A simple statistical mechanical description of the atmosphere composed of small particles around massive spherical body

The atmosphere of small particles around a spherical massive body is theoretically described starting from statistical mechanical principles combined with the field approach. It is assumed that the system is in thermodynamic equilibrium and that the small particles are explicitly independent and therefore subjected to the Boltzmann statistics. The model system is the atmosphere of small particles that are attracted to the spherical massive body while their complete approach to the surface of this body is hindered by thermal motion. The gravitational attraction between the molecules and the massive object is described by introducing a potential of the attractive field and by considering that the massive object is the source of the field. The above assumptions lead to the formulation of the variational problem based on the 2nd law of thermodynamics in the form of the consistently-related system of differential equations for the gravitational potential and the distribution of the molecules within the atmosphere.