Field Equation of Correlation Function of Mass Density Fluctuation for
  Self-Gravitating Systems
  We study the mass density distribution of the Newtonian self-gravitating
system. Modeling the system either as a gas in thermal equilibrium, or as a
fluid in hydrostatical equilibrium, we obtain the field equation of correlation
function $\xi(r)$ of the mass density fluctuation itself. It can apply to the
study of galaxy clustering on Universe large scales. The observed $\xi(r)\simeq
(r_0/r)^{1.7}$ follows from first principle.
  The equation tells that $\xi(r)$ depends on the point mass $m$ and Jeans
wavelength scale $\lambda_{0}$, which are different for galaxies and clusters.
It explains several longstanding, prominent features of the observed
clustering: the profile of $\xi_{cc}(r)$ of clusters is similar to
$\xi_{gg}(r)$ of galaxies but with a higher amplitude and a longer correlation
length, the correlation length increases with the mean separation between
clusters $r_0\simeq 0.4d$ as the observed scaling, and on very large scales
$\xi_{cc}(r)$ exhibits periodic oscillations with a characteristic wavelength
$\sim 120$Mpc. With a set of fixed model parameters, the solution $\xi(r)$ for
galaxies and for clusters, the power spectrum, the projected, and the angular
correlation function, simultaneously agree with the observational data from the
surveys, such as Automatic Plate Measuring (APM), Two-degree-Field Galaxy
Redshift Survey (2dFGRS), and Sloan Digital Sky Survey (SDSS), etc.
