Given the current level of technological development, colonizing other planets seems extremely dangerous and pointless, regardless of the level of technical and financial investment. It is possible to imagine the creation of long-term bases on Mars, as well as the approximation of Martian conditions to Earth's, according to James Green's plan. Nevertheless, the colonization of Mars, Venus, and Titan are extremely dissimilar projects, and we still have a lot of problems even with the colonization of continental Antarctica. On the other hand, we know how to build orbital stations, so colonizing outer space currently seems even more promising than any “soft terraforming” that borders on ecological disaster for the world whose homeostasis we are trying to interfere with.

I think orbital stations can be modular and expanded almost indefinitely. If such technologies can be developed, then Lagrange points, rather than planets and satellites, will prove to be no less promising for long-term space settlements. I will discuss them in more detail below.

Lagrange points are a phenomenon of celestial mechanics; they are also called “libration points.” They arise because in a system of stars and much smaller bodies (satellites, planets, asteroids), any orbit does not occur around the star itself, but around a common center of mass. Despite the fact that in the “Sun-Earth” system this center of mass almost coincides with the Sun itself, in any such system exactly five points are formed in which the mutual attraction of two bodies cancels each other out, and a sufficiently small object (the size of dozens of asteroids or a large city) can revolve around the center of mass at approximately the same angular velocity as two massive bodies. As a result, it will remain virtually motionless relative to these two objects.

Celestial mechanics of Lagrange points

Centrifugal forces arise because an object, once set in motion, tends to move in a straight line rather than in a circle. Calculating centrifugal forces is an important aspect of solving the “three-body problem,” which Joseph Louis Lagrange worked on at the end of the 17th century. It was not Lagrange who first guessed the existence of points with such orbital equilibrium, but Leonhard Euler. He wrote about “collinear points” that are located on the same line and are three of the five Lagrange points. There are five libration points in the Sun-Earth-Moon system.

The first Lagrange point (L1) is located approximately halfway between the Earth and the Moon. If there were a space station at this point, it would repeat the phases of the Moon, i.e., the months on it would be synodic. Although all orbital forces at the Lagrange point are zero, this equilibrium is unstable. If a body at the Lagrange point deviates to the left or right, the combined gravitational pull of the Earth, Moon, and Sun will quickly return it to its place. However, if it shifts even slightly toward the Earth or the Moon, the gravitational pull of the planet or satellite will prevail, and the structure will fall toward the Earth or the Moon at an accelerated rate.

The second and third Lagrange points (L2 and L3) are also located on a straight line connecting the Earth and the Moon, but L2 is far beyond the far side of the Moon, and L3 is at the same distance on the other side of the Earth, i.e., in the opposite direction. At these two points, three forces cancel each other out: the Moon's gravitational pull, the Earth's gravitational pull, and centrifugal force.

As far as we can tell, points L2 and L3 are much “wider” than L1. In the event of a “slip” away from point L2 or L3, it would be easy to detect and activate engines that would return the spacecraft or station to a stable position. The diameter of points L2 and L3 is about 800,000 kilometers each.

While points L1, L2, and L3 can be considered conditionally stable, points L4 and L5 look much more promising. Both are located in the plane of Earth's orbit and rotate with Earth. One of these points is 60° ahead of Earth, and the other is 60° behind it. Together with Earth, these points are located at the vertices of two equilateral triangles, each of which has the Sun, Earth, and one of the Lagrange points as its vertices.

Two more planets similar to Earth could be located at the Lagrange points L4 and L5, and, theoretically, such a structure could even be created artificially. However, while towing a planet to a specific point in orbit is still the stuff of science fiction, there are no fundamental obstacles to placing an orbital station at a Lagrange point.

Newton formulated the laws of gravity and celestial mechanics at the end of the 17th century, summarizing and rethinking Kepler's laws. One of the most famous problems in celestial mechanics is the N-body gravitational problem, as well as its special case, the three-body problem. It describes the gravitational interaction of three bodies under conditions of mutual attraction and, naturally, is applicable to any bodies at Lagrange points. The three-body problem in its general form was most thoroughly studied by Henri Poincaré at the end of the 19th century, and Poincaré concluded that it has no general solution. Indeed, so far, the three-body problem has not been solved mathematically, but only statistically. Partial solutions to the three-body problem were found by Leonard Euler in 1765. In the three-body problem, we are dealing with a coordinate system for co-rotating bodies.

The coordinate system shown here for co-rotating objects allows us to track the movement of Lagrange points relative to each other and relative to the three bodies themselves.

The exact solutions proposed by Euler made it possible to determine the positions of points L2 and L3. Since L3 is always on the other side of the Sun relative to Earth, at various times there have been ufological hypotheses about the existence of a “Counter-Earth” at this point — a planet no less habitable than Earth itself, but reliably hidden from astronomical observations. Such ideas were finally debunked only with the development of coronagraphs, but they pushed scientific research in the right direction. Apparently, large objects cannot remain at the L3 point for long, but the L4 and L5 points would be very useful for us in the future for setting up long-term space bases.

L4 and L5

In general terms, the creation of a long-term colony at a Lagrange point no longer seems unfeasible. If mineral extraction on asteroids is mastered, the materials needed for development can be towed not to Earth, but to a Lagrange point. Since there is no natural gravity there, during the construction phase of the station, it will be possible to lay huge structures (tens of kilometers in diameter) with virtually no consideration for material resistance. Artificial gravity similar to Earth's can be created at the station after it is completed by spinning the structure around its axis.

Such projects at the intersection of futurology and science fiction have been discussed since the 1960s. Apparently, the idea of placing a large man-made structure at a libration point was first proposed in 1961 by Arthur C. Clarke in his novel A Fall of Moondust. At the same time, he considered the colonization of the L1 point. In 1945, he first calculated the point at which it would be possible to place such an artificial Earth satellite that would complete a daily rotation around the Earth in 24 hours and, accordingly, coincide with the planet itself in this indicator. He described this project in the article “EXTRA-TERRESTRIAL RELAYS Can Rocket Stations Give World-wide Radio Coverage?”, considering such a station as a radar station rather than an inhabited settlement. Indeed, such an orbit exists purely mathematically. For example, the International Space Station orbits the Earth in about an hour and a half, while an object near the Moon would do so in about a month. According to Clark's calculations, an object located at an altitude of about 38,000 kilometers above the Earth's surface would complete a “24-hour orbit.” This is a geostationary orbit, which in 2021 had about 500 active satellites.

In 1975, space enthusiasts Keith and Carolyn Henson founded the L5 Society. This organization quickly gained notoriety thanks to the interest of Princeton University physicist Gerard O'Neill, who debated the creation of cylindrical space settlements.

The charter of the L5 Society stated that the organization should be dissolved at a general meeting of members at the L5 space station, thereby acknowledging that the Society's mission had been accomplished. In 1987, the L5 Society merged with the National Institute of Aeronautics and Astronautics.

Today, the exploration of the L4 and L5 Lagrange points is of interest mainly to telecommunications companies. These points are also priority outposts in the event of the emergence of space weapons. Satellites located at L4 and L5 could transmit signals simultaneously to Earth and the Moon. Lagrange points are calmer places than even geostationary orbit, with less stringent requirements for maintaining a station at a fixed point. In addition, geostationary orbit is already becoming too crowded, so during the 21st century, the deployment of new satellites will have to begin at Lagrange points — at least at L1. Currently, L4 and L5 are being considered as locations for positioning, navigation, and timing (PNT) systems, as well as platforms for patrolling geostationary orbit (SSA). In addition, space observatories could be installed at L4 and L5 for early warning of magnetic storms and approaching asteroids.

Naturally, this gravitational stability has led to the Lagrange points already being full of space debris (of natural origin). In geosynchronous orbit, mutual attraction between active and decommissioned satellites is already creating so-called “geopotential wells.” A similar phenomenon is observed at points L4 and L5, because many small stones, space dust, and asteroid fragments have accumulated in these areas. Modern telescopes have made it possible to detect clusters of natural space debris at points L1, L4, and L5, named “Kordylewski clouds” after the Polish scientist Kazimierz Kordylewski, who predicted their existence in 1956.

The existence of such clouds at points L4 and L5 was only definitively confirmed in 2018. The confirmation was obtained at a private Hungarian observatory headed by Judit Szlisz-Balogh, which means that Earth has at least two dust satellites, each about 10,000 kilometers in diameter. The cloud in the L5 region appears to be stable and ancient, but it is still difficult to analyze the approximate size of the fragments in it, as the clouds are very dim. On the one hand, such clouds can be very dangerous for long-term stations at Lagrange points. On the other hand, such clouds should facilitate the search for Lagrange points near other planets in the solar system and therefore deserve further study. Apparently, such clouds formed in the Sun-Neptune (Neptune's Trojan asteroids) and Sun-Mars (Mars' Trojan asteroids) systems.

What is currently located at Lagrange points

A list of objects located at Lagrange points is provided on Wikipedia. Currently, only the points closest to Earth (L1 and L2) are being explored, but I will discuss them in more detail here. Currently, an impressive array of equipment is accumulating at the Lagrange points in the Earth-Moon and Earth-Sun systems, and artificial satellites in these areas are clearly more noticeable than space dust. So.

At point L1 are:

They will be joined by the IMAP space observatory, scheduled for launch in September 2025, as well as the SWFO-L1 and NEO Surveyor spacecraft, which are expected to begin operations in 2027. The scientific objectives of these devices are to take space photographs of the Earth, study solar wind, and observe Earth's weather from space. Most of the devices are not stationary, but revolve around the Lagrange point in a Lissajous figure orbit. This movement not only increases the satellite's field of view, but also copes with gravitational instability, which causes objects to gradually slip out of the L1-L3 near-Earth points.

The following are currently located at the L2 point between the Sun and Earth:

In addition, these devices are currently providing a wealth of information about the movement of comets and discovering exoplanets.

Prospects

The Lagrange points L4 and L5 are not yet being purposefully explored. The trajectories of the OSIRIS-Rex and Hayabusa spacecraft passed by them. The European Space Agency plans to launch the Vigil spacecraft in 2031, which will be sent to the Lagrange point L5. It will observe solar flares, coronal mass ejections on the Sun, geomagnetic storms, and other heliophysical phenomena. The prospect of deploying relay transmitters at Lagrange points, as I mentioned above, also remains relevant.

In 2012, NASA announced plans to deploy a manned space station at the L2 point. The station had the working name “Gateway Spacecraft”. Below, you can see its general appearance:

Since point L2 is located behind the far side of the Moon, it was assumed that such a station could simplify observation of the lunar hemisphere invisible from Earth, assist in the study of asteroids, and serve as a transit point on the way to Mars. However, the project now appears to have been abandoned, as it would be difficult to supply such a station with the current level of technology, and towing asteroids to the station or to Earth remains in the realm of science fiction from both a scientific and industrial point of view. It is more likely that the first inhabited lunar station will be built on the moon itself, rather than near its orbit.

Despite all the difficulties, Lagrange points seem to be the most convenient outposts for exploring the solar system — probably only for unmanned missions. Points L4 and L5 are far beyond the Earth's magnetosphere, so their inhabitants-colonists would be defenseless against solar wind streams with the current level of technology. In addition, solar flares could sever communication with such distant colonies for a long time, which would most likely put an end to their work. However, Lagrange points in any planetary or satellite system are quiet havens with well-known and predictable properties, so there is no doubt that they would be easier to colonize than planets or satellites. Of particular interest are the numerous Lagrange points that must exist between the satellites of giant planets; it would be most convenient to study Jupiter and Saturn from these points.