Solar system

It would seem that in Universe can be arranged easier and more reliable than our Solar system? The decisive role here is played by one force - the force of gravity; the motion of each of the planets around the Sun obeys clear and unambiguous laws - Kepler's laws; this movement occurs in almost the same planet common to all, with the exception of Pluto, the plane...

It would seem that in Universe can be arranged easier and more reliable than our Solar system?

In reality, everything is not so simple. The fact is that each of the planets of the solar system is affected not only by the power of solar gravity, but also by the force of gravity of the remaining planets. This attraction causes perturbations in the motion of each of the planets of the solar system. The planet deviates somewhat from its normal path, predetermined by the laws of Kepler, however, each time again returning to it. If we take into account that the mutual arrangement of the planets of the solar system changes all the time, it becomes obvious that the general picture of their movement is very complicated.

And a legitimate question arises. Can not the perturbations of the planetary motions of the solar system lead to an irreparable catastrophe? Where is the guarantee that every time, descending from invisible space rails, the planet will necessarily return to the "native" orbit? And if the deviation is too great? And can not all this "inner build-up", a kind of vibration, lead to the complete collapse of the solar system?

The answer to this question can only be given by calculations. It is necessary to calculate the motion of each planet of the solar system taking into account all possible perturbations caused by the influence of other planets, and then everything will become clear. But it's easy to say: calculate. Of course, in principle, such a problem is solvable, in any case, with a certain degree of accuracy. The displacements of celestial bodies are controlled by gravitational forces acting between them. The magnitude of these forces depends on the mass of celestial bodies and their mutual distances. In addition, the further movement of any body is also determined by the speed at which it is possessed. It can be said that in the current state of the system of celestial bodies, i.e, in their mutual positions and velocities, its future is unequivocally (again, with some degree of accuracy).

Therefore, the task is to, knowing the relative location and speed of the planets of the solar system at a given moment, to calculate their future movements. However, in mathematical terms this problem is very complicated. The fact is that in any system of moving cosmic bodies there is a constant redistribution of masses, and thanks to this, the magnitude and direction of the forces acting on each body change. Even for the simplest case of the motion of three interacting bodies there is still no complete mathematical solution in general form. The exact solution to this problem, known in celestial mechanics called "tasks three bodies" can only be obtained in certain cases, when it is possible to introduce known simplifications. The more difficult is the exact calculation of the motion of the nine interacting, continuously moving planets of the solar system; it is beyond the power even of modern mathematics with its powerful computer technology.