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The kinematic properties of the Sco-Cen association have been studied using the spatial velocities of young stars. New kinematic age estimates for the three components of the association with the age of UCL and LCC being $17.7\pm2.4$ Myrs and the age of US being $6.4\pm1.7$ Myrs have been obtained. The parameters of the residual velocities US, UCL, and LCC ellipsoid have been estimated., Comment: 11 pages, 2 figures, 4 tables

The kinematics of the young stellar association near the Sun TW Hya is studied. Kinematic estimates of the age of this association were obtained in two ways. The first method -- analysis of stellar trajectories integrated back in time -- gave an estimate of the age $t=4.9\pm1.2$ Myr. The second was to analyze the instantaneous velocities of stars and showed that there is a volume expansion of the stellar system with an angular velocity coefficient $K_{xyz}=103\pm12$ km s$^{-1}$ kpc$^{-1}$. Based on this effect, the time interval that passed from the beginning of the expansion of the TW Hya association to the present moment was found, $t=9.5\pm1.1$ Myr. The following principal semi-axes of the residual velocity ellipsoid are determined: $\sigma_{1,2,3}=(5.25,1.84,0.35)\pm(0.34,0.63,0.26)$ km s$^{-1}$., Comment: 10 pages, 3 figures, the secular equation (10) was missed

The kinematics of the $\epsilon$ Cha young stellar association close to the Sun has been studied based on a list of candidate stars from the Dickson-Vandervelde work. The working sample consists of 26 stars with parallaxes, proper motions from the Gaia~DR3 catalog and radial velocities taken from literary sources. The orbits of the stars back to the past were constructed, and the moment when the association had a minimum spatial size was determined, as well as an analysis of the dependencies of the velocities $U,V,W$ on the coordinates $x,y,z$ was carried out. It is shown that the initial sample is divided into two parts with different kinematic properties. The first sample included 9 stars. Based on the construction of the orbits of these 9 stars, an age estimate of $t=4.9\pm0.8$ million years was obtained. An expansion coefficient in the $xz$ plane with the value $K_{xz}=135\pm19$ km/s/kpc was also found for them, on the basis of which another age estimate $t=7.2\pm1.0$ million years was obtained. The second sample included 17 stars. The construction of their orbits gave an estimate of age $t=0.2\pm0.3$ million years, and based on the gradient $\partial W/\partial z=707\pm248$ km/s/kpc, a second estimate of their age $t=1.4\pm0.5$ million years was obtained. This suggests that the $\epsilon$ Cha association either consists of two groupings of different ages, or a younger one arose as a result of a recent outbreak of star formation within a common star system. The question of the gravitational connection of the groupings has not been considered in the framework of this work., Comment: 14 pages, 8 figures and 2 tables

The trajectories of the clusters $\eta$ Cha, $\epsilon$ Cha and Cha I, Cha II, constructed backward in time, have been studied. We concluded that the hypothesis about the joint formation of all four of these clusters from one molecular cloud cannot be completely excluded. However, 10-15 Myr ago, all these four clusters were located at approximately the same height above the plane of the Galaxy. Thus, the gas-dust clouds from which all these four clusters were formed were located on one broad front. It is possible that the appearance of the Cha I, Cha II, $\epsilon$ Cha and $\eta$ Cha clusters may be associated with the impact on such a front of shock waves formed after supernova explosions in the Scorpius-Centauri association. New estimates of the kinematic ages of the clusters Cha I and Cha II are obtained as $0.12\pm0.19$ and $0.05\pm0.15$, respectively. It is shown that the minimum size of the Cha I-north and Cha I-south clusters corresponded to the time of $0.55\pm0.24$ Myr and $0.04\pm0.18$ Myr ago, respectively, and approximately 1.5 Myr ago the distance between the trajectories of these two groupings was minimal., Comment: 9 pages, 5 figures, 1 table, accepted to Research in Astron. and Astrophys

A spectral analysis of the vertical positions and velocities of 374 open star clusters (OSCs) was carried out. We took these OSCs from the Hunt, Reffert catalog; they have an average age of about 10 million years, and are located on the galactic plane XY in a narrow zone inclined by 25 degrees to the galactic axis Y. The following estimates of the parameters of the Radcliffe wave were obtained: a) the maximum value in periodic perturbations of vertical coordinates $Z_{max}=92\pm10$ pc with the wavelength of these perturbations $\lambda_z=4.82\pm0.09$ kpc; b)~maximum value of the velocity of vertical disturbances $W_{max}=4.36\pm0.12$ km s$^{-1}$ with disturbance wavelength $\lambda_W=1.78\pm0.02$ kpc. Note that the results of the vertical velocity analysis are first-class in accuracy and completely new., Comment: 6 pages, 3 figures, Accepted to RAA

We have studied the kinematics of a unique sample of young open star clusters (OSCs) with high vertical velocities, $15

Studies of the dynamics of globular clusters assume different values of bar parameters (mass, velocity, size) and analyse the results of orbit classifications over the range of the chosen values. It is also a usual thing that a spherical bulge component is converted into the bar to obtain a non-axisymmetric potential from an axisymmetric one. The choice of bar parameters and the way the bar is converted from the bulge introduce systematics into the orbit classifications that we explore in the present study. We integrate orbits of 30 bulge globular clusters residing in the inner area of the Galaxy ($R \lesssim 5$ kpc) backwards in time for three different potentials, two of which are obtained by fitting the rotation curve, and one is taken from the surrogate $N$-body model representing our Galaxy. We analyse each orbit in terms of dominant frequencies obtained from its coordinate spectra. We find that the bar pattern speed is a key factor in orbital classification. With an increase of it, frequencies deviate more and more from the ``bar'' frequency ratio 2:1. The bar-to-bulge mass ratio (assuming the total mass of the bar plus the bulge is fixed) and size of the bar play a smaller role. We also find that, in the $N$-body potential, the fraction of orbits that follow the bar is higher than in those obtained from fitting the rotation curve., Comment: Updated: now accepted in MNRAS

We have estimated the spiral pattern speed in the Galaxy $\Omega_p$ from a large sample of young open star clusters (OSCs). For this purpose, we have used 2494 OSCs younger than 50 Myr. Their mean proper motions, line-of-sight velocities, and distances were calculated by Hunt and Reffert (2023) based on data from the Gaia~DR3 catalogue. Three methods have been applied to estimate $\Omega_p$. They all are based on the linear Lin-Shu spiral density wave theory. We have obtained an estimate of $\Omega_p=24.26\pm0.52$~km s$^{-1}$ kpc$^{-1}$ by the first method, which is most reliable in our view, using the velocity perturbations $f_R$ and $f_\theta$ found through a spectral analysis of the radial, $V_R$, and residual rotation, $\Delta V_{\rm circ},$ velocities. Using the second method, we have found the velocity perturbations $f_R$ and $f_\theta$ by solving the basic kinematic equations together with the Galactic rotation parameters and obtained an estimate of $\Omega_p= 23.45\pm0.53$~km s$^{-1}$ kpc$^{-1}$. We have found $\Omega_p= 28.9\pm2.8$~km s$^{-1}$ kpc$^{-1}$ by the third method based on an analysis of the position angles of OSCs at their birth time $\theta_{\rm birth}$., Comment: 15 pages, 5 figures, 1 table. arXiv admin note: text overlap with arXiv:2203.12902, arXiv:1903.09313, arXiv:2207.03412

We invoke the estimates of the amplitudes of the velocity perturbations $f_R$ and $f_\theta$ caused by the influence of a spiral density wave that have been obtained by us previously from three stellar samples. These include Galactic masers with measured VLBI trigonometric parallaxes and proper motions, OB2 stars, and Cepheids. From these data we have obtained new estimates of the spiral pattern speed in the Galaxy $\Omega_p:$ $24.61\pm2.06$, $24.71\pm1.29$ and $25.98\pm1.37$~km s$^{-1}$ kpc$^{-1}$ from the samples of masers, OB2 stars, and Cepheids, respectively. The corotation radii for these three samples $R_{\rm cor}/R_0$ are $1.16\pm0.09$, $1.15\pm0.06$ and $1.09\pm0.06,$ suggesting that the corotation circle is located between the Sun and the Perseus arm segment., Comment: 12 pages, 2 figures, 2 tables

An overview of the methods used to estimate the mass of the Galaxy and the results obtained by various authors recently according to modern data is given. In particular, the estimates obtained based on the analysis of the galactic rotation curve, on the kinematics of the Galactic dwarf satellites and globular clusters, on the streams of such dwarf galaxies, on escape speed, as well as on halo stars are considered. Estimates of the Galaxy mass in the form $M (

The work is devoted to the analysis of the influence of the galactic bar on the orbital motion of globular clusters in the central region of the Galaxy. For this task, 45 globular clusters were selected, 34 of which belong to the bulge/bar and 11 to the disk. The most accurate astrometric data from the Gaia satellite (Vasiliev and Baumgardt, 2021), as well as new refined average distances (Baumgardt and Vasiliev, 2021), were used to form the 6D-phase space required for orbit integration. The orbits of globular clusters are obtained both in an axisymmetric potential and in a potential including a bar. In this case, the mass, rotation velocity, shape and scale length of the bar were varied. A comparison is made of such orbital parameters as apocentric and pericentric distances, eccentricity and maximum distance from the galactic plane. It is shown that the mass of the bar exerts the greatest influence on the orbital motion, which is expressed mainly in an increase in both the apocentric and pericentric distances in the vast majority of globular clusters. The eccentricities of the orbits in the overwhelming majority also change significantly, and there is a change both upward and downward, especially in the range of values from 0.2 to 0.8. The greatest changes in parameters are observed in globular clusters with high radial velocities and small pericentric distances. The change in orbital parameters depending on the bar rotation velocity is less pronounced. The influence of the geometric parameters of the bar is insignificant in the accepted range of their changes. Several examples show that globular clusters in the bulge are more affected by the bar than those belonging to the disk., Comment: 29 pages, 10 figures, 6 tables

The kinematics of about 2000 classical Cepheids of the Milky Way with data from Gaia\,EDR3 catalog has been studied. For some of these stars, there are line-of-sight velocities. On the basis of the nonlinear rotation model, the parameters of the rotation curve of the Galaxy were determined. The circular linear rotation velocity of the near-solar neighborhood around the Galaxy center was $V_0=236\pm 3$~km s$^{-1}$ for the assumed Sun's galactocentric distance $R_0=8.1\pm0.1$~kpc. Analysis of residual velocities of Cepheids based on the linear Ogorodnikov-Milne model showed the presence of the following significantly different from zero gradients: $\partial U/\partial x,$ $\partial U/\partial z,$ $\partial V/\partial x,$ $\partial V/\partial z$ and $\partial W/\partial x,$ which behaves differently depending on the selection radius. The most interesting is the gradient $\partial W/\partial x\sim-0.5\pm0.1$~km s$^{-1}$ kpc$^{-1}$ (positive rotation of this star system around the galactic axis $y$, $\Omega_y$) since the velocities $W$ are free of galactic rotation. Here we have an indirect influence of various effects leading to a perturbation of the vertical velocities of the galactic disk stars. Based on a simpler model, a more accurate estimate of this rotation is obtained, $\Omega_y=0.51\pm0.07$~km s$^{-1}$ kpc$^{-1}$., Comment: 20 pages, 4 figures, 3 tables. Accepted to be published in Research in Astronomy and Astrophysics

In recent years, radio interferometric observations have achieved high accuracy in determining the absolute values of trigonometric parallaxes and proper motions of maser radiation sources and radio stars. The error in determining the trigonometric parallaxes of these objects averages about 10 microarcseconds, which allows us to confidently study the geometric and kinematic properties of the distribution of stars located at great distances from the Sun, up to the center of the Galaxy. This article provides an overview of the main results of studying the structure and kinematics of the Galaxy, which were obtained by various scientific teams using VLBI observations of masers and radio stars. The main attention is paid to the results of studying the Galaxy obtained by the authors of this work., Comment: 22 pages, 11 figures. Accepted for publication in IzvPulkovo (ISSN 0367-7966) Issue 227

The review is devoted to the Radcliffe Wave recently discovered by Alves et al. from the analysis of molecular clouds. These authors singled out a narrow chain of molecular clouds, elongated almost in one line, located at an inclination of about 30$^o$ to the galactic axis y. The Radcliffe Wave itself describes damped vertical oscillations of molecular clouds with a maximum oscillation amplitude of about 160 pc and a characteristic wavelength of about 2.5 kpc. To date, the presence of the Radcliffe Wave has been confirmed in the vertical distribution of a) interstellar dust, b) sources of maser radiation and radio stars, which are very young stars and protostars closely associated with molecular clouds, c) low-mass stars of the T Tau type, d) more massive OB stars and e) young open clusters of stars. The Radcliffe Wave is also traced in the vertical velocities of young stars. Most of the considered results of the analysis of the vertical velocities of various young stars show that the oscillations of the vertical positions and vertical velocities of stars in the Radcliffe Wave occur synchronously. The nature of the Radcliffe Wave is completely unclear. The majority of researchers associate its occurrence with the assumption of an external gravitational impact on the galactic disk of a striker such as a dwarf satellite galaxy of the Milky Way., Comment: 19 pages, 12 figures, accepted for publication in Astrophysics, V. 65, Issue 4, November 2022. arXiv admin note: text overlap with arXiv:2207.00245

This paper provides a new catalog of orbits and their parameters for a practically complete list of currently known galactic globular clusters (GCs), compiled by Vasiliev (2019) based on the most accurate modern measurements of their velocities and positions. The integration of the orbits of 152 globular clusters for 5 Gyr backward was performed using the new average proper motions obtained from the Gaia EDR3 catalog (Vasiliev and Baumgardt, 2021) and new average distances (Baumgardt and Vasiliev, 2021) in the axisymmetric three-component potential with spherical bulge, disk component, and spherical dark Navarro-Frank-White halo (Bajkova and Bobylev, 2016). The new orbital parameters are compared with the orbital parameters constructed by us earlier (Bajkova and Bobylev, 2021) in the same gravitational potential using proper motions obtained from the Gaia DR2 catalog (Vasiliev, 2019) and with the distances from the Harris catalog (2010)., Comment: 21 pages, 2 tables, 5 figures. Accepted for publication in IzvPulkovo (ISSN 0367-7966) Issue 227. arXiv admin note: text overlap with arXiv:2108.08507

A linear Ogorodnikov-Milne model is applied to study the three-dimensional kinematics of classical Cepheids in the Milky Way. A sample of 832 classical Cepheids from Mr'oz et al. (2019) with distances, line-of-sight velocities, and proper motions from the Gaia DR2 catalogue is used. The Cepheid space velocities have been freed from the differential Galactic rotation found by us previously based on a nonlinear rotation model. Based on a complete Ogorodnikov-Milne model, involving the line-of-sight velocities and proper motions of stars, we have estimated the angular velocity of rotation around the Galactic $y$ axis, $\Omega_y=0.64\pm0.17$~km s$^{-1}$ kpc$^{-1}$. We think that this rotation is associated with the warp of the Galactic thin disk. Our calculations using only the proper motions of Cepheids under the assumption of no deformations due to the disk warp have shown the presence of a residual rotation around the $y$ axis with an angular velocity $\Omega_y=0.54\pm0.15$~km s$^{-1}$ kpc$^{-1}$ and the presence of a positive rotation around the $x$ axis with an angular velocity $\Omega_x=0.33\pm0.10$~km s$^{-1}$ kpc$^{-1}$., Comment: 14 pages, 2 tables, 2 figures

We study the kinematics of a sample of classical Cepheids younger than 120 Myr. For these stars, the estimates of distances taken from Skowron et al., which are based on the period-luminosity relation, and the line-of-sight velocities and the proper motions from the Gaia catalog are available. There are also distance estimates derived from the trigonometric parallaxes contained in the Gaia ERD3 catalog. A method, which relies on comparison of the first-order derivative of the Galactic rotation angular velocity, showed the need to lengthen the distance scales determined by Skowron et al. by about 10%. This conclusion was confirmed by direct comparison to the distances predicted on using the trigonometric parallaxes. With taking into account this result, we obtained new estimates of the Galactic rotation parameters and the parameters of a spiral density wave., Comment: 14 pages, 6 figures, 2 tables

We have analyzed the kinematics of 9750 OB2 stars with proper motions and parallaxes selected by Xu et al. from the Gaia EDR3 catalogue. The relative parallax errors for these stars do not exceed 10\%. Based on the entire sample of stars, we have found the velocities $(U,V)_\odot=(7.17,7.37)\pm(0.16,0.24)$ km s$^{-1}$ and the components of the angular velocity of Galactic rotation: $\Omega_0 =29.700\pm0.076$ km s$^{-1}$ kpc$^{-1}$, $\Omega^{'}_0 =-4.008\pm0.022$ km s$^{-1}$ kpc$^{-2}$, and $\Omega^{''}_0 = 0.671\pm0.011$ km s$^{-1}$ kpc$^{-3}$, where the linear rotation velocity of the Galaxy at the solar distance is $V_0=240.6\pm3.0$ km s$^{-1}$ for the adopted $R_0=8.1\pm0.1$ kpc. There are 1812 OB2 stars with measured line-of-sight velocities, and the space velocities $V_R$ and $\Delta V_{circ}$ have been calculated from them. Based on a spectral analysis independently for the radial and residual tangential velocities, we have obtained the following estimates: $f_R=4.8\pm0.7$ km s$^{-1}$, $f_\theta=4.1\pm0.9$ km s$^{-1}$, $\lambda_R=2.1\pm0.2$ kpc, $\lambda_\theta=2.2\pm0.4$ kpc, $(\chi_\odot)_R=-116\pm12^\circ$, and $(\chi_\odot)_\theta=-156\pm14^\circ$ for the adopted four-armed ($m = 4$) spiral pattern. Thus, both velocity perturbation amplitudes are nonzero at a high significance level., Comment: 13 pages, 2 figures, 2 tables. arXiv admin note: text overlap with arXiv:2203.12902, arXiv:1903.09313, arXiv:1906.10151, arXiv:2207.01924

We have analyzed the kinematics of OB stars from the list by Xiang et al. (2021) that contains $\sim$13 000 single OB stars. For these stars there are photometric distance estimates and proper motions from the Gaia catalogue and line-of-sight velocities from the LAMOST catalogue. Based on a sample of single OB stars and using the photometric distances and proper motions of stars from the Gaia EDR3 catalogue, we have found the group velocity components $(U_\odot,V_\odot,W_\odot)=(9.63,9.93,7.45)\pm(0.27,0.34,0.10)$ km s$^{-1}$, and the following parameters of the angular velocity of Galactic rotation: $\Omega_0=29.20\pm0.18$ km s$^{-1}$ kpc$^{-1}$, $\Omega^{'}_0=-4.150\pm0.046$ km s$^{-1}$ kpc$^{-2}$ and $\Omega^{''}_0=0.795\pm0.018$ km s$^{-1}$ kpc$^{-3}$, where the error per unit weight $\sigma_0$ is 9.56 km s$^{-1}$ and $V_0=236.5\pm3.3$ km s$^{-1}$ (for the adopted $R_0=8.1\pm0.1$ kpc). Based on the same OB stars, we have found the residual velocity dispersions $(\sigma_1,\sigma_2,\sigma_3)=(15.13,9.69,7.98)\pm(0.07,0.05,0.04)$ km s$^{-1}$. We show that using the line-of-sight velocities increases significantly the space velocity dispersion and leads to a biased estimate of the velocity $U_\odot$. A comparison of the distances scales used has shown that the photometric distances from Xiang et al. (2021) should be lengthened approximately by 10%., Comment: 19 pages, 5 figures, 4 tables

We have analyzed the kinematics of OB2 stars with proper motions and parallaxes selected by Xu et al. from the Gaia EDR3 catalog. The relative parallax errors for all the stars in this sample do not exceed 10\%. Based on a sample of 9750 stars, the group velocity components $(U,V,W)_\odot=(7.21,7.46,8.52)\pm(0.13,0.20,0.10)$~km/s were obtained and the parameters of the angular velocity of rotation of the Galaxy: $\Omega_0 =29.712\pm0.062$~km/s/kpc, $\Omega^{'}_0=-4.014\pm0.018$~km/s/kpc$^{2}$ and $\Omega^{''}_0=0.674\pm0.009$~km/s/kpc$^{3}$. The circular velocity of rotation of the solar neighborhood around the center of the Galaxy is $V_0=240.7\pm3.0$~km/s for the assumed distance of the Sun to the galactic center $R_0=8.1\pm0.1$~kpc. It is shown that the influence of the systematic correction to the trigonometric parallaxes of the Gaia EDR3 catalog with the value $\Delta\pi=-0.040$~mas does not exceed the $\sim1\sigma$ level of the errors of the sought-for kinematic parameters of the model. Based on the proper motions of OB stars, the following variances of the residual velocities were found: $(\sigma_1,\sigma_2,\sigma_3)=(11.79,9.66,7.21)\pm(0.06,0.05,0.04)$~km/s. It is shown that the first axis of this ellipsoid slightly deviates from the direction to the center of the Galaxy $L_1=12.4\pm0.1^\circ$, and the third axis is oriented almost exactly to the north pole of the Galaxy, $B_3=87.7\pm0.1^\circ.$, Comment: 12 page, 2 figures, 2 tables

We have analyzed the kinematics of open star clusters (OSCs) with the proper motions and distances calculated by Hao et al. based on Gaia EDR3 data. The mean line-of-sight velocities are known for a number of clusters from this list. We show that the Galactic rotation parameters determined from samples of OSCs with various ages are in good agreement between themselves. The most interesting results have been obtained from a sample of 967 youngest OSCs with a mean age of 18 Myr. In particular, we have found the following parameters of the angular velocity of Galactic rotation using only their proper motions and distances: $\Omega_0 =28.01\pm0.15$ km s$^{-1}$ kpc$^{-1},$ $\Omega^{'}_0=-3.674\pm0.040$ km s$^{-1}$ kpc$^{-2},$ and $\Omega^{''}_0=0.565\pm0.023$ km s$^{-1}$ kpc$^{-3}$. The circular rotation velocity of the solar neighborhood around the Galactic center here is $V_0=226.9\pm3.1$ km s$^{-1}$ for the adopted Galactocentric distance of the Sun $R_0=8.1\pm0.1$ kpc. The parameters of the spiral density wave have been determined from the space velocities of 233 young clusters. The amplitudes of the radial and tangential velocity perturbations produced by the spiral density wave are $f_R=9.1\pm0.8$ km s$^{-1}$ and $f_\theta=4.6\pm1.2$ km s$^{-1}$, respectively; the perturbation wavelengths are $\lambda_R=3.3\pm0.5$ kpc and $\lambda_\theta=2.6\pm0.6$ kpc for the the adopted four-armed spiral pattern. The Sun's phase in the spiral density wave has been found to be $(\chi_\odot)_R\approx-180^\circ$., Comment: 14 pages, 4 figures, 2 tables. arXiv admin note: text overlap with arXiv:1903.09313, arXiv:1609.08341, arXiv:1906.10151, arXiv:1809.10512

Up-to-date data on 2214 classical Cepheids have been used. The model of an exponential matter density distribution in the Galactic thin disk has been applied. New estimates of the radial disk scale length $h_R,$ the distance of the Sun from the symmetry plane $z_\odot$, and the vertical disk scale height $h_z$ have been obtained. Based on samples of 1087 Cepheids younger than 120 Myr and 1127 Cepheids older than 120 Myr, we have found $h_R=2.30\pm0.09$ kpc and $h_R=1.96\pm0.12$ kpc, respectively. It has turned out that an unambiguous estimate of $h_R$ cannot be obtained from their overall radial distribution. However, we have constructed the radial distribution of 806 Cepheids of different ages at the time of their birth from which we have found $h_R=2.36\pm0.24$ kpc. We show that $h_z$ depends strongly on the age of stars. For example, from 705 Cepheids younger than 120 Myr with heliocentric distances $r<6$ kpc we have found $z_\odot=-17\pm4$ pc and $h_z=75\pm5$ pc. From 393 Cepheids older than 120 Myr at $r<6$ kpc, we have found $z_\odot=-39\pm11$ pc and $h_z=131\pm10$ pc., Comment: 13 pages, 8 figures, 2 tables

We have studied the influence of an evolving gravitational potential of the Milky Way Galaxy on the orbital motion of 152 globular clusters with proper motions from the Gaia EDR3 catalogue and mean distances from Baumgardt and Vasiliev (2021). To construct a semicosmological evolving model potential with changing masses and sizes of the Galactic components, we have used the algorithm described in Haghi et al. (2015). The adopted axisymmetric three-component model potential of the Galaxy includes a spherical bulge, a flat Miyamoto--Nagai disk, and a spherical Navarro--Frenk--White dark matter halo.The orbits are integrated backward in time. We compare the orbital parameters of globular clusters derived in static and evolving potentials when integrating the orbits for 5 and 12 Gyr backward. For the first time we have studied the influence of separately a change in the masses and a change in the sizes of the Galactic components. The changes in the masses and sizes of the components are shown to act on the orbital parameters in the opposite way. At small Galactocentric distances this influence is maximally compensated for. The orbits of distant globular clusters and those with a large apocenter distance undergo the biggest changes. We show that on time scales up to $-5$~Gyr the orbits of globular clusters in the case of a potential with both changing masses and changing sizes of the components undergo, on average, minor changes compared to the case of a static potential. These changes fit into the limits of the statistical uncertainties caused by the errors in the data. So, on these time scales the Galactic potential may be deemed static. We provide tables with the orbital parameters of globular clusters derived in both static and evolving potentials., Comment: 21 pages, 10 figures, 3 tables

We provide new values of the orbital parameters of 152 globular clusters, which are calculated using the new mean proper motions obtained from the Gaia EDR3 catalog data. The orbits were integrated 5 Gyr back in an axisymmetric three-component potential with a spherical bulge, disk component, and spherical dark halo in the Navarro-Frenk-White form, which we refined using the rotation curve of objects with large galactocentric distances up to 200 kpc. The obtained orbital parameters were compared with the orbital parameters of the same globular clusters calculated earlier in the same gravitational potential using proper motions from the Gaia DR2 catalog data. The objects whose orbits underwent significant changes were identified., Comment: 16 pages, 6 figures, 1 table

We have performed Monte Carlo simulations of the trajectories of several runaway stars using their parallaxes and proper motions from the Gaia EDR3 catalogue. We have confirmed the hypothesis that the stars AE Aur and $\mu$Col are a product of the multiple system breakup $\sim$2.5 Myr ago and the Orion Trapezium may be the parent cluster for this pair of stars. We show that the data from the Gaia EDR3 catalogue for the star $\iota$Ori, mainly the parallax, do not allow us to talk about the breakup of the multiple system of AE Aur, $\mu$Col, and $\iota$Ori. The existence of close pair encounters between the stars HD 30112 and HD 43112 $\sim$1 Myr ago has been confirmed. Close triple encounters confirm the hypothesis that the stars HD 30112 and HD 43112 escaped from the parent cluster Col 69. We show that the stars HIP 28133 and TYC 5368-1541-1 have a nonzero probability of escape from the region within 10 pc of the center of the Orion Trapezium cluster and a fairly high probability (about 8\%) that they were both at distances less than 20 pc from the center of the Orion Trapezium $\sim$2.5 Myr ago. It has been established for the first time that the stars Gaia EDR3 3021115184676332288 and Gaia EDR3 2983790269606043648 have a probability of about 0.5\% that they broke up as a binary system $\sim$1.1 Myr ago. The star Gaia EDR3 3021115184676332288 has a probability of about 16\% that it escaped from the region within 10 pc of the center of the Orion Trapezium cluster $\sim$1 Myr ago., Comment: 15 pages, 9 figures, 3 tables

Using data from the literature, we made a list of individual estimates of the solar Galactocentric distance, which were performed after 2017 by different methods. These values have not yet been used to calculate the best value of mean $R_0$. For the sample containing 21 estimates, based on the standard approach, we found the weighted mean ${\overline R_0}=8.14$ kpc with the dispersion $\sigma=0.16$ kpc, and using the median statistics, we obtained the estimate $R_0=8.15\pm0.11$ kpc. For practical use, the value $R_0=8.1\pm0.1$ kpc can be recommended., Comment: 12 pages, 3 figures, 4 tables

We have studied stellar candidates for close (within 1 pc) encounters with the Solar system. For all of the stars under consideration the kinematic characteristics have been taken from the Gaia EDR3 catalogue. The parameters of the encounters of these stars with the Solar system have been calculated using three methods: (1) the linear one, (2) by integrating the orbits in an axisymmetric potential, and (3) by integrating the orbits in a potential with a spiral density wave. All three methods are shown to yield similar results. We have selected five stars that are good candidates for reaching the boundaries of the Oort cloud and passing through it. Based on the second method, in good agreement with the other two methods, we have obtained the following estimates of the encounter parameters for the star GJ 710: $t_{min}=1.320\pm0.028$ Myr and $d_{min}=0.020\pm0.007$ pc. It is also interesting to note the star Gaia EDR3 510911618569239040 with parameters $t_{min}=-2.863\pm0.046$ Myr and $d_{min}=0.057\pm0.079$ pc., Comment: 10 pages, 4 tables and 0 figures. arXiv admin note: substantial text overlap with arXiv:2006.16555

To construct the rotation curve of the Galaxy, classical Cepheids with proper motions, parallaxes and line-of-sight velocities from the Gaia DR2 Catalog are used in large part. The working sample formed from literature data contains about 800 Cepheids with estimates of their age. We determined that the linear rotation velocity of the Galaxy at a solar distance is $V_0=240\pm3$~km s$^{-1}$. In this case, the distance from the Sun to the axis of rotation of the Galaxy is found to be $R_0=8.27\pm0.10$~kpc. A spectral analysis of radial and residual tangential velocities of Cepheids younger than 120 Myr showed close estimates of the parameters of the spiral density wave obtained from data both at present time and in the past. So, the value of the wavelength $\lambda_{R,\theta}$ is in the range of [2.4--3.0] kpc, the pitch angle $i_{R,\theta}$ is in the range of [$-13^\circ$,$-10^\circ$] for a four-arm pattern model, the amplitudes of the radial and tangential perturbations are $f_R\sim12$~km s$^{-1}$ and $f_\theta\sim9$~km s$^{-1}$, respectively. Velocities of Cepheids older than 120 Myr are currently giving a wavelength $\lambda_{R,\theta}\sim5$~kpc. This value differs significantly from one that we obtained from the samples of young Cepheids. An analysis of positions and velocities of old Cepheids, calculated by integrating their orbits backward in time, made it possible to determine significantly more reliable values of the parameters of the spiral density wave: wavelength $\lambda_{R,\theta}=2.7$~kpc, amplitudes of radial and tangential perturbations are $f_R=7.9$~km s$^{-1}$ and $f_\theta=5$~km s$^{-1}$, respectively., Comment: 17 pages, 12 figures, 2 tables

We have studied the kinematic properties of young pre-main-sequence stars. We have selected these stars based on data from the Gaia DR2 catalogue by invoking a number of photometric infrared surveys. Using 4564 stars with parallax errors less than 20\%, we have found the following parameters of the angular velocity of Galactic rotation: $\Omega_0 =28.84\pm0.10$ km s$^{-1}$ kpc$^{-1}$, $\Omega^{'}_0=-4.063\pm0.029$ km s$^{-1}$ kpc$^{-2}$ and $\Omega^{''}_0=0.766\pm0.020$ km s$^{-1}$ kpc$^{-3}$, where the Oort constants are $A=16.25\pm0.33$ km s$^{-1}$ kpc$^{-1}$ and $B=-12.58\pm0.34$ km s$^{-1}$ kpc$^{-1}$. The circular rotation velocity of the solar neighborhood around the Galactic center is $V_0=230.7\pm4.4$ km s$^{-1}$ for the adopted Galactocentric distance of the Sun $R_0=8.0\pm0.15$ kpc. The residual velocity dispersion for the stars considered is shown to be low, suggesting that they are extremely young. The residual velocity dispersion averaged over three coordinates is $\sim$11 km s$^{-1}$ for Herbig Ae/Be stars and $\sim$7 km s$^{-1}$ for T Tauri stars., Comment: 12 pages, 3 figures and 2 tables

Based on published data, we have produced a sample of 256 radio sources whose trigonometric parallaxes and proper motions were measured by VLBI. This sample contains Galactic masers associated with massive protostars and stars in active star-forming regions. It also includes young low-mass stars from the Gould Belt region whose radio observations were performed in continuum. Based on this, most complete sample of sources to date, we have estimated the velocities $(U,V,W)_\odot$ and the parameters of the angular velocity of Galactic rotation $\Omega_0, \Omega^{(1)}_0, ... , \Omega^{(4)}_0$ and obtained a new estimate of the distance fromthe Sun to the Galactic center, $R_0=8.15^{+0.04}_{-0.20}$ kpc. The parameters of the Galactic spiral density wave have been found from the series of radial, $V_R$, and residual tangential, $\Delta V_{circ}$, velocities of stars. The amplitudes of the radial and tangential velocity perturbations are $f_R=7.0\pm0.9$ km s$^{-1}$ and $f_\theta=3.8\pm1.1$ km s$^{-1}$, the perturbation wavelengths are $\lambda_R=2.3\pm0.2$ kpc and $\lambda_\theta=2.0\pm0.4$ kpc, and the Sun's phases in the spiral density wave are $(\chi_\odot)_R=-163^\circ\pm9^\circ$ and $(\chi_\odot)_\theta=-137^\circ\pm10^\circ$ for the adopted four-armed spiral pattern., Comment: 13 pages, 6 figures, 1 table. arXiv admin note: text overlap with arXiv:1903.09313, arXiv:1906.10151

We present orbits and their properties for 152 globular clusters of the Milky Way galaxy obtained using average Gaia DR2 proper motions and other astrometric data from the list of Vasiliev (2019). For orbit integrating we have used the axisymmetric model of the Galactic potential based on the Navarro-Frenk-White dark halo, and modified by Bajkova and Bobylev (2016) using circular velocities of Galactic objects in wide region of Galactocentric distances (up to 200 kpc) from Bhattacharjee et.al. (2014) catalog. Based on the analysis of the obtained orbits, we have modified the composition of the subsystems of globular clusters presented in Massari et. al. (2019)., Comment: 18 pages, 3 figures, 2 tables, accepted to RAA. arXiv admin note: text overlap with arXiv:2007.02350

We have studied a sample of more than 25 000 young stars with proper motions and trigonometric parallaxes from the Gaia DR2 catalogue. The relative errors of their parallaxes do not exceed 10\%. The selection of stars belonging to active star-forming regions was made by Marton et al. based on data from the Gaia DR2 catalogue by invoking infrared measurements from the WISE and Planck catalogues. Low-mass T Tauri stars constitute the majority of sample stars. The following parameters of the angular velocity of Galactic rotation have been found from them: $\Omega_0 =28.40\pm0.11$ km s$^{-1}$ kpc$^{-1}$, $\Omega^{'}_0=-3.933\pm0.033$ km s$^{-1}$ kpc$^{-2}$ and $\Omega^{''}_0=0.804\pm0.040$ km s$^{-1}$ kpc$^{-3}$. The Oort constants are $A=15.73\pm0.32$ km s$^{-1}$ kpc$^{-1}$ and $B=-12.67\pm0.34$ km s$^{-1}$ kpc$^{-1}$, while the circular rotation velocity of the solar neighborhood around the Galactic center is $V_0=227\pm4$ km s$^{-1}$ for the adopted Galactocentric distance of the Sun $R_0=8.0\pm0.15$ kpc., Comment: 12 pages, 4 figures, 4 tables

We analyze the spatial and kinematic properties of a large sample of young T Tauri type stars in a 500 pc radius solar neighborhood, closely related to the Gould belt. The following parameters of the exponential density distribution have been determined: the average $(z_G)_\odot=-25\pm5$ pc and scale height $h_G=56\pm6$ pc. We propose a method of excluding background stars from the samples, which are located at large heights with respect to the symmetry plane of the Gould belt. We discovered that the expansion effect for the entire star system, $K_G=6\pm1$ km s$^{-1}$ kpc$^{-1}$, is determined mainly by the dynamics of the Scorpius-Centaurus association. We show that the angular velocity of the residual intrinsic rotation of the Gould belt can reach $\Omega_G=6.9\pm0.2$ km s$^{-1}$ kpc$^{-1}$ and that this rotation is opposite to the galactic rotation., Comment: 14 pages, 4 figures. Accepted to Astrophysical Bulletin

The kinematic properties of young stars that have not yet reached the stage of the main sequence are studied. The selection of these stars was recently carried out by Marton et al. (2019) and Vioque et al. (2020) according to the Gaia DR2 catalog using a number of photometric infrared surveys. We have determined the rotation parameters of the Galaxy and the parameters of the ellipsoids of the residual velocities. The linear velocity of the circular rotation of a solar region around the center of the Galaxy, found using 4431 stars, is equal to V_0=229.1+-4.4 km/s. The following ellipsoid parameters of their residual velocities are found from low-mass stars (of type T Tau): $\sigma_{1,2,3}=(9.45,6.99,6.61)\pm(0.94,0.43,0.32)$ km/s. For stars of intermediate masses (Herbig Ae/Be stars), their values turned out to be somewhat larger $\sigma_{1,2,3}=(13.67,9.25,7.26)\pm(2.40,2.44,0.88)$ km/s. Distant stars from both Catalogs trace the local spiral arm well. For 1212 stars, a new estimate of the pitch angle of the Local spiral arm is equal to i=-8.9+-0.1 deg., Comment: 13 pages, 5 figures, 2 tables

The analysis of the orbits of 47 dwarf satellite galaxies of the Milky Way, built using three models of the Galactic gravitational potential with different masses, is presented. The models of the Galactic potential were chosen based on the analysis of a large number of the Galaxy mass estimates known from the literature. The astrometric data needed for calculation of the initial positions and velocities (6D phase space) of the dwarf galaxies are also taken from the literature, where the average proper motions were determined on the basis of the data from the Gaia DR2 Catalog. We present the orbits and their properties of all 47 dwarf galaxies obtained by integration for 13.5 Gyr backward in all three models of the Galactic potential and give a comparison of the orbital parameters. For each model of the Galactic potential we have identified dwarf galaxies that are not connected gravitationally with the Milky Way., Comment: 24 pages, 7 figures, 4 tables

We consider 36 candidates for close (within 1 pc) encounters with the Solar system. These stars have been selected in accordance with the results of an analysis of their motion obtained by various authors. For most stars from this list the kinematic characteristics have been taken from the Gaia DR2 catalogue. The parameters of the encounters of these stars with the Solar system have been calculated using three methods: (1) the linear one, (2) the epicyclic one, and (3) by integrating the orbits in an axisymmetric potential. We have concluded that the epicyclic method works quite well only on a time interval no longer than $\pm$1 Myr. Based on the third method, in good agreement with the first method, for the first time we have obtained the following estimates of the encounter parameters for the star Gaia DR2 3130033734235815424: $t_{min}=-0.62\pm0.12$ Myr and $d_{min}=0.30\pm0.10$ pc., Comment: 14 pages, 2 Figures, 4 Tables

We employ Gaia DR2 proper motions for 151 Milky Way globular clusters from Vasiliev (2019) in tandem with distances and line-of-sight velocities to derive their kinematical properties. To assign clusters to the Milky Way thick disk, bulge, and halo we follow the approach of Posti et al. (2018) who distinguished among different Galactic stellar components using stars's orbits. In particular, we use the ratio $L_{z}/e$, the $Z$ projection of the angular momentum to the eccentricity, as population tracer, which we complement with chemical abundances extracted from the literature and Monte-Carlo simulations. We find that 20 globular clusters belong to the bar/bulge of the Milky Way, 35 exhibit disk properties, and 96 are members of the halo. Moreover, we find that halo globular clusters have close to zero rotational velocity with average value $<\Theta>$ =1$\pm$ 4 km s$^{-1}$. On the other hand, the sample of clusters that belong to the thick disk possesses a significant rotation with average rotational velocity 179 $\pm$ 6 km s$^{-1}$. The twenty globular clusters orbiting within the bar/bulge region of the Milky Way galaxy have average rotational velocity of 49 $\pm$ 11 km s$^{-1}$., Comment: 25 pages, 10 Figures, 5 Tables. Accepted to Astrophysical Journal

The kinematic properties of the Scorpius-Centaurus association were studied using spatial velocities of approximately 700 young T Tauri stars. Their proper motions and trigonometric parallaxes were selected by Zari et al. from the Gaia DR2 catalog, and radial velocities were taken from various sources. The linear expansion coefficients new estimate of the association $K=39\pm2$ km/s/kpc is obtained by considering the influence of the galactic spiral density wave with an amplitude of radial disturbances $f_R=5$ km/s and solar phase in the wave $-120^\circ$. The proper rotation of the association is shown to be small. The residual velocity ellipsoid of these stars has semimajor axes $\sigma_{1,2,3}=(7.72,1.87,1.74)\pm(0.56,0.37,0.22)$ km/s and is positioned at an angle $12\pm2^\circ$ to the galactic plane., Comment: 14 pages, 2 figures, 2 tables

We have studied the kinematic properties of the candidates for hot subdwarfs (HSDs) selected by Geier et al. from the Gaia DR2 catalogue. We have used a total of 12 515 stars with relative trigonometric parallax errors less than 30\%. The HSDs are shown to have different kinematics, depending on their positions on the celestial sphere. For example, the sample of low-latitude $(|b|<20^\circ)$ HSDs rotates around the Galactic center with a linear velocity $V_0=221\pm5$ km s$^{-1}$. This suggests that they belong to the Galactic thin disk. At the same time, they lag behind the local standard of rest by $\Delta V_\odot\sim16$ km s$^{-1}$ due to the asymmetric drift. The high-latitude ($|b|\geq20^\circ$) HSDs rotate with a considerably lower velocity, $V_0=168\pm6$ km s$^{-1}$. Their lagging behind the local standard of rest is already $\Delta V_\odot\sim40$ km s$^{-1}$. Based on the entire sample of 12 515 HSDs, we have found a positive rotation around the $x$ axis significantly differing from zero with an angular velocity $\omega_1=1.36\pm0.24$ km s$^{-1}$ kpc$^{-1}$. We have studied the samples of HSDs that are complete within $r<1.5$ kpc. Based on them, we have traced the evolution of the parameters of the residual velocity ellipsoid as a function of both latitude $|b|$ and coordinate $|z|.$ The following vertical disk scale heights have been found: $h=180\pm6$ and $290\pm10$ pc from the low- and high-latitude HSDs, respectively. A new estimate of the local stellar density $\Sigma_{out}=53\pm4~M_{\odot}$/kpc$^2$ kpc$^{-2}$ has been obtained for $z_{out}=0.56$ kpc from the high-latitude HSDs., Comment: 18 pages, 4 figures, 4 tables

The evolution of the parameters of the residual velocity ellipsoid of hot subdwarfs (HSDs) with their position relative to the Galactic plane is traced, using the HSDs selected by Geier et al. from the Gaia DR2 catalog. Parameters of the Galactic rotation are determined for two $|z|$ zones. These are used to estimate the gradient of the circular rotation velocity, $V_0,$ versus $|z|,$ found to be $\Delta V_0/\Delta |z|=-71\pm7$ km s$^{-1}$ kpc$^{-1}$. The size of the residual velocity ellipsoid is $(\sigma_1,\sigma_2,\sigma_3)=(36.1,27.6,22.8)\pm(0.4,0.8,0.6)$ km/s for HSDs at $|z|<0.5$ kpc and $(\sigma_1,\sigma_2,\sigma_3)=(56.9,55.8,39.7)\pm(0.9,1.1,0.8)$ km/s for HSDs at $|z|\geq0.5$ kpc. When forming the HSD residual velocities, the Galactic rotation was taken into account using individual approaches for each $z$ zone. Parameters of the residual velocity ellipsoids for HSDs located in four plane-parallel layers are also determined. The size of the ellipsoid increases with $z,$ and the inclination of the first axis relative to the Galactic plane also increases. This inclination is close to zero in zones close to the Galactic plane, $z\sim\pm0.2$ kpc, and rises to $\mp12\pm4^\circ$ for $z\sim\pm0.9$ kpc., Comment: 15 pages, 3 figures, 5 tables

Passing through the Galactic disk, a massive object such as a globular cluster, can trigger star formation process leading to the birth of open clusters. Here, we analyze such possible evolutionary relationship between globular and open clusters. To search for the closest rapprochement between objects we computed backwards the orbits of 150 Galactic globular and 232 open clusters (younger than 100 Myr) with proper motions, derived from the Gaia DR2 Catalog. The orbits were computed using the recently modified three-component (disk, bulge and halo) axisymmetric Navarro-Frenk-White potential, which was complemented by non-axisymmetric bar and spiral density wave potentials. We obtained a new estimate for the frequency of impacts of globular clusters about the Galactic disk, which is equal to 4 events for 1 million years. In the framework of the considered scenario, we highlight the following nine pairs of globular and open clusters, with rapprochement within 1 kpc at the time of the intersection the Galactic disk by a globular cluster for the latest 100 Myr: NGC 104 - Turner 3, NGC 104 - NGC 6396, NGC 104 - Ruprecht 127, NGC 5139 - Trumpler 17, NGC 5139 - NGC 6520, NGC 6341 - NGC 6613, NGC 6838 - NGC 6520, NGC 7078 - NGC 7063, NGC 6760 - Ruprecht 127., Comment: 9 pages, 3 Figures, 4 Tables, accepted in MNRAS, 2019

We have studied a sample containing about 6000 OB stars with proper motions and trigonometric parallaxes from the Gaia DR2 catalogue. The following parameters of the angular velocity of Galactic rotation have been found: $\Omega_0=29.70\pm0.11$ km s$^{-1}$ kpc$^{-1}$, $\Omega'_0=-4.035\pm0.031$ km s$^{-1}$ kpc$^{-2}$, and $\Omega''_0= 0.620\pm0.014$ km s$^{-1}$ kpc$^{-3}$. The circular rotation velocity of the solar neighborhood around the Galactic center is $V_0=238\pm5$ km s$^{-1}$ for the adopted Galactocentric distance of the Sun $R_0=8.0\pm0.15$ kpc. The amplitudes of the tangential and radial velocity perturbations produced by the spiral density wave are $f_\theta=4.4\pm1.4$ km s$^{-1}$ and $f_R=5.1\pm1.2$ km s$^{-1}$, respectively; the perturbation wavelengths are $\lambda_\theta=1.9\pm0.5$ kpc and $\lambda_R=2.1\pm0.5$ kpc for the adopted four-armed spiral pattern. The Sun's phase in the spiral density wave is $\chi_\odot=-178^\circ\pm12^\circ$., Comment: 14 pages, 2 tables, 4 figures. arXiv admin note: substantial text overlap with arXiv:1903.09313, arXiv:1904.12686, arXiv:1809.10512, arXiv:1609.08341

We consider open star clusters (OSCs) with the proper motions, parallaxes, and line-of-sight velocities calculated by various authors from Gaia DR2 data. The distance scale factor has been found by analyzing the separate solutions of the basic kinematic equations to be $p=1.00\pm0.04.$ It shows that the distances calculated using the parallaxes from the Gaia DR2 catalogue do not need any correction factor. We have investigated the solutions obtained from various OSC samples differing in both age and accuracy of their parallax and line-of-sight velocity measurements. The solution obtained from a sample of 930 OSCs satisfying the constraints on the age logt<9 and the relative trigonometric parallax error <30% is recognized to be the best one, with 384 OSCs in this sample having the mean line-of-sight velocities calculated from at least three probable members of the corresponding clusters. As a result of the simultaneous solution of all the basic kinematic equations, we have found the following kinematic parameters from this sample: $(U,V,W)_\odot=(8.53,11.22,7.83)\pm(0.38,0.46,0.32)$ km s$^{-1}$, $\Omega_0=28.71\pm0.22$ km s$^{-1}$ kpc$^{-1}$, $\Omega'_0=-4.100\pm0.058$ km s$^{-1}$ kpc$^{-2}$, and $\Omega''_0= 0.736\pm0.033$ km s$^{-1}$ kpc$^{-3}$. The linear rotation velocity at the adopted at the adopted solar distance $R_0=8\pm0.15$ kpc is $V_0=229.7\pm4.6$ km s$^{-1}$. An analysis of the proper motions for these 930 OSCs has shown that, apart from the rotation around the Galactic z axis, there is rotation of the entire sample around the x axis with an angular velocity of $0.48\pm0.15$ km s$^{-1}$ kpc$^{-1}$ differing significantly from zero., Comment: 12 pages, 1 figure, 2 tables. arXiv admin note: text overlap with arXiv:1903.09313

We have selected a sample of 326 young $(\log t<8)$ open star clusters with the proper motions and distances calculated by various authors from Gaia DR2 data. The mean values of their line-of-sight velocities have also been taken from various publications. As a result of our kinematic analysis, we have found the following parameters of the angular velocity of Galactic rotation: $\Omega_0=29.34\pm0.31$ km s$^{-1}$ kpc$^{-1}$, $\Omega'_0=-4.012\pm0.074$ km s$^{-1}$ kpc$^{-2}$, and $\Omega''_0=0.779\pm0.062$ km s$^{-1}$ kpc$^{-3}$. The circular rotation velocity of the solar neighborhood around the Galactic center is $V_0=235\pm5$ km s$^{-1}$ for the adopted Galactocentric distance of the Sun $R_0=8.0\pm0.15$ kpc. The amplitudes of the tangential and radial velocity perturbations produced by the spiral density wave are $f_\theta=3.8\pm1.2$ km s$^{-1}$ and $f_R=4.7\pm1.0$ km s$^{-1}$, respectively; the perturbation wavelengths are $\lambda_\theta=2.3\pm0.5$ kpc and $\lambda_R=2.2\pm0.5$ kpc for the adopted four-armed spiral pattern. The Sun's phase in the spiral density wave is close to $-120\pm10^\circ.$, Comment: 14 pages, 5 figures. arXiv admin note: text overlap with arXiv:1809.10512, arXiv:1609.08341

Based on a large sample of 133 Galactic globular clusters we obtained a new estimate of the frequency of globular-cluster impacts onto the Galactic plane, which we found to be equal to three events per 1 Myr. Our computations involving new kinematical data do not support the well-known hypothesis about the possible origin of the open cluster Stephenson~2 as a result of the massive globular cluster $\omega$ Cen crossing the Galactic disk. Our results also do not support the well-known hypothesis that the globular cluster NGC6397 could trigger the formation of the open cluster NGC6231. We found for the first time six globular clusters, which could have triggered the formation of an open cluster when crossing the Galactic plane. These are the globular clusters NGC104, NGC2808, NGC6362, NGC6540, NGC6749, and NGC6752. For each of these clusters we identify one or several open clusters, which were possibly born via such scenario. In our opinion, of greatest interest are the pairs NGC104-Ruprecht 129, and NGC6362-Pismis 11., Comment: 17 pages, 6 figures, 2 tables