# The radius, at which a galaxy group stops the Hubble stream, and the group mass: an exact analytical solution

## TL;DR

This paper derives an exact analytical relation between the radius where a galaxy group's gravitational influence halts the Hubble flow and the group's mass, providing a precise tool for understanding cosmic structures.

## Contribution

It introduces an exact analytical formula linking the stopping radius of the Hubble flow to the mass of galaxy groups or clusters.

## Key findings

- Derived an exact relation between stopping radius and group mass.
- Provides a new method to estimate galaxy group masses.
- Enhances understanding of gravitational effects on cosmic expansion.

## 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.