Relative proper motions and cluster membership probabilities (P µ ) have been derived for ∼ 2500 stars in the field of the open star cluster NGC 3766. The cluster has been observed in B and V broadband filters at two epochs separated by ∼ 6 years using a wide-field imager mounted on the WFI@ESO2.2m telescope. All CCD frames were reduced using the astrometric techniques described in Anderson et al. (2006). The proper motion r.m.s. error for stars brighter than V ∼ 15 mag is 2.0 mas yr −1 but it gradually increases up to ∼4 mas yr −1 at V ∼ 20 mag. Using proper motion data, membership probabilities have been derived for the stars in the region of the cluster. They indicate that three Be and one Ap stars are member of the cluster. The reddening E(B −V ) = 0.22±0.05 mag, a distance 2.5±0.5 kpc and an age of ∼ 20 Myr are derived using stars of P µ > 70%. Mass function slope x = 1.60 ± 0.10 is derived for the cluster and cluster was found to be dynamically relaxed. Finally, we provide positions, calibrated B and V magnitudes, relative proper motions and membership probabilities for the stars in the field of NGC 3766. We have produced a catalog that is electronically available to the astronomical community.

Context. NGC 6809 is a luminous metal-poor halo globular cluster that is relatively easy to study due to its proximity and low concentration. Because of its high Galactic latitude (b = −23• ), interstellar reddening and contamination is not very high. Aims. We aim to determine the relative proper motion and membership probability of the stars in the wide area of globular cluster NGC 6809. To target cluster members reliably during spectroscopic surveys and both spatial and radial distributions in the cluster outskirts without including field stars, a good proper motion and membership probability catalogue of NGC 6809 is required. Methods. The archival data of two epochs with a time-base line of 7.1 years have been collected with Wide Field Imager (WFI) mounted on the 2.2 m MPG/ESO telescope. The CCD images of both epochs have been reduced using the astrometric techniques as described in Anderson et al. (2006). The calibrated UBVI magnitudes have been derived using Stetson's secondary standard stars. Results. We derived the relative proper motion and membership probabilities for ∼12 600 stars in the field of globular cluster NGC 6809. The measurement error in proper motions for the stars of V ∼ 17 mag is 2.0 mas yr −1 , gradually increasing up to ∼3 mas yr −1 at V = 20 mag. We also provide the membership probability for the published different types of sources in NGC 6809. An electronic catalogue with proper motion and membership probability for the stars will be available to the astronomical community.

We present 12 new transit light curves of the hot-Jupiter TrES-3b observed during 2012−2018 to probe the transit timing variation (TTV). By combining the midtransit times determined from these 12 transit data with those reestimated through uniform procedure from 71 transit data available in the literature, we derive new linear ephemeris and obtain the timing residuals that suggest the possibility of TTV in the TrES-3 system. However, the frequency analysis shows that the possible TTV is unlikely to be periodic, indicating the absence of an additional body in this system. To explore the other possible origins of TTV, the orbital decay and apsidal precession ephemeris models are fitted to the transit time data. We find the decay rate of TrES-3b to be ms yr−1, and the corresponding estimated modified stellar tidal quality factor of is consistent with the theoretically predicted values for the stars hosting the hot-Jupiters. The shift in the transit arrival time of TrES-3b after 11 years is expected to be T shift ∼ 69.55 s, which is consistent with the rms of the timing residuals. Besides, we find that the apsidal precession ephemeris model is statistically less probable than the other considered ephemeris models. It is also discussed that despite the fact that the linear ephemeris model appears to be the most plausible model to represent the transit time data, the possibility of the orbital decay cannot be completely ruled out in the TrES-3 system. To confirm this, further high-precision and high-cadence follow-up observation of transits of TrES-3b would be important.

We present a comprehensive analysis (photometric and kinematical) of the poorly studied open cluster NGC 4337 using 2MASS, WISE, APASS, and Gaia DR2 databases. By determining the membership probabilities of stars, we identified the 624 most probable members with membership probability higher than 50% by using proper motion and parallax data taken from Gaia DR2. The mean proper motion of the cluster is obtained as and μ y  = 1.49 ± 0.006 mas yr−1. We find the normal interstellar extinction toward the cluster region. The radial distribution of members provides a cluster radius of 7.′75 (5.63 pc). The estimated age of 1600 ± 180 Myr indicates that NGC 4337 is an old open cluster with a bunch of red giant stars. The overall mass function slope for main-sequence stars is found as within the mass range 0.75−2.0 , which is in fair agreement with Salpeter’s value (x = 1.35) within uncertainty. The present study demonstrates that NGC 4337 is a dynamically relaxed open cluster. Using the Galactic potential model, Galactic orbits are obtained for NGC 4337. We found that this object follows a circular path around the Galactic center. Under the kinematical analysis, we compute the apex coordinates (A, D) by using two methods: (i) the classical convergent point method and (ii) the AD-diagram method. The obtained coordinates are (A conv, D conv) = (96.°27 ± 0.°10, 13.°14 ± 0.°27) and (A ◦, D ◦) = (100.°282 ± 0.°10, 9.°577 ± 0.°323) respectively. We also computed the Velocity Ellipsoid Parameters, matrix elements (μ ij ), direction cosines (l j , m j , n j ), and the Galactic longitude of the vertex (l 2).