LAUSR

Abstract The work on the kinematical parameters and spatial shape structure have been performed with Gaia DR2 astrometry data of the new recently southern discovered open clusters UFMG 1, UFMG 2, and UFMG 3 in the vicinity (∼1.3 degrees radius) of the rarely studied NGC 5999. The apexes positions with AD‑diagram method are computed for about 107, 168, 98, and 154 members of these star clusters, respectively. Our calculated values of apex coordinates are ( A o , D o ) = (102 $$_{.}^{^\circ }$$ 40 ± 1.02 and ‒4 $$_{.}^{^\circ }$$ 60 ± 0.47; NGC 5999), (96 $$_{.}^{^\circ }$$ 69 ± 1.10 and ‒0 $$_{.}^{^\circ }$$ 58 ± 0.045; UFMG 1), (97 $$_{.}^{^\circ }$$ 47 ± 1.09 and 1 $$_{.}^{^\circ }$$ 56 ± 0.051; UFMG 2), and (98 $$_{.}^{^\circ }$$ 65 ± 1.12 and ‒0 $$_{.}^{^\circ }$$ 26 ± 0.060; UFMG 3). Velocity Ellipsoid Parameters (VEPs) for those clusters are also computed, i.e., space velocities $$\left( {\bar {U},\bar {V},\bar {U}} \right)$$ due to Galactic coordinates, dispersion velocities (σ 1 , σ 2 , σ 3 ) due to matrix elements μ ij , projected distances ( X , Y , Z ) on the disk plane, and the Solar elements ( S ⊙ , l A , b A ). According to an approximation of spatial and kinematical shape, UFMGs and NGC 5999 seem to have a spatial difference in their spatial locations, but they appear to have formed in the same region of the Galactic disk. The total cumulative mass M C ; including the total number of main-sequence N MS and non-main-sequence N non-MS stars of these clusters also evaluated here with a second-order polynomial of mass-luminosity relation in order to get clusters tidal radii (pc). Finally, we concluded that NGC 5999, UFMG 1, and UFMG 2 are dynamically relaxed (i.e., τ ≫ 1), and the fourth one in non-relaxed.