Mathematical Model of the Solar System with Regard for the Velocity of Gravitation

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

“…, n} and i = j. In accordance with paragraph 2, point M j attracts point M i with force (6) where the delay of gravity τ j,i (t) in equality (6) satisfies relation…”

“…The existence of functions τ 2,1 (t) and τ 1,2 (t), which satisfy relations (3) and 5, is shown in [6]. Based on the implicit function theorem [7, p. 449-453], these functions are continuous and differentiable.…”

“…are satisfied. It follows from relations (6) and 7that vector functions r i (t), i = 1, n, are solutions of the following system of differential equations with deviating argument and functional equations…”

“…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.…”

“…This article is devoted to the law of universal gravitation, taking into account the finiteness of the speed of gravity and its application to the construction of a mathematical model of motion of a finite number of bodies. Such a model is not a system of ordinary differential equations, as in classical celestial mechanics [5], but a system of differential equations with a deviating argument and functional equations, as in [6]. The dynamics of bodies, taking into account the finiteness of the gravity velocity, is characterized by properties that are impossible in the case of c g = ∞.…”