2019 **Abstract:** The gravitational field of a galaxy group or cluster slows down the Hubble stream and turns it speed to zero at some radius R 0 . We offer an exact analytical relation between R 0 and the mass of the group.

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“…This equation coincides with equation ( 11) from (Baushev 2019) and allows to find L0 for an arbitrary sphericallysymmetric mass distribution M (r0) (see (Baushev 2019) for details).…”

“…On the other hand, the N-body simulations may not be considered as having no disadvantages (Baushev et al 2017;Baushev & Pilipenko 2018), and the analytical approach seems preferable in simple cases, since it allows to obtain a precise and compact equation for v(r0). For instance, Baushev (2019) offered an exact analytical equation for the radius L0, at which a spherically-symmetric object of mass M stops the Hubble flow 1 , i.e., v(L0) = 0. We use the same approach in this letter, and our aim is to generalize the result of (Baushev 2019) and find the full velocity profile v(r0) in the spherically-symmetric case.…”

“…In order to find the relationship between the primordial perturbation depth ϑ1 and the present-day void underdensity we apply the method used in (Baushev 2019;Baushev 2020). The time passed between a = a1 and a = a0 is .…”

“…density is 200 times greater than the critical one. According to an exact analytical solution (Baushev 2019) the corresponding radius of the zero velocity surface is 706 kpc. This value is in excellent agreement with the direct measurement of the zero velocity radius of 0.7 Mpc by Karachentsev et al (2003).…”