught and angled against the solar wind.

[QUOTE]

The L-3 point behind the Sun appears in science fiction primarily as a location for Counter Earths, as I’ve discussed before, although in this case the stability calculation may break down, since the third body (the counter-Earth) is comparable in mass to the second (Earth itself), and perturbations from Venus are significant.

Earth-Moon

The Earth-Moon system is unusual in the Solar System in representing a large body with a single, large-but-not-too-large satellite, thus establishing relatively stable Lagrange points that are not too susceptible to perturbation from neighbouring objects. 

The L-4 and L-5 points of the Earth-Moon system are a classic location in science fiction for space habitats, as I’ve discussed before in the context of Gerard O’Neill’s influential non-fiction book The High Frontier (1976) and the novels of space colonisation inspired by it including Mack Reynolds’ Lagrange Five (1979), The Lagrangists (1983), Chaos in Lagrangia (1984) and Trojan Orbit (1985, written with Dean Ing).

An interesting modern example which explores this concept and navigating between the two stable Lagrange points is Kevin J Anderson and Doug Beason’s short story If I fell, would I fall? (Amazing Stories, Sep 1988, also known as Rescue at L-5). In this story, a war on Earth strands the nascent space colonies at both points, at a stage where they are still dependent on supplies. The story follows a pilot attempting a daring journey between a surviving L-4 colony called Aguinaldo and a desperate L-5 colony in an experimental craft to bring essential materials. This requires some careful manoeuvring:

“When we release you from the Aguinaldo, you will turn the sail so that it faces the Sun, taking the full momentum of the solar photons. You will then be moving ‘backward’ in orbit, relative to L-4. In about three hours, this will provide enough braking to slow you from our normal orbital velocity down to three kilometers per second. You must then turn your sail edgewise—you will drop like a stone toward Earth, skim past it at a distance of about an extra Earth radius, and then head back up to where you started.” On the stereotank a blue dashed line appeared, tracing Ramis’s planned trajectory. “But while you’ve been going down and coming back up, the Moon, L-4, and L-5 have been continuing their own orbits. By the time you return to the starting point, L-5 will be there instead of L-4.”

Such L-4 or L-5 habitats are now routine elements of solar system colonisation narratives, including modern examples such as The Expanse (novels by James S A Corey, 2011-2021; TV series, 2015-2022) and For All Mankind (TV series, 2019-). Authors including Stephen Baxter and Alexis Latner have suggested their further use for imagined space telescopes. The abundant L-5 narratives and the potential uses for high technology manufacturing in zero gravity and solar power also led Bill Higgins and Barry Gehm to create a science fictional rendition (i.e. filk) of the folk song Home on the Range, called, inevitably Home on Lagrange (first published 1978), which opens with a memorable first verse and chorus:

Oh, give me a locus where the gravitons focus,
Where the three-body problem is solved.
Where microwaves play down at three degrees K,
And the cold virus never evolved.

Home, home on Lagrange!
Where the space debris always collects.
We possess, so it seems, two of man’s greatest dreams:
Solar power and zero-gee sex.

However while L-4 and L-5 provide the most common examples, the other Lagrange points of the Earth-Moon system have also attracted attention.

The L-1 location, on a line directly between the Earth and the Moon, interested a writer for one of the earliest science fiction pulp magazines. Into Space was a short story by Sterner St Paul (aka. S P Meek) which appeared in Astounding Stories of Super Science in February 1930. In it, an inventor comes up with a device that acts as a negative pole of gravity (i.e. equivalent to the south pole of a magnet if normal gravity was the north). Using this as a propulsion device to venture into space for the very first time, he sends back a despairing radio signal.

“It is now thirty hours since I left the earth and I should be on the moon, according to my calculations. But I am not, and never will be. I am caught at the neutral point where the gravity of the earth and the moon are exactly equal.
I had relied on my momentum to carry me over this point. Once over it, I expected to reverse my polarity and fall on the moon. My momentum did not do so. If I keep my polarity as it was when I left the earth, both the earth and the moon repel me. If I reverse it, they both attract me, and again I cannot move. If I had equipped my space flier with a rocket so that I could move a few miles, or even a few feet, from the dead line, I could proceed, but I did not do so, and I cannot move forward or back.”

Unfortunately, in a warning of the dangers of adventurousness without thought, this is his last message, and it is discovered that Earth has acquired a new satellite.

In A Fall of Moondust (novel, 1961), Arthur C Clarke established a more deliberate space station at the L-1 point:

“Balanced here between Earth and Moon, in a cosmic tightrope act made possible by one of the obscurer consequences of the law of gravitation, the satellite was an astronautical maid-of-all-work. Ships passing in both directions took their fixes from it, and used it as a message center — though there was no truth in the rumor that they stopped to pick up mail. Lagrange was also the relay station for almost all lunar radio traffic, because the whole earthward-facing side of the Moon lay spread beneath it.”

More importantly for the plot of this novel, it is also home to a 100 centimetre infrared telescope which is diverted from its usual astronomical duties to search for a missing vessel on the lunar surface.

Not all uses of this point in fiction are so technical. The animated series Thunderbirds are Go (TV series, 2015-2020), set in a near-term future with routine spaceflight, visited Earth-Moon L-1 in the 2019 episodes “Signals (parts 1 and 2)” where, it is revealed to house the Midpoint Salvage Exclusion Zone - a dumping ground of space debris and recovered materials. As astronaut Alan Tracy notes:

“Because of the equal gravity pull from the Earth and the Moon, space junk that gets put here, stays here. But when it does try to float away… boom!”

A laser canon is used to vapourise any such escapee debris - and anything else that moves. While the series usually paid reasonable attention to scientific plausibility, using this fundamentally unstable point for storage makes a lot less sense than doing so at L-4 or L-5, although possibly it was seen as convenient for vessels to drop off material on route between Earth and lunar bases.

Uses of the Earth-Moon L-2 and L-3 points are less obvious. The latter is on the opposite side of Earth to the Moon, and at a comparable distance. Given how hard this point would be for humans to reach and its lack of obvious advantages, it has been largely ignored. L-2 lies above the lunar darkside and hidden from Earth. It is exactly this isolation which motivates its use in Murray Leinster’s City on the Moon (novel, 1957), where it hosts a scientific research space station exploring dangerous technologies out of sight of the people on Earth’s surface.

Sun-Mars

The Sun-Mars Lagrange points have stability limited by the influence of the relatively massive Earth not far inside Mars’ orbit, and the very massive Jupiter outside it. There are nonetheless a few examples of possible uses in both science and science fiction.

Perhaps the most attention has been paid to the Sun-Mars L-1 point. This is a logical site for any device intended to modify the impact of solar irradiation on Mars in order to improve its habitability for humans. Two possible technologies have been proposed to be sited here, and both appear as possible projects in the science fictional board game Terraforming Mars (2016), as well as in scientific and other literature. A soletta would be a mirror ring which directs a larger fraction of sunlight onto Mars’ surface than would otherwise hit it, increasing the temperature. By contrast a magnetic shield would be a device which diverts the solar wind as it passes through the L-1 point, causing most of it to miss Mars and so reduce the erosion of the atmosphere by constant high-energy particle bombardment.

Terraforming Mars also includes a project card for a "Lagrange Observatory", from which detailed measurements of the planet’s ongoing modification progress can be taken. The intended location of this is unclear but would most logically be sited at L-1 or L-2.

Elsewhere in science fiction, novels in The Expanse series (e.g. Tiamat’s Wrath, James S A Corey, 2019) mention characters from a “Mars Trojan” - most likely in this context to be an artificial space habitat at the Sun-Mars L-4 or L-5 Lagrange point.

Sun-Jupiter

Jupiter and the Sun are the two most massive objects in the Solar System. The first asteroids identified to lie at a Lagrange point occupy the relatively deep gravitational valleys formed by the L-4 and L-5 points of the Jupiter-Sun system. The first of these, identified in 1906, was asteroid 588 Achilles. This established a convention whereby these asteroids were given names from Greek myths of the Trojan Wars (largely Homer’s Illiad) and so these became known as Trojan asteroids or just Trojans. While it was quickly decided that those in the L-4 region should be named after Greeks and L-5 after Trojans, Patroclus and Hektor were named before this convention was devised and so exist as “spies” in their respective enemy camps. There are now over fifteen thousand large objects known in the Jupiter Trojans, with many smaller ones still lying below our capacity to detect. The term trojan point is now widely used to refer to any L-4 or L-5 gravitational minimum, and trojans to the objects orbiting within them.

Human exploitation of the Trojan asteroids has typically been overshadowed in science fiction by their neighbours in the asteroid belt (which orbits between Mars and Jupiter and so is closer to Earth). They nonetheless appear in a variety of asteroid mining and solar system colonisation narratives and as another possible stop-over point on journeys towards the outer solar system, as, for example, in Poul Anderson’s Out of the Iron Womb! (aka Holmgang, Planet Stories, Summer 1955), which is set on and near asteroid 588 Achilles, or the novels of The Expanse series.

Given the gravitational stability and the number of objects in these relatively small regions, the Jupiter Trojan points may also be a logical location for alien fleets to regroup after entering the solar system. This was actually a key plot point in the 1990s television series Space: Above and Beyond (TV, 1995-1996). This military science fiction follows a squadron of pilots fighting battles on two fronts, against a poorly-understood alien race known as Chigs and against human-built AI androids known as Silicates. In the series’ feature-length pilot episode, the initial incursion of the Chigs into the Solar System was held and repulsed by a group of inexperienced pilots known as the Wildcards in a devastating Battle of the Belt, which actually took place in the Jupiter L-5 Trojans.

“For the next hour, here’s your best chance of staying alive.” McQueen’s lip twisted and his head shook slightly as if he were battling a seizure. “The Trojan asteroid belt trails Jupiter’s orbit. Our objective is to hide in the debris. This may be as difficult as engaging the enemy. You’re gonna have to react to the pitch and yaw of the asteroids in order to keep out of sight and shielded from whatever kind of LIDAR the aliens are using. Intelligence says they’ll fly right by.”

“Sir, I don’t understand, sir. We’re just going to hide from them?” Low asked. 

“Marines hide? I don’t think so. Once they’re by you, ambush them.”

- Extract from novelisation Space: Above and Beyond (novel, 1995) by Peter Telep, based on a script by Glen Morgan and James Wong.

This event continues to have repercussions throughout the series, and establishes the Wildcards as a new elite squadron. Another military engagement in the Jupiter Trojans can be found in The Expanse (TV episode "Winnipesaukee", 2021) where a conflict took place between human fleets near the greek spy asteroid 618 Patroclus.

A number of other authors have noted the Jupiter L-4 and L-5 points’ relatively stability in the solar system. In particular, they may be useful for anything which requires comparative stability over long time periods. Oliver Morton made use of this in his short fiction piece The Albion Message which appeared in Nature magazine’s Futures section (which publishes a one-page stand-alone story each week) on 30th Nov 2005 (and later anthologised). His story imagines a code embedded in Earth-animal DNA by ancient aliens, which points to a pyramidal structure that is eventually found by the (real-world) Square Kilometer Array radio telescope. Since these aliens visited Earth more than 100 million years ago, the Sun-Jupiter Trojans presented a logical location which would be both stable, reasonably distant from solar or planetary activity, and reasonably obvious to intelligent searchers at a later date.

The Lagrange points between Jupiter and the Sun span a large fraction of the Solar System, but Jupiter also has a system of its own in miniature. This is seldom discussed, given the complexity of the tight-packed moon system (in which the moons are of comparable mass and so disrupt one another’s Lagrange Points) and the vast impact of Jupiter’s strong magnetic field and its tidal effects. However an interesting example can be found in A Deeper Sea (short story, Asimov’s Oct 1989) by Alexander Jablokov. This story describes the recognition by humans of cetacean (i.e. whale and dolphin) intelligence, and the establishment of communications between them. This culminates in a mission in 2033 to see whether a cyborg sperm whale can navigate in Jupiter’s atmosphere. The research is carried out from Jupiter Forward, a space station in the Jupiter-Ganymede trailing (i.e. L-5) Lagrange point.

The Outer Solar System

Perhaps unsurprisingly, trojans of the outer solar system rarely appear in science fiction. The perturbations caused by Jupiter and the more elliptical orbits of the outer planets tend to disrupt their stability more easily (although trojan asteroids are now known for most planets). Saturn, Uranus and Neptune all have known trojan asteroids (although only one in Saturn’s case and 2 in the case of Uranus). Many of Neptune’s are likely to be originally Oort cloud objects, captured on their way in towards the Sun on cometary orbits.

In science fiction, an example of the rare use of outer solar system trojans can be found in the opening of The Adults by Larry Niven (novella, Galaxy, June 1967), which was later expanded by Niven into his 1973 novel Protector. Here a prospector is exploring asteroids in the Uranus-Sun L5 point, looking for radioactive ores, and finds an ancient space probe, Mariner XX, which he photographs in situ and then collects to sell to collectors of spaceflight memorabilia:

“The Mariner XX, the ancient Pluto fly-by. Ages ago the ancient empty shell must have drifted back toward the distant sun, hit the thin trojan-point dust and coasted to a stop. The hulk, lightly pitted with dust holes, was still rotating with the stabilizing impulse imparted three generations back.”

However plans to exploit this potentially rich find are put on hold by the arrival of an alien spacecraft.

Extrasolar Lagrange Points

The geometry which gives rise to the five Lagrange points of relative gravitational stability will apply in any system in which two large bodies exist, although their stability depends on the relative mass of the two objects, their separation, the mass of the object at the Lagrange point, and the presence of any other nearby objects.

Perhaps naturally, a number of science fiction narratives have considered Lagrange points in other solar systems. Some of these fit the familiar pattern of space habitats seen in Solar System fiction. The space station Babylon 5, from the 1994-1998 television series of the same name, for example, is canonically at the L-5 point between Epsilon Eridani and its planet Epsilon Eridani III, and the series uses hyperspace jumpgates located at other lagrange points. In other cases, as in Poul Anderson’s Admiralty (short story, 1965, incorporated in novel The Star Fox), they act as convenient locations for spaceships either to rendezvous or hide while expending minimum power to avoid detection.

A more interesting use of the Trojan points can be found in Hal Clement’s short story Trojan Fall (Astounding, June 1944). This centres on a criminal called La Roque fleeing the Solar System in a private ship. In search of another world, he ends up in a binary system of two red dwarf stars (as I discussed in Scarlet Skies). On a previous escapade, he had hidden on the Jupiter asteroid Hector. Attempting to do the same and get some rest, he places his ship at the trojan point of this binary system. Unfortunately for La Roque, these stars are close to equal in mass and the orbit isn’t stable due to tidal forces. As the navigator of a patrol ship coming across the end result of this decision notes:

“But I have never seen a binary star where the mass ratio was anywhere near twenty-five to one; and if it’s less, the Trojan solution to the three-body problem doesn’t work. Don’t ask me why; I couldn’t show you the math; but I know it’s true — the stability function breaks, with surprising sharpness, right about the twenty-five-to-one mass ratio. Our elusive friend didn’t know that, any more than you did, and parked his ship right in the path of a rapidly moving sun.”

Other authors have been more creative. An L-1 point appears in the recent Star Trek: Discovery episode “Lagrange Point” (2024). The series arc involves a search for technology left behind by the ancient race known in the Star Trek universe as The Progenitors, who seeded life that gave rise to many intelligent species on different worlds. In this episode, the large progenitor artefact being sought proves to be located at the L-1 point directly between two black holes. This location acts both to stabilise the cache against outside forces and to act as a test of the technology level of anyone trying to reach it.

L-1 also interested Stephen Baxter in his three linked stories under the umbrella title The Saddle Point Sequence (Science Fiction Age, July 1996) which explore the first contact between humans and an alien race called the Prion who are capable of establishing gateways between solar systems. These have to be sited at gravitational balance points in the target system. In the third part, Fusion Summer, humans are negotiating for a new gateway, to be established under Earth control, between our Solar System and a binary in which a neutron star is accreting from a white dwarf. The person making the decision rejects the apparently obvious L-4 or L-5 points:

 “This system must have a Saddle Point on the line between the neutron star and its parent — somewhere in the middle of that column of hydrogen attracted from the primary.”

“Of course.” She looked at me suspiciously. “There’s a gravitational equilibrium there, the LI Lagrange point.”

“That’s where I want the UN gateway, Brind.”

She looked thoughtful — no, rather her face emptied of expression, and I imagined mips being diverted to the data channel connecting her to the Prion. “But LI is unstable, Meacher. It would be difficult to maintain the gateway’s position. Anyway, there would be a net flow of hot hydrogen through the gateway, into the transmitter at the Solar System end. We won’t be able to use the gateway for two-way travel.”

In stellar binary systems, with two stars typically in the mass ratio range 1-10 (as would be the case for a neutron star and a class F dwarf), the Lagrange points continue to exist, but tidal forces disrupt the stability of L-4 and L-5, and the L-1 point is notable for being on the path of any material overflowing from one star onto the other, as discussed in the comment above. In fact, this initially puzzling choice proves to be part of a deliberate strategy: a limiting factor in human space expansion in this narrative had been the shortage of accessible hydrogen gas in the outer Solar System.

Lagrangian Futures

The ongoing interest from both the scientific and science fiction communities springs from a range of factors. The mathematical elegance of Lagrange’s solutions to the three body problem remains, despite their limited range of applicability as stable points. The profound effect of these solutions on shaping the Solar System was demonstrated by the discovery of Jupiter’s Trojans, and trojan asteroids have now been located in the orbits of every major planet except Mercury, in the orbits of the dwarf planets Ceres and Vesta, and in the moon system of Saturn. Their scientific uses have been demonstrated by astronomers, who have now sent satellite missions to every Earth-Sun Lagrange point except L-3, and to the Earth-Moon L-2 point (with other missions planned).

Their potential for use by human spaceflight and colonisation may not have been demonstrated practically, but nonetheless is clear and has been extensively explored both in fiction and in serious scientific and technical design studies - and indeed by the many texts which skirt the boundaries between the two categories. Creative scenario building is a recognised area of long term planning in both military and civil spheres, and for the Earth-Moon L-5 in particular, fictional thought experiments have explored many of the potential consequences for (and barriers to) human colonisation. Similarly, our constantly growing understanding of the trojan and Lagrange points of our Solar System have shaped the evolution of science fiction stories which use them, modifying the descriptions of these locations, and spreading an understanding of interplanetary dynamics to a broader audience than it might otherwise have reached. For authors interested in giving their narratives scientific plausibility and an authoritative voice, the use of the Lagrange points is a clear advantage over higher technology but less plausible solutions for station-keeping and base construction.

While imaging the Lagrange points in extrasolar planetary systems lies outside our current capabilities, the first candidate trojan masses have been tentatively identified within the last few years. Such studies have the potential to give insights into planet formation processes. Collision between the proto-Earth and a planetoid dubbed Theia, forming at an Earth-Sun trojan point and perturbed by Venus or Jupiter, is a suggested mechanism for the formation of Earth’s unusually large moon, for example. Such lessons will inevitably affect our estimates for habitability in the Universe, particularly given the impact of the Moon on Earth’s seasons and long-term stability.

Lagrange points, and particularly the relatively stable trojan points at L-4 and L-5, will no doubt continue to interest both scientists and writers and readers of science fiction over the coming years. And perhaps, if human spaceflight ever becomes commercially viable, humans will one day be truly at home on Lagrange.