# Satellites of the planets and Lagrange points

Different planets "own" a different number of satellites. These planetary satellites are distributed in the Solar System is clearly uneven. The giant Jupiter has 15 of them, Saturn according to some data - more than 20, and as we approach the Sun the number satellites sharply decreases. Mars has only two satellites - the famous Phobos and Deimos, Mercury and Venus they are not at all. Earth is the only natural satellite - Moon.

However, it is still necessary to specify what to call the satellite of the planet. We are used to the fact that our Moon is a globular body, but in fact, in general, the satellites of planets can be other - invisible. It is important only that they are connected with this planet by gravity forces. In what states can there be a solid in general? In the form of separate shapeless blocks and in the form of... dust, dust clouds. As for individual blocks, it is quite possible that Earth has several such satellites. But no one was able to register them, although there are some indirect evidence of their existence. Are the invisible companions of the planets dusty?

As early as the 18th century, the famous French mathematician Lagrange, studying the problem of the motion of three interacting bodies, came to the conclusion that under certain conditions these bodies can form in the space of a very curious equilateral triangle. It goes without saying that with the passage of time each of the three bodies will move in its orbit relative to the common center of mass. But the thing is that with these movements they will always remain at the vertices of an equilateral triangle. This triangle itself is constantly changing, then shrinking, then stretching and turning about the center of mass. But it always remains equilateral. Thus, in a three-body system, there may be some kind of equilibrium Lagrange points. And if the system consists of only two bodies, such as the Earth-Moon system? Then in it there is still, so to speak, the potential point of Lagrange, forming with the other two bodies the vertices of an equilateral triangle. And since in the plane in which two bodies move already, it is always possible to construct a pair of equilateral triangles with two coincident vertices, where these two bodies are, then, obviously, two Lagrange points must always exist in the two-body system. Although for the time being these points can remain unoccupied. However, if any body is at the Lagrange point and at the same time it instantly loses its speed relative to the Earth and the Moon, it will fall into a gravitational trap and remain in it forever, or at least for a very long time. At first, while the trap is still empty, it works badly - the particles fly unobstructed through the "equilibrium zone" and leave their way. But as the "trap" is filled with matter, the "capture" process will accelerate. Now the flying particles can collide with those that have already fallen into invisible nets, and, losing speed, replenish the "catch". Although this process is extremely slow, it could be expected that for many hundreds of millions of years, a significant amount of matter would have accumulated at the Lagrange points of the Earth-Moon system: in fact, in the near-earth space there are many dust particles, and possibly even larger bodies.

At the beginning of this century, satellites of planets were found, where the Lagrange points of the "Sun-Jupiter" system are in theory. Near each of these points of Lagrange, astronomers have found several asteroids. All of them were given the names of heroes of the ancient Greek epic about the Trojan War. A large group was called "Greeks", the smaller group was called "Trojans". However, similar satellites of the planet Earth, the possible existence of which stemmed from the theory, for a long time could not be detected. The fact is that you can see such a satellite of the planet Earth only when the corresponding point of Lagrange is located in the sky opposite to the Sun, and at the same time is far enough from the light strip Milky Way. And to all this, it is necessary that the night be moonless...

Such favorable combinations are very rare in nature. Astronomers photographed Lagrange points for years, but no trace of solid substances were not detected. And only a few years ago, at last, it was possible to photograph "invisible" satellites of planet Earth. They were quite impressive: the diameter of each of them is comparable with the diameter of the Earth. However, mass of these dust clouds by space standards is quite insignificant - only about 20 thousand tons. And the density of such satellites is not at all great - one speck of dust per cubic kilometer. It is not surprising that they were so difficult to detect. Nevertheless, with clouds of cosmic matter located near the points of Lagrange, apparently, it is necessary to seriously consider when choosing the trajectories of the motion of spacecraft. On the other hand, it is very tempting to create space orbital stations at the points of Lagrange. Their position in space for a long time almost does not have to be corrected. But then, probably, there will be a need to somehow get rid of the substance accumulated in these areas. It can be dangerous for plant structures and interfere with scientific observations.