Each planet in the Solar System orbiting the Sun has Lagrange points, the most famous of which in the case of Earth is L2, where the James-Webb telescope is in orbit. However, in L4 and L5 must also be able to find the equivalent of the asteroids that we call Trojans, as in the case of Jupiter. Astronomers have long been left empty-handed searching for them, but today a second Earth Trojan has finally been discovered.
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[EN VIDÉO] Lucy, the new NASA probe that will explore the Trojan asteroids On October 16, NASA will send its new probe, Lucy, into space. The device will head for Jupiter to study asteroids orbiting in the same orbit as the gas giant, called “Trojans”. The studies carried out by Lucy will make it possible to learn more about the history of the solar system.
the great mathematician Henri Poincaré thought to have shown a little more than a century ago that it was not possible to find a general analytic solution describing the orbits of three bodies, unlike the case with two bodies completely solved by Newton with elementary functions. It was therefore necessary to stick to integration techniques digital from equations different from these predecessors.
In fact, he was wrong as shown from the beginning of the XXand century, the mathematician Karl Frithiof Sundman. The general solution exists but when one wants to use it, the necessary calculations are very long and slow to execute. The arrival of computers after the Second World War will also change the situation by allowing numerical integration methods to show their power, such as the Nobel Prize Richard Feynman shows it well in his freshman physics class.
In any case, there were already exact but specific analytical solutions to the three-body problem, the best known of which is of course that of Joseph Lagrange. From the XVIIIand century, he had shown that he always existed for two bodies, for example the Sun and the Earth, a series of five points since called ” Lagrange points where a third small body could be in a state of balance and relative immobility in relation to the other two bodies.
Some of these points are stable, like L4 and L5, that is to say that if the third deviates a little from these points it will undergo a force tending to maintain it there, while others, like L2 , are unstable.
It is for this reason that several famous observation satellites such as Plank and today the James Webbas explained in the Cnes video below on this subject.
You may know the L5s on Earth, but do you know the five L-points in space? These are the Lagrange points and they are very useful for positioning certain satellites… or space telescopes like Webb. The space to be in fact ! We explain it all to you in this video. © Cnes
Trojans all over the solar system
The Lagrange points are theoretical neither for theastronautics nor for astronomy because it has long been known that the Lagrange points L4 and L5 of the Sun-Jupiter system have trapped during the history of the Solar System many small celestial bodies, asteroids which have been called trojans and which are on theorbit of Jupiter 60° forwards or backwards.
In fact, the first Trojan asteroid was discovered in 1906 by Max Wolf precisely near Jupiter, in L4. He preceded the gas giant of 60° in its orbit, illustrating for the first time the predictions made by Lagrange in 1772. Today we know several thousand of them associated with Jupiter and a few dozen in total for VenusMarch, Uranus and Neptune.
In theory, the Earth should also have some, but the hunt for Trojans on our Blue Planet is paradoxically in no way obvious, despite the proximity of L4 and L5 to the Sun-Earth system. In fact, as Futura explained in the previous article below, it was not until 2011 that the first body of this kind was discovered: 2010 TK7.
As explained in a press release from theESAone could hope to detect Earth Trojans only on the occasion of small Windows of observation just before sunrise or after sunset, when one of the Lagrange points peaks on the horizon while the Sun is hidden below. However, these windows are short, do not allow long observations and above all, unfortunately, require telescopes to be pointed at angles close to the horizon where the observation conditions are the worst.
Drone footage of the SOAR telescope at Cerro Pachón in Chile, part of the Cerro Tololo Inter-American Observatory, a program of NSF’s NOIRLab. The Gemini South Telescope and the Vera C.-Rubin Observatory are visible in the background. © CTIO, NOIRLab, SOAR, NSF, AURA, JP Burgos
Future keys to the colonization of the Solar System?
But, today, members of NOIRLab (National Optical-Infrared Astronomy Research Laboratory) and two open access publications in famous journals NatureCommunications and The Astrophysical Journal Letters confirm the existence in L4 of a second Trojan asteroid for Earth that was initially detected on December 12, 2020 with the instruments of Pan-STARRS1 in Hawaii.
Observed more closely in particular using the telescope SOAR (Southern Astrophysical Research) of 4.1 meters on Cerro Pachón in Chile, the Trojan 2020 XL5with its size of over a kilometer, is about three times larger than 2010 TK7.
The better determination of its orbital parameters leaves no doubt about its nature. Observations also show that it is probably a C-type asteroid, therefore one of those that make up about 75% of the asteroids in the Solar System. They are very dark and are thought to be chemically and mineralogically similar to meteorites carbonaceous chondrites. It is therefore a memory of the chemical composition of the primitive solar system.
2020 XL5 being in some way at hand, it could be the object of missions, perhaps manned, potentially very talkative on the cosmogony of the Solar System. If other trojans of its kind exist, they could be used as a base where to exploit materials necessary for the construction space colonies that Jeff Bezos dreams of.
Celestial mechanics calculations, however, indicate that 2020 XL5 will not stay forever in L4. About 4,000 years all the same before the combination of gravitational disturbances from the other planets of the Solar System dislodges it.
The great mathematician Lagrange changed the face of mathematics and physics by laying the foundations of variational calculus and analytical mechanics. His work in celestial mechanics is fundamental, but Lagrange had also begun to clear the territory where Évariste Galois would discover group theory. © Henri Poincaré Institute, YouTube
In short: first Trojan asteroid for Earth
Article by Jean-Baptiste Feldmann, published on 07/30/2011
We suspected their existence around the Earth as for other planets of the Solar System. The first Trojan asteroid around our planet is called 2010 TK7.
Since the discovery in 1906 of the first Trojan asteroid near Jupiter, astronomers had not yet been able to find any around the Earth. These celestial bodies placed at the Lagrange points L4 and L5 (60 degrees ahead or behind the orbit of their planet) are however legion in the Solar System. There are at least 4,000 of them around Jupiter (including Patroclus and Menoetius), 4 for Saturn (2 for Tethys and 2 for Dione), 5 for Mars and 7 for Neptune. Scientists had not yet found any around the Earth because these asteroids are quite small and especially close to the Sun when looking for them from our planet.
It is by peeling the data acquired during the Mission Wisethis orbiting telescope that mapped the sky in infrared for just over a year, that astronomers have discovered a asteroid Trojan at the Lagrange point L4. This object provisionally dubbed 2010 TK7 measures about 300 meters in diameter and is 80 million kilometers from our planet. His discovery was confirmed by images taken at the Canada-France-Hawaii Telescope.
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