The asymptotic behavior as $N\to\infty$ of the trajectories of $N$ point masses interacting in accordance with Newton's law of gravitation

For systems of particles interacting according to Newton's law of gravitation, the asymptotics of their trajectories are found. It is shown that these asymptotics are connected with the characteristics of Vlasov's equation, describing a collision-free plasma. An estimate of the difference between the trajectories of point masses and the corresponding characteristics of Vlasov's equation is found. It is proved that for small hydrodynamic times the motion of point masses is near to the motion of mass points in a constant field of force, defined by the initial mass distribution (the law of free fall). This law of free fall continues to hold when the particles pass through distances substantially exceeding the initial mutual distances between them.
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