Non-Keplerian Behavior and Instability of Motion of Two Bodies Caused by the Finite Velocity of Gravitation

Law of universal gravitation with finite velocity of gravity and mathematical model of motion of a finite number of material points

“…When finding the trajectories of movement of points M i , i = 1, n, it is necessary to use, in addition to the equations of system (8), also initial or boundary conditions (see [6], [8], [9]). System (8), together with these conditions, is a mathematical model of the movement of points M i , i = 1, n, that takes into account the finiteness of the speed of gravity.…”

“…it follows that even if the complexity of the equations of system (8) is not taken into account, studying system (8) at large n is a more difficult task than studying system (9). Despite this, it is possible to find such properties of system (8) that are not characteristic of system (9) (see [6], [9]).…”

“…This system, together with the initial or boundary conditions considered in [9], [11] is a mathematical model of the motion of two points with masses m 1 and m 2 . System (10) has been thoroughly investigated in the works [8][9][10][11][12].…”

“…In [9], the problem of two bodies of arbitrary masses was studied taking into account the speed of gravity. The non-Kaplerian behavior and instability of the motion of these bodies are also shown.…”

“…In [8], systems of differential equations with delays and constraints on delays and derivatives of solutions, which are used in [9] and [10], are studied.…”