We present and analyze kinematics and orbits for a sample of 488 open clusters in the Galaxy. The velocity ellipsoid for our present sample is derived as ($\sigma_{U}$, $\sigma_{V}$, $\sigma_{W})$=$(28.7$, 15.8, 11.0) km s$^{-1}$ which represents a young thin disc population. We also confirm that the velocity dispersions increase with the age of cluster subsample. The orbits of open clusters are calculated with three Galactic gravitational potential models. The errors of orbital parameters are also calculated considering the intrinsic variation of the orbital parameters and the effects of observational uncertainties. The observational uncertainties dominate the errors of derived orbital parameters. The vertical motions of clusters calculated using different Galactic disc models are rather different. The observed radial metallicity gradient of clusters is derived with a slope of $b=-0.070\pm0.011$ dex kpc$^{-1}$. The radial metallicity gradient of clusters based on their apogalactic distances is also derived with a slope of $b=-0.082\pm0.014$ dex kpc$^{-1}$. The distribution of derived orbital eccentricities for open clusters is very similar to the one derived for the field population of dwarfs and giants in the thin disc.Comment: Accepted for Publication in MNRAS, 25 pages, 14 figures, 6 table

Based on Gaia Early Data Release 3 (EDR3), we estimate the proper motions of 46 dwarf galaxies of the Milky Way (MW). The uncertainties in proper motions, determined by combining both statistical and systematic errors, are smaller by a factor of 2.5 when compared with Gaia Data Release 2. We have derived orbits in four MW potential models that are consistent with the MW rotation curve, with total mass ranging from 2.8 × 1011 M ⊙ to 15 × 1011 M ⊙. Although the type of orbit (ellipse or hyperbola) are very dependent on the potential model, the pericenter values are firmly determined, largely independent of the adopted MW mass model. By analyzing the orbital phases, we found that the dwarf galaxies are highly concentrated close to their pericenter, rather than to their apocenter as expected from Kepler’s law. This may challenge the fact that most dwarf galaxies are MW satellites, or alternatively indicates an unexpectedly large number of undiscovered dwarf galaxies lying very close to their apocenters. Between half and two-thirds of the satellites have orbital poles that indicate them to orbit along the vast polar structure, with the vast majority of these co-orbiting in a common direction also shared by the Magellanic Clouds, which is indicative of a real structure of dwarf galaxies.

Abstract.We report the first results of star counts carried out with the National Astronomical Observatories (NAOC) • 49 00 .0 (J2000) (Galactic coordinates: l = 169.95The field of view is 0.95 deg 2 , and the spatial scale was 1 .67. Since star counts at high galactic latitudes are not strongly related to the radial distribution, they are well suited to study the vertical distribution of the Galaxy. In our model, the distribution of stars perpendicular to the plane of the Galaxy is given by two exponential disks (thin disk plus thick disk) and a de Vaucouleurs halo. Also, based on star counts, we derive the scale heights of the thin disk to be 320 +14 −15 pc and of the thick disk to be 640 +30 −32 pc, respectively, with a local density of 7.0 ± 1% of the thin disk. The errors of scale heights and the corresponding space number density normalization are estimated at a 68% confidential level. The density law for the Galactic halo population is also investigated. We find that the observed counts support an axial ratio of c/a ≤ 0.6 for a de Vaucouleurs r 1/4 law, implying a more flattened halo. We consider that it is possible that the halo has two subpopulations-a flattened inner halo and a spherical outer halo in the Milky Way, and such a halo model might resolve many of the divergences in star count results. We also derive the stellar luminosity function (SLF) for the thin disk, and it partly agrees with the Hipparcos luminosity function.