  The most probable state of an infinite self-gravitating gas in the dynamical
equilibrium is defined by `gravitational haziness', a parameter representing
many-body effects and formally like the temperature in the case of thermal
equilibrium. A kinetic equation is constructed using a concept of statistical
equipartition of the virial among subsystems of the self-gravitating gas. A
closed equation for the gravitational potential is conjectured as a special
property of the kinetic equation. An equilibrium particle distribution function
in the phase space, an analog of the Maxwell-Boltzmann weight, and a galaxy
equation of state are found for all `gravitational haziness'. The first law of
a `hazydynamics' (thermodynamics) states that the total mass of an astronomical
stellar collection is the sum of the Archimedes displaced mass and an excess
`gobbled' mass determined by the `gravitational haziness' and history.
