Astrometry of stars in star clusters was not much explored for many decades in the last century until the advent of CCD. Photographic plates were yielding a poor number of stars in star-rich clusters with the epoch gap of many decades. With wide field CCD data, it is now possible to probe much fainter regions of stellar clusters to achieve precise proper motions with the epoch gap now being reduced to a few years. Applications of such studies are numerous. These include, deriving precise fundamental parameters of star clusters using most probable cluster members based on membership probabilities values calculated using proper motions, finding absolute proper motions and using them to understand space motion of a star cluster in the Galaxy. To get precise positions and proper motions for large number of stars in the cluster regions, we need wide and high quality images taken at good (~1 arcsec) seeing conditions. For this purpose, we have selected the two epoch data set taken with wide-field imager mounted on 2.2-m telescope installed at La Silla, Chile. We have used the exclusive software developed by Anderson et al. (2006) to calculate proper motions of the stars in the clusters regions. One of the main aim of the present study is to provide proper motions and membership probabilities in the region of globular cluster NGC 6809 (M55) in the wider region and fainter magnitudes than previous studies of the cluster. We have derived precise proper motions and astrometric membership probabilities for 12600 stars down to V ∼ 20 mag in 26 × 22 area. The measurement error in proper motions for the stars of V ∼ 17 mag is 2.0 mas/yr, gradually increasing up to ∼3 mas/yr at V = 20 mag. We also provide the membership probability for the published variables and X-ray sources in the cluster region. All the known SX Phe and RR Lyrae found in our data are most probable cluster members based on our membership catalogue.
Open cluster NGC 3766 was studied for the first time with the aim of astrometry. Proper motions and membership of ~2500 stars were estimated and the membership catalogue was used to determine reddening, distance, age and mass function slop of the cluster using stars with membership probability >70%. Mass segregation was observed for NGC 3766 and the cluster was found to be dynamically relaxed. To understand the space motion of the globular cluster NGC 6121 (M4), we used Southern Proper Motion (SPM) catalogue in combination with 2MASS catalogue to determine space velocity components of the cluster. The cluster was found to be having a disk-like kinematics. In addition to this, we did time series analysis of the globular cluster NGC 4590 (M68) using the CCD data taken with 104-cm Sampurnand telescope and searched variable stars in its area. The search prospered with the detection of 40 known and 9 new probable variable stars for which we present phased light curves and periods.
To conclude, astrometry has entered an all new era which is going to see a rather fast boost with the GAIA data coming up in the coming years.