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 0.4 d 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 .