Jewish university scientists in Jerusalem offered a new way to predict the behavior of a system of three bodies, bypassing significant shortcomings of the methods applied at present. This is reported in the article published in the Celestial Mechanics and Dynamical Astronomy magazine. Briefly about the approach that solve one of the greatest problems of physics and mathematics is described in a press release on Phys.org.
Since the times of Henri Poincare (1854-1912), French mathematics and physics, it was known that the task of three bodies does not have a deterministic solution. The movement of objects that interact with each other by the law of Newton, strongly depends on their initial position and speeds, so the behavior of the system seems random (in other words, chaos arises). Although computer simulation is also not able to give long-term forecasts, in 1976 scientists have concluded that it is necessary to look for a statistical solution.
Despite significant successes in this area, all currently available approaches do not take into account two significant points. First, the chaotic movement of the system alternates with regular and susceptible to decay, when two bodies begin to rotate around the common center of the masses, and the third alternately approaches and is removed from them. If you present all the variety of system states in the form of a phase space in which each point corresponds to a certain state, then large areas of space will be described by regular movement, including after decay.
Secondly, an unlimited range of gravity strength implies an endless amount of phase space, so so far scientists have assumed an arbitrary “area of strong interaction” and when calculating probabilities, only configurations inside it took into account.
In the new work, the researchers offered to use the flow of the volume of the phase space to predict the fate of the system, and not the phase volume itself. In other words, all points (state status) are moved in some volume of space (the states are in one to another), as if forming a fluid flow. Such a stream is limited, so there is no problem of infinity of the phase space and you can not enter the areas of strong interaction.
The theory based on streams, with high accuracy predicts the likelihood of running out of each body in simulation at certain assumptions. It is expected that the new approach will allow to solve many astrophysical problems, including the process of occurrence of pairs of compact objects (neutron stars or black holes), creating gravitational waves.