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).

A study of cluster characteristics and internal kinematical structure of the middle-aged Pleiades open star cluster is presented. The individual star apexes and various cluster kinematical parameters including the velocity ellipsoid parameters are determined using both Hipparcos and Gaia data. Modern astrometric parameters were taken from the Gaia Data Release 1 (DR1) in combination with the Radial Velocity Experiment Fifth Data Release (DR5). The necessary set of parameters including parallaxes, proper motions and radial velocities are used for n=17 stars from Gaia DR1+RAVE DR5 and for n=19 stars from the Hipparcos catalog using SIMBAD data base. Single stars are used to improve accuracy by eliminating orbital movements. RAVE DR5 measurements were taken only for the stars with the radial velocity errors not exceeding 2 km/s. For the Pleiades stars taken from Gaia, we found mean heliocentric distance as 136.8 ± 6.4 pc, and the apex position is calculated as: A CP = 92 • .52 ± 1 • .72, D CP = −42 • .28 ± 2 • .56 by the convergent point method and A 0 = 95 • .59 ± 2 • .30 and D 0 = −50 • .90 ± 2 • .04 using AD-diagram method (n=17 in both cases). The results are compared with those obtained historically before the Gaia mission era.

The kinematical parameters, spatial shape and structure of the open cluster IC 2391 and the associated stellar stream are studied here using Gaia-DR2 (GDR2) astrometry data. The apex positions are determined for the open cluster IC 2391 (data taken from Cantat-Gaudin et al.) and for the kinematical stream's stars mentioned in Montes et al. using both convergent point and AD-diagram methods. The values of apex coordinates are: (A, D) CP =(6. h 17 ± 0. h 004, −6. • 88 ± 0. • 381; for cluster) & (6. h 07 ± 0. h 007, −5. • 00 ± 0. • 447; stream) and (A 0 , D 0 )= (6. h 12 ± 0. h 004, −3. • 4 ± 0. • 3; cluster) & (6. h 21 ± 0. h 007, −11. • 895 ± 0. • 290; stream). The results are in good agreement with the previously calculated values. The positions of the stars in the disk and the spatial dispersion velocities are determined. The paths of cluster and associated stream are traced in the disk by orbit calculation back in time to their places of formation. A possible genetic relationship between the cluster and the stream has been detected. The approximation of the spatial and kinematical shape of the stream and the cluster is made. According to this study, even though currently the cluster and the stream seem to have spatial difference in their locations but they appear to have formed in the same region of the Galactic disk.

In this paper, we present our results for the photometric and kinematical studies of old open cluster NGC 188. We determined various astrophysical parameters like limited radius, core and tidal radii, distance, luminosity and mass functions, total mass, relaxation time etc. for the cluster using 2MASS catalog. We obtained the cluster's distance from the Sun as 1721±41 pc and log (age)= 9.85±0.05 at Solar metallicity. The relaxation time of the cluster is smaller than the estimated cluster age which suggests that the cluster is dynamically relaxed. Our results agree with the values mentioned in the literature. We also determined the clusters apex coordinates as (281• .88, −44• .76) using AD-diagram method. Other kinematical parameters like space velocity components, cluster center and elements of Solar motion etc. have also been computed.

We investigated the luminosity function (LF) and initial mass function (IMF) of some open clusters having different ages. To calculate the LF, we followed the classical definition by van Rhijn (1936). Statistical investigation of the dispersion around a range of magnitudes concerning what is called Wielen dip revealed that the dip is unreal. To confirm the unreality of the dip, we computed the IMF for these open clusters, the statistical investigation of the IMF confirmed the results obtained using the LF, that is, there is no dip for these open clusters under study.

In the present paper, we aim to determine the kinematical properties, velocity ellipsoid, and Oort constants using a sample of halo red giants. The study is based mainly on the space and radial velocities of about 1583 red giant stars collected from the SEGUE-1 and SEGUE-2 surveys. We divided the sample into three subsamples, the inner halo, the outer halo and the stars near the galactic plane. The fitting of the radial velocity equation gives a the mean of Oort constants, A = 15.6 ± 1.6 km s -1 kpc -1 and B= -13.9 ± 1.8 km s -1 kpc -1 , the angular velocity |A-B|= 29.5±0.2 km s-1 kpc -1 implying a rotational velocity of 221.25 ± 26.66 km s -1 if we take the distance to the Galactic center as 7.5 kpc.

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The membership determination for open clusters in noisy environments of the Milky Way is still an open problem. In this paper, our main aim is to provide the membership probability of stars using proper motions and parallax values of stars using Gaia Third Data Release astrometry. Apart from the Gaia astrometry, we have also used other photometric data sets like the UKIRT Infrared Deep Sky Survey, WISE, the American Association of Variable Star Observers (AAVSO) Photometric All-Sky Survey, and Pan-STARRS1 in order to understand cluster properties from optical to mid-infrared regions. We selected 438 likely members with membership probabilities higher than $50\%$ and G ≤ 20 mag. We obtained the mean value of proper motion as μx = 1.27 ± 0.001 and μy = −0.73 ± 0.002 mas yr−1. The cluster’s radius is determined as ${7{^{\prime }_{.}}5}$ (5.67 pc) using radial density profile. Our analysis suggests that NGC 1348 is located at a distance of 2.6 ± 0.05 kpc. The mass function slope is found to be 1.30 ± 0.18 in the mass range 1.0–4.1 M⊙, which is in fair agreement with Salpeter’s value within the 1σ uncertainty. The present study validates that NGC 1348 is a dynamically relaxed cluster. We computed the apex coordinates (A, D) for NGC 1348 as (A°, D°) = (−23.°815 ± 0.°135, −22.°228 ± 0.°105). In addition, calculations of the velocity ellipsoid parameters (VEPs), matrix elements μij, direction cosines (lj, mj, nj), and the galactic longitude of the vertex have been conducted in this analysis.