  We calculate the distribution function of astronomical objects (like galaxies
and/or smooth halos of different kinds) gravitational fields due to their tidal
in- teraction. For that we apply the statistical method of Chandrasekhar
(1943), used there to calculate famous Holtzmark distribution. We show that in
our approach the distribution function is never Gaussian, its form being
dictated by the potential of interaction between objects. This calculation
permits us to perform a theoretical analysis of the relation between angular
momentum and mass (richness) of the galaxy clusters. To do so, we follow the
idea of Catelan & Theuns (1996) and Heavens & Peacock (1988). The main
difference is that here we reduce the problem to discrete many-body case, where
all physical properties of the system are determined by the interaction
potential V(r_ij). The essence of reduction is that we use the multipole (up to
quadrupole here) expansion of Newtonian potential so that all hydrodynamic,
"extended" characteristics of an object like its density mass are "integrated
out" giving its "point-like" charac- teristics like mass and quadrupole moment.
In that sense we make no difference between galaxies and smooth components like
halos. We compare our theoretical results with observational data.
