Dynamics of astrophysical objects against the cosmological background

In this paper we consider dynamical behavior of astrophysical objects (galaxies and dwarf galaxies) taking into account both gravitational attraction between them and cosmological expansion of the Universe. First, we obtain the general system of equations and apply them to some abstract systems of galaxies. Then we investigate the collision between the Milky Way and Andromeda in future. We distinguish two models. For the first one, we do not take into account the influence of Intra-Group Matter (IGrM). In this case we demonstrate that for currently known parameters of this system the collision is hardly plausible because of the angular momentum. These galaxies will approach the minimum distance of about 290 Kpc in 4.44 Gyr from present and then begin to run away irreversibly from each other. For the second model, we take into account dynamical friction due to IGrM. We find a characteristic value of the IGrM particle velocity dispersion $\tilde\sigma=2.306$. For $\tilde\sigma\leq2.306$ the merger will take place, but for the bigger values of $\tilde\sigma$ the merger can be problematic. If the temperature of the IGrM particles is $10^5$ K, this characteristic value of $\tilde\sigma$ corresponds to the IGrM particle mass 17 MeV. Therefore, for the IGrM particles with masses less than 17 MeV the merger becomes problematic. We also define the region in the vicinity of our Local Group where the formation of Hubble flows starts. For such processes the zero-acceleration surface (where gravitational attraction is balanced by cosmological accelerated expansion) plays the crucial role. We show that such surface is absent for the Local Group. Instead, we find two points and one circle with zero acceleration. Nevertheless, there is a nearly closed area around the MW and M31 where the absolute value of the acceleration is approximately equal to zero. Hubble flows are formed outside of this area.