It would seem that in the Universe can be arranged easier and more reliable than our Solar system . A crucial role is played by force of gravity; the motion of each planet around the Sun is subject to clear and unambiguous laws – the laws of Kepler; this movement is almost the same, common to all planets, except Pluto’s, the plane.
In reality things are not so simple. The fact is that on each of the planets of the Solar system is not only the power of solar gravity, but the force of attraction of the other planets. This pull causes disturbances in the movement of each of the planets of the Solar system. Several planet deviates from its normal path prescribed by the laws of Kepler, however, every time returning to it. When you consider that the mutual position of the planets of the Solar system changes all the time, it becomes obvious that the overall picture of their movement very difficult.
And so the question arises. If the perturbations of the planetary movements of the Solar system lead to irreparable disaster? Where is the guarantee that whenever getting off the rails invisible space, the planet will return to a “native” orbit? But if the deviation is too large? And if all this “inside buildup”, a kind of vibration, to cause Ravalomanana system?
The answer to this question can give only calculations. It is necessary to calculate the movement of each planet of the Solar system by considering all possible perturbations caused by the influence of other planets, and then all will become clear. But it’s easy to say to calculate. Of course, in principle this problem is solvable, at least with any degree of accuracy. The movements of the heavenly bodies is governed by the force of gravity acting between them. The magnitude of these forces depends on the mass of the heavenly bodies and their mutual distances. In addition, further movement of any body is determined by the speed at which it possesses. We can say that in the modern state system of celestial bodies, i.e. in their mutual positions and speeds, definitely (again with some degree of accuracy) concluded its future.
Therefore, the challenge consists in knowing the position and speed of the planets of the Solar system at the moment, calculating their future move. However, mathematically, this task is very complex. The fact is that in any system moving cosmic bodies there is a constant redistribution of mass and hence change the magnitude and direction of the forces acting on each body. Even for the simplest case of the motion of three interacting bodies is still no complete mathematical solution in the General form. The exact solution of this problem is known in celestial mechanics entitled “three-body problem “, it is possible to obtain only in certain cases where there is a possibility to enter a known simplification. The more difficult an exact calculation of the motion, nine interactive, constantly moving planets in the Solar system; it is beyond the power of modern mathematics, with its powerful computing technology.