  The estimation of the main parameters of star clusters is significant in
astrophysical studies. The most important aspect of using the Gaia DR2 survey
lies in the positions, parallax, and proper motions of cluster stars with
homogeneous photometry that make the membership probability determine with high
accuracy. In this respect, depending on Gaia DR2 database, an analysis of the
open star cluster Melotte 72 is taking place here. It is located at a distance
of 2345+/-108 pc with an age of 1.0+/-0.5 Gyr. In studying the radial density
profile, the radius is found to be 5.0+/-0.15 arcmin. The reddening, the
luminosity and mass functions, the total mass of the cluster, and the galactic
geometrical distances (X_Sun, Y_Sun, Z_Sun), and the distance from the galactic
center (R_g ) have been estimated as well. Our study has shown a dynamical
relaxation behavior of Melotte 72.
