Lagrange points: definition, prospects for their use in space activities

The absence of gravity, or, as astronomers call this phenomenon, Lagrange points (after the mechanic, astronomer and mathematician from France of the Enlightenment era - Joseph Louis Lagrange), briefly denoted L1 and further to L5, are not just points. This is a huge space of space - in many millions of kilometers, where the laws of gravity do not work. And this means that any object that accidentally gets there cannot get back. Giant space areas, designated as Lagrange points, where no movement is possible, will capture it and never release it. And if released, it is very soon.

Lagrange points


In 1736, the famous Italian was born in Turin, France, who, along with Euler, became the greatest mathematician of the eighteenth century. Particularly famous for his exceptional mastery of generalization and synthesis of various scientific material.Joseph Louis Lagrange wrote a treatise on analytical mechanics, which immediately became a classic of mathematical science, since many fundamental mathematical principles were established in it, including the principle of possible displacements. It was Lagrange who finally mathematized the mechanics.

He also made a huge contribution to the theory of numbers, mathematical analysis, numerical methods, probability theory. It was he who created the calculus of variations. However, his contribution to astronomy is no less. His discovery - the Lagrange point - for several centuries agitated all the near-scientific minds, and this is still happening. One can imagine how much interesting things have accumulated in this space for four and a half billion years!


Not only dust clouds, asteroids and hidden planets can be there. Many people suspect that it was in these inaccessible, non-gravitational spaces that the notorious “green men” from other planets hid and observed from their wonderful “plates” how technical progress on Earth was moving, bringing humanity to its complete degradation.

In these past centuries of such a plan, scientific speculation has not ceased, but it will soon be put to an end. Mankind has come close to finally uncovering this secret. The two spacecrafts involved in the study of the Sun have switched to studies of another plan. And they are about to reach these mysterious spaces, denoted by L4 and L5, and find out on the spot what Lagrange points hide in themselves.

three body problem


Even if these messengers of the Earth do not find alien ships there, anyway, many scientists will simply be happy to discover at these points any cosmic rock fragments of an incredible age. And there certainly is hidden an amazing population of a wide variety of objects. Astronomers will search for celestial bodies using special tools that are stored on board space probes.

Of course, all these are only assumptions, and perhaps no celestial bodies will be detected there. Although Joseph Louis Lagrange was sure that a lot could be found. These future discoveries could provide the missing information about how the Solar System was formed, and understand many of the colossal interactions that formed the Moon as well.Perhaps this knowledge will warn earthlings against future collisions of cosmic bodies with our planet.

The essence of the teachings

Lagrange points in space were discovered in 1772, when the mathematician calculated such a phenomenon: the Earth, as it was already known, has a gravitational field, and it must necessarily neutralize the attraction of the Sun precisely at the indicated points in space. And these are the only areas where an object really needs to become weightless. The five points of Lagrange are extremely interesting in their full composition. However, L4 and L5 are the most intriguing. These are the only stable areas. For example, the Lagrange points L2 and L1 will also be delayed by a flying asteroid, but after a while it is released into further flight, but if an object falls into L4 or L5 space, it can say goodbye to the rest of space even forever.

It is not far from Earth, only some one hundred and fifty million kilometers, and these points are located directly on the orbital plane, but most likely, it will not work out. These are Lagrange points of the Earth: L4 is sixty degrees ahead of our planet, and L5 is at the same angle behind it, and together we revolve around the Sun. Probably, they protect the Earth from the fall of asteroids and other cosmic bodies on it, depriving them of their own movement in their non-gravitational space.The most interesting thing is that the same picture is observed around other planets, and the presence of such areas has already been discovered.

joseph louis lagrange


Max Wolf in 1906 discovered an asteroid, which he called Achilles. He was between Jupiter and Mars, behind the main asteroid belt. Examining the data, the scientist realized that Achilles was trapped in J4 as Lupus. After this discovery, a wave of searches for similar examples has risen. All the finds at such points were named after the heroes of the Trojan War. At the moment, they found a little less than a thousand asteroids that were caught in their anti-gravity networks Jupiterian points of Lagrange. The earth, the moon - that is what most interested scientists.

Trojan asteroids around other planets are difficult to spot. Not found on Saturn, only one on Neptune. But the Earth carefully hides its space storerooms, and that it is stored there, has not yet been investigated. We are waiting for information from the probes that have started searching — what will they find out from what is hidden from us Lagrange points?

Lagrangian ground moon points


The sun is too close to L4 and L5, which is why they are so difficult to see from Earth. At night, the L5 area is almost at the horizon and quickly leaves, while L4, on the contrary, is hidden in the dawn rays.In addition, you need to examine the huge areas larger than the moon in its fullest incarnation. However, the search still goes. In the 90s, a telescope located in Hawaii was used for these studies. Interesting facts were not found, but because the researchers gradually cooled down to this mystery.
Most recently, an automatic search was launched to explore asteroids located near the Earth, with particular attention to space sites in areas of Lagrange points. However, nothing has been found so far. The special hope of scientists is for the probes of the STEREO spacecraft, which can somewhat clarify the situation. Recall that they are not adapted to the search for asteroids, but to the study of solar storms. However, they were launched in 2006 clearly in orbit - one in front, the other behind the Earth, and therefore will be able to observe not only solar activity. To do this, when approaching the L4 and L5 zones, our aircraft will be reconfigured to a slower flight, which will not allow them to fall into a gravitational trap.

Lagrangian points

Where did the moon come from?

Why does our Earth have such a massive satellite, where it came from - these questions have always worried mankind.Today, many scientists believe that it was formed from a variety of space debris, fragments of a space object the size of the planet Mars, which crashed into the Earth four billion years ago. How did it happen that after such a collision the Earth still exists? After all, it should have been the opposite: the Earth was smithereens and no moon. And then the huge cosmic body itself fell apart into pieces from a blow and formed our favorite companion of poets from the wreckage, how so?

Only one explanation. This space object must be formed somewhere nearby in order not to have time to accelerate in flight. This hypothesis is confirmed by the detection in the lunar soil of exactly the same amount of oxygen isotopes, as on Earth. Mars has a different relationship. But how could such a huge celestial body form here, literally next to it, unnoticed and not collide with the Earth much earlier? But if it was formed in one of the Lagrange points, it explains everything. Formation is close to the Earth - therefore, oxygen isotopes have the same amount. In the same orbit, the speed could be close to the same. And if the probes flying to the Lagrange points, find the remains of this space object, the theory, we can assume, is proven.

lagrangian points l2

A threat

Some astronomers have suggested that in such vast spaces as the Lagrange points, the body may well be the size of a planet, because the substance necessary for its formation has been gathered there for four and a half billion years. Planets and then made up of cosmic dust and gas, and L4 and L5 were and remain excellent batteries for this purpose. Well, maybe not a planet, but an asteroid of ominous dimensions may well hide there.

But this is a ticking time bomb hidden from prying eyes. The nearest planets, especially Venus, can have such a gravitational influence that will gradually pull this colossus out of the Lagrange point and direct it directly to the Earth. And if they find such a cosmic body there, they will have to blow it up, and take the fragments for examination.

The task of the three bodies

The solar system has a huge number of effects, naturally associated with the movement of the planets, the Moon, the Earth. The same effect are Lagrange points. How will the spacecraft interact with them? Here is the Earth, and the Moon flies around it in a circular orbit, and nothing else in nature seems to be there.This is a limited three-body task, where the third is the spacecraft under consideration and its motion. If it is on the line that connects the Moon and the Earth, then you will feel two gravitational accelerations - the attraction of the Moon, the attraction of the Earth, plus a third one - the centripetal - will add to these accelerations, because this line itself constantly rotates.

In orbit

Of course, there can not exist a point where all these accelerations intersect, will be reset. This will be the equilibrium point, otherwise it is the Lagrange point (or libration point). There are five such points. The first three connect the Moon and the Earth, these are the collinear Lagrange points. The spacecraft placed at any of these points will hang there, and if it deviates slightly, it will find its own orbit in the vicinity.

Moreover, it will inevitably change, because the Moon does not go around the Earth in a circle, but its orbit is slightly elongated. And the sun affects, of course. But this method has a future, because it is low-cost to adjust the apparatus’s orbit in the territory where the Lagrange points are located. Here you can use low-thrust engines.The vicinity of such points is convenient to use for even manned space flights.

Lagrangian ground points sun

Earth-Sun system

Here, too, there are five points of libration, and space research has set itself completely different tasks than in the development of near-moon. The first flights were carried out since 1978 and several interesting missions had time to be realized. The main goal is to monitor the solar activity and the solar wind. This has become more possible when using the L1 Lagrange point. L2 is interesting for astrophysicists, because the device from the vicinity of this point can use a telescope shielded from solar radiation, because it is constantly directed to the other side of it. Astrophysical observations can be carried out with the most pure calculations.

Projects associated with the Lagrange points, Luna-Earth, in our country are now practically not engaged, giving this topic to European and American scientists. And they are engaged in solar points, having already accumulated vast experience. However, large programs ended with the Soviet Union.

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