In this paper, we proceed to develop a new approach which was formulated first in Ershkov (2017) for solving Poisson equations: a new type of the solving procedure for Euler-Poisson equations (rigid body rotation over the fixed point) is suggested in
the current research. Meanwhile, the Euler-Poisson system of equations has been successfully explored for the existence of analytical way for presentation of the solution. As the main result, the new ansatz is suggested for solving Euler-Poisson equations: the Euler-Poisson equations are reduced to the system of 3 nonlinear ordinary differential equations of 1-st order in regard to 3 functions; the elegant approximate solution has been obtained via re-inversion of the proper analytical integral as a set of quasi-periodic cycles. So, the system of Euler-Poisson equations is proved to have the analytical solutions (in quadratures) only in classical simplifying cases: 1) Lagrange case, or 2) Kovalevskaya case or 3) Euler case or other well-known but particular cases.
We introduce here in the current research the revisiting of approach to the dynamics of Sun center relative to barycenter of Solar system by using self-resulting photo-gravitational force of the Sun as the main reason of such motion. In case of slowl
y moving in the direction outwards with respect to the initial position of barycenter of Solar system (together with the current position of Solar system barycenter, of course) with average established velocity not less than 1050 Km/day, we should especially note that hierarchical configuration of Solar system will be preferably the same during this motion. As the main findings, we have suggested algorithm how to move towards stars using Solar self-resulting photo-gravitational force. The obvious physically reasonable assumption is that the Solar system will have been increasing its size during the evolution in a future (due to losses of the total angular momentum taking into account the tidal phenomena).
