Abstract. In this paper, we consider dynamical behavior of astrophysical objects such as galaxies and dwarf galaxies taking into account both the gravitational attraction between them and the 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. Here, we distinguish two models. For the first one, we do not take into account the influence of the 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 the dynamical friction due to the IGrM. Here, we find a characteristic value of the IGrM particle velocity dispersionσ = 2.306. Forσ ≤ 2.306, the merger will take place, but for the bigger values of σ the merger can be problematic. If the temperature of the IGrM particles is 10 5 K, then this characteristic value ofσ 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 the Hubble flows starts. For such processes, the zero-acceleration surface (where the gravitational attraction is balanced by the 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. The Hubble flows are formed outside of this area.
Abstract. In the Randall-Sundrum model with one brane, we found the approximate and exact solutions for gravitational potentials and accelerations of test bodies in these potentials for different geometrical configurations. We applied these formulas for calculation of the gravitational interaction between two spheres and found the approximate and exact expressions for the relative force corrections to the Newton's gravitational force. We demonstrated that the difference between relative force corrections for the approximate and exact cases increases with the parameter l (for the fixed distance r between centers of the spheres). On the other hand, this difference increases with decreasing of the distance between the centers of the spheres (for the fixed curvature scale parameter l). We got the upper limit for the curvature scale parameter l 10 µm. For these values of l, the difference between the approximate and exact solutions is negligible.PACS numbers: 04.50.-h, 11.25.Mj, 98.80.-k applications and constraints2 Non-relativistic limit of
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