Our little stabilization

The sun always rises in the east, the seasons change regularly, there are 365 or 366 days a year, winters are cold, summers are warm… Boring. But let's enjoy this boredom! First, it won't last forever. Secondly, our little stabilization is only a special and temporary case in the chaotic solar system as a whole.

The movement of the planets, moons and all other objects in the solar system seems to be orderly and predictable. But if so, how do you explain all the craters we see on the Moon and many of the celestial bodies in our system? There are a lot of them on Earth too, but since we have an atmosphere, and with it erosion, vegetation and water, we do not see the earth thicket as clearly as in other places.

If the solar system consisted of idealized material points operating solely on Newtonian principles, then, knowing the exact positions and velocities of the Sun and all the planets, we could determine their location at any time in the future. Unfortunately, reality differs from Newton's neat dynamics.

space butterfly

The great progress of natural science began precisely with attempts to describe cosmic bodies. The decisive discoveries explaining the laws of planetary motion were made by the "founding fathers" of modern astronomy, mathematics and physics - Copernicus, Galileo , Kepler i Newton. However, although the mechanics of two celestial bodies interacting under the influence of gravity is well known, the addition of a third object (the so-called three-body problem) complicates the problem to the point where we cannot solve it analytically.

Can we predict the motion of the Earth, say, a billion years ahead? Or, in other words: is the solar system stable? Scientists have tried to answer this question for generations. The first results they got Peter Simon from Laplace i Joseph Louis Lagrange, no doubt suggested a positive answer.

At the end of the XNUMXth century, solving the problem of the stability of the solar system was one of the greatest scientific challenges. king of Sweden Oscar II, he even established a special award for the one who solves this problem. It was obtained in 1887 by the French mathematician Henri Poincare. However, his evidence that perturbation methods may not lead to correct resolution is not considered conclusive.

He created the foundations of the mathematical theory of motion stability. Alexander M. Lapunovwho wondered how quickly the distance between two close trajectories in a chaotic system increases with time. When in the second half of the twentieth century. Edward Lorenz, a meteorologist at the Massachusetts Institute of Technology, built a simplified model of weather change that depends only on twelve factors, it was not directly related to the movement of bodies in the solar system. In his 1963 paper, Edward Lorentz showed that a small change in the input data causes a completely different behavior of the system. This property, later known as the "butterfly effect", turned out to be typical of most dynamical systems used to model various phenomena in physics, chemistry or biology.

The source of chaos in dynamical systems is forces of the same order acting on successive bodies. The more bodies in the system, the more chaos. In the Solar System, due to the huge disproportion in the masses of all components compared to the Sun, the interaction of these components with the star is dominant, so the degree of chaos expressed in Lyapunov exponents should not be large. But also, according to Lorentz's calculations, we should not be surprised by the thought of the chaotic nature of the solar system. It would be surprising if a system with such a large number of degrees of freedom were regular.

Ten years ago Jacques Lascar from the Paris Observatory, he made over a thousand computer simulations of planetary motion. In each of them, the initial conditions differed insignificantly. Modeling shows that nothing more serious will happen to us in the next 40 million years, but later in 1-2% of cases it may complete destabilization of the solar system. We also have these 40 million years at our disposal only on the condition that some unexpected guest, factor or new element that is not taken into account at the moment does not appear.

Calculations show, for example, that within 5 billion years the orbit of Mercury (the first planet from the Sun) will change, mainly due to the influence of Jupiter. This may lead to Earth colliding with Mars or Mercury exactly. When we enter one of the datasets, each one contains 1,3 billion years. Mercury may fall into the Sun. In another simulation, it turned out that after 820 million years Mars will be expelled from the system, and after 40 million years will come to collision of Mercury and Venus.

A study of the dynamics of our System by Lascar and his team estimated the Lapunov time (ie, the period during which the course of a given process can be accurately predicted) for the entire System at 5 million years.

It turns out that an error of only 1 km in determining the initial position of the planet can increase to 1 astronomical unit in 95 million years. Even if we knew the initial data of the System with an arbitrarily high, but finite accuracy, we would not be able to predict its behavior for any period of time. To reveal the future of the System, which is chaotic, we need to know the original data with infinite precision, which is impossible.

Moreover, we don't know for sure. total energy of the solar system. But even taking into account all the effects, including relativistic and more accurate measurements, we would not change the chaotic nature of the solar system and would not be able to predict its behavior and state at any given time.

Everything can happen

So, the solar system is just chaotic, that's all. This statement means that we cannot predict the Earth's trajectory beyond, say, 100 million years. On the other hand, the solar system undoubtedly remains stable as a structure at the moment, since small deviations of the parameters characterizing the paths of the planets lead to different orbits, but with close properties. So it is unlikely that it will collapse in the next billions of years.

Of course, there may be already mentioned new elements that are not taken into account in the above calculations. For example, the system takes 250 million years to complete an orbit around the center of the Milky Way galaxy. This move has consequences. The changing space environment disrupts the delicate balance between the Sun and other objects. This, of course, cannot be predicted, but it happens that such an imbalance leads to an increase in the effect. comet activity. These objects fly towards the sun more often than usual. This increases the risk of their collision with the Earth.

Star after 4 million years Gliese 710 will be 1,1 light years from the Sun, potentially disrupting the orbits of objects in The Oort Cloud and an increase in the likelihood of a comet colliding with one of the inner planets of the solar system.

Scientists rely on historical data and, drawing statistical conclusions from them, predict that, probably in half a million years meteor hitting the ground 1 km in diameter, causing a cosmic catastrophe. In turn, in the perspective of 100 million years, a meteorite is expected to fall in size comparable to that which caused the Cretaceous extinction 65 million years ago.

Up to 500-600 million years, you have to wait as long as possible (again, based on the available data and statistics) вспышка Or supernova hyperenergy explosion. At such a distance, the rays could impact the Earth's ozone layer and cause a mass extinction similar to the Ordovician extinction - if only the hypothesis about this is correct. However, the emitted radiation must be directed precisely at the Earth in order to be able to cause any damage here.

So let's rejoice in the repetition and small stabilization of the world that we see and in which we live. Math, statistics and probability keep him busy in the long run. Fortunately, this long journey is far beyond our reach.