Exocosmonautics and Lagrange points or stay away from super-Earths
Romantic science fiction of the 20th century, and even more so space operas, apparently hardly took into account the factor of significant differences in gravity between different planets on which one has to occasionally land or colonize them. As I have already written in several publications, especially “The Super-Earth as an Illusion” and “The Hykeans, Descendants of the Neptunes,” we are currently so obsessed with the idea that among exoplanets there will be many habitable or even habitable ones, that in the place of a mini-Neptune we are always ready to see a super-Earth . However, such a misconception is not unique to our time. Even at the beginning of the 20th century, Venus was considered the “young sister” of the Earth (since it was assumed that the closer the planet is to the Sun, the later it was formed), that a tropical era similar to the Mesozoic could reign there, exotic forests rustle, and vast oceans… Due to strong mineralization, they can be filled with “seltzer water”. The climate of Venus and its greenhouse effect is a topic for a separate publication, and for now I will limit myself to a link to This A 2019 study hypothesizes that the runaway greenhouse effect on Venus has existed for only just over 700 million years, and before that, conditions could have existed there that were quite comfortable for life. And in this article we will try to discuss the phenomenon of gravity wells and their danger when approaching super-Earths. I would especially like to thank the respected @ilmarinen for his interesting publications about gravity maneuvers in the now closed MacLeod corporate blog, under the impression of which I began to write this article.
This diagram from seven years ago most clearly demonstrates how the exoplanets discovered by Kepler are distributed by mass and type. Transit method imposes limitations, but the general picture is that the Galaxy is dominated by Neptunes and mini-Neptunes, perhaps with a significant proportion of super-Earths, and rocky planets are quite rare (if not in absolute terms, then at least in relative terms). Accordingly, planets much larger than Earth predominate, and the location of the planets relative to each other in different planetary systems also suggests that the configuration familiar to us from the Solar System (small rocky planets located closer to the star, cold and icy gas giants located beyond the snow line) is rare . It often happens that hot Jupiters are close to the star and therefore can complicate the formation of rocky planets, leaving several asteroid belts in the outer parts of the system. Here's a more recent chart on the relative number of exoplanets discovered as of 2022:
But the dataset collected by the Kepler and TESS telescopes reveals a number of common features that most star systems share:
At the center of the system there are one, two, or less often several stars.
Some planets are close to the star, and it is in this part that the “habitable zone” may be located (where liquid water can exist on the surface of the planet)
Behind the nearby planets there is a snow line, where volatile substances are constantly in the solid phase and can cover stone blocks. Therefore, most systems are characterized by the presence of one or more asteroid belts
Behind the snow line there are several cold gas giants, in which mainly those remnants of hydrogen and its compounds that did not go into the formation of the star have accumulated
Behind the gas giants lies a vast outer belt of icy bodies, reminiscent of the Kuiper Belt.
At the far outskirts, the entire system is surrounded by a spherical region resembling an Oort cloud. From there, comets fly into the inner part of the system
It can already be assumed that most stellar systems are characterized by gravitational heterogeneity and unpredictability. In a system where the gas giants are located both close to the star and behind the snow line, many randomly located Lagrange points should form, and winding gravitational corridors should arise along which it would be possible to cruise between these points. Colonization of Lagrange points is a separate topic, which I hope to return to in one of the following articles. Nevertheless, it is logical to assume that settling Lagrange points in new star systems would be safer than immediately trying to colonize promising exoplanets.
Gravity corridors
The study of gravitational corridors in the Solar System is closely related to the planning of gravitational maneuvers. The gravity maneuver, also called the “gravitational slingshot effect,” allows you to save fuel on a spacecraft by bringing the vehicle closer to a large planet in a controlled manner and “throwing” it in the desired direction, taking advantage of the centrifugal force of the planet. The idea that this phenomenon existed and how it could be used was first formulated Friedrich Arturovich Zander and Yuri Vasilyevich Kondratyuk back in the late 20s – 30s of the XX century. The most famous gravity maneuver was used for acceleration of Voyagers, who have now left the solar system. Here is a well-known diagram illustrating the pattern of gravitational maneuvers in our system:
In 2009, Stefan Jerg, Oliver Junge from the Munich Institute of Technology and Shane Ross from Virginia Tech assumed, that a spaceship can move along gravitational corridors on approximately the same principle as a sailing ship used ocean currents. In this case, long-distance space travel can be significantly reduced in cost.
Below is a computer model describing the gravitational corridors of the Solar System, one of the frames of which I have given.
In this model, gravitational paths look like flexible tubes stretched between planets and satellites. These corridors connect Lagrange points at which a relatively small physical body (a spaceship, a space station or even a space city) will be motionless relative to two large celestial bodies, since at this point their mutual gravitational influence nullifies the centripetal and centrifugal forces. According to Shane Ross, relative to the surrounding space, these corridors are clearly low-energy, so a physical body that accelerates into such a corridor seems to “fall” from one Lagrange point to another. This is the essence of the gravity maneuver.
Since the system of satellites of the giant planet is similar to a “solar system” in miniature, there is no doubt that such satellites also have their own Lagrange points. If these points can be mapped both in the Solar System and around the extrasolar giant planets, then it will be possible to move between them with minimal energy and fuel consumption (some fuel will be needed for maneuvers associated with course correction), without falling into the gravitational zone the giant himself.
You can't fly away from super-earth
Thus, the primary targets for colonization in new star systems in the future may be Lagrange points, and not rocky planets. The properties of Lagrange points in the vicinity of a red or yellow dwarf or a large planet (gas giant) should, in principle, be known and predictable in any star system. Super-Earth, in turn, is a much more dangerous place (even excluding such fantastic fears that it could be inhabited by warlike intelligent beings that have not yet entered space, or have extremely hostile biosphere). But we are, naturally, interested in a super-Earth with a dense atmosphere, and such a super-Earth can be mistaken for either a mini-Neptune or a Hykean.
In this case, we are interested in a specific physical dependence, which may even bring us closer to resolving the Fermi paradox. It turns out that, despite the repeatedly proven validity of the principle of mediocrity, the prospects for the transformation of any civilization into a cosmic one are directly related to the values of the second and third cosmic speed in a given star system. The second escape velocity is the speed required to escape the planet's gravity. The third escape velocity is the speed required to escape the gravity of the star. On Earth, the second escape velocity is about 11.2 km/s, and the third escape velocity is 16.65 km/s.
On Earth, exactly the conditions have arisen under which the second escape velocity is relatively small, which is quite achievable on a chemical engine of the size that Sergei Pavlovich Korolev could design. But as the radius of the planet increases, the second escape velocity also increases, and the volume of fuel required to launch a spacecraft into orbit increases exponentially.
Orbital radii and velocities using the example of TRAPPIST-1
This illustration shows that, depending on the temperature and spectral class of the star, the habitable zone and snow line in its system of the corresponding star shifts. It is in a red dwarf system, such as TRAPPIST-1, that the habitable zone is located almost close to the star.
As shown in this diagram, TRAPPIST-1 has two planets in its habitable zone, 1d and 1e (with 1d being about 300 times lighter than Earth, possibly meaning it does not have an iron core). Therefore, the second escape velocity on these planets should be small. However, TRAPPIST-1d is 45 times closer to its star than Earth is to the Sun. Therefore, the third escape velocity when launching from the TRAPPIST-1d orbit (adjusted for the fact that the red dwarf TRAPPIST-1 is smaller than the Sun) is 85 km/s.
According to Tsiolkovsky's formulawhich he introduced in 1903, an increase in the speed that an aircraft develops under the influence of the thrust of a rocket engine (final speed), leads to an exponential increase in the volume of fuel required to reach this speed. When using this liquid oxygen-methane mixturewhich is included in the Starship design, exiting TRAPPIST-1d orbit into interstellar space will require approximately a million times more fuel than exiting Earth orbit.
Thus, if a technological civilization were to develop on an Earth-like planet near a red or orange dwarf, its physicists and engineers might find space or even orbital flight unfeasible. But, if in the case of TRAPPIST-1 insurmountable problems arise only with the third cosmic speed, it may not be possible to escape from super-Earths even to the nearest planets in their own star system. Elio Quiroga, a professor at the Universidad Atlántico Medio (Las Palmas, Spain), tried to study this problem quite recently (in February 2024).
He constructed a graph in which the second escape velocity relates to the mass of the planet. According to modern estimates, most super-Earths should be 10 or more times more massive than the Earth, but even if we find ourselves on a planet 4 times larger than the Earth, it is not possible to fly away from it on an Earth spaceship. Even if the ship has sufficient supplies of very compact antimatter fuelwhich I hope to touch on in a future article, the spacecraft will probably not withstand the overload.
Quiroga in his work tried to calculate the escape coefficient from an exoplanet (Fex) and exoplanetary escape velocity (Vex.) For Earth it takes the value Fex equal to 1. At the same time, the window of opportunity for the development of astronautics turns out to be even narrower than the range of values in the above graph. At Fex <0.4 the planet is unlikely to be able to retain an atmosphere, and at values of Fex > 2.2 It is not possible to fly away from the planet – the point is not only that this would require too much fuel, but also that the space rocket would not withstand its own weight. Quiroga believes that intelligent inhabitants of a super-Earth would be convinced purely mathematically of the impossibility of space flight, and therefore would hardly come up with the idea of SETI or another form of interplanetary contact.
At the same time, there is also the factor of the powerful atmosphere of the super-Earth. It can extend tens of times higher than the Earth's atmosphere, and can also be denser, windier, and laden with vapor. In this case, an earthly ship risks burning out in the dense layers of such an atmosphere, without even penetrating the lower boundary of the clouds.
Here is a table of values calculated by Quiroga for some of the planets discovered by Kepler.
About the dimensions of alien spacecraft
This problem is considered from another angle in article Michael Hippke, astrophysicist from Sonneberg Observatory in Thuringia. He looked at how feasible it would be to launch a spacecraft from Kepler-20b, a super-Earth located 922 light-years from the solar system in the constellation Lyra. This planet is probably a super-Earth, and not a mini-Neptune, it is about 10 times heavier than the Earth, the second cosmic speed on it is 2.4 times greater than the Earth's. According to Hippke's calculations, putting a 6.6-ton satellite into orbit on this planet would require more than 60,000 tons of fuel, this displacement of a medium aircraft carrier. To launch a ship with 50 tons of cargo on board, as in the Apollo mission, it would have required 440,000 tons of fuel, and the rocket itself would have been comparable in size to the Egyptian pyramids.
Hippke believes that on a watery super-Earth, which we would call an ocean planet, it would be difficult to obtain sufficient quantities of not only fuel, but also metals, which cannot be returned as a result of launching from orbit (see above about the atmospheric factor). On the other hand, the predominance of the ocean over land could lead to the fact that super-Earthlings would come up not with rockets, but with a space elevator installed on a vast and relatively light floating platform.
All of these factors can be disappointing explanations for the Fermi Paradox. Perhaps most technological civilizations, if they exist, simply do not come up with a formula similar to the Drake equation, nor the idea of SETI.
Conclusion
I will try to summarize the following set of considerations that would be useful to our civilization when colonizing other star systems.
It is possible to colonize red dwarf systems only if there are sufficient reserves of high-energy fuel, or when using zero-transportation, since the third escape velocity in the habitable zone of such stars is too high
In the solar system, you need to learn how to build long-term bases at Lagrange points, and then look for such points in other star systems as priority targets for settlement
It is almost impossible to fly away from a wild planet-ocean after we land on it (find an island) or splash down
It is difficult to land on super-Earth, so to develop super-Earths it is necessary to master the technology of the lightest possible space elevator, unwound from orbit or from a satellite
Cosmonautics is a rare privilege given to human civilization
