The influence of galactic aberration on precession parameters determined from VLBI observations

The influence of proper motions of sources due to Galactic aberration on precession models based on VLBI data is determined. Comparisons of the linear trends in the coordinates of the celestial pole obtained with and without taking into account Galactic aberration indicate that this effect can reach 20 μ as per century, which is important for modern precession models. It is also shown that correcting for Galactic aberration influences the derived parameters of low-frequency nutation terms. It is therefore necessary to correct for Galactic aberration in the reduction of modern astrometric observations.     

Forecasting the polar motions of the deformable Earth

A mathematical model for the complicated phenomenon of the polar oscillations of the deformable Earth that adequately describes the astrometric data of the International Earth Rotation Service is constructed using celestial mechanics and asymptotic techniques. This model enables us to describe the observed phenomena (free nutation, annual oscillations, and trends) simply and with statistical reliability. The model contains a small number of parameters determined via a least-squares solution using well-known basis functions. Interpolations of the polar trajectory for intervals of 6 and 12 yrs and forecasts for 1–3 yrs are obtained using the theoretical curve. The calculated coordinates demonstrate a higher accuracy than those known earlier.     

The empirical Melchior laws and parametric excitation of the Chandler wobble

Models of the motion of the terrestrial reference frame with respect to an inertial frame can describe the motions of the Earth-Moon system, which are traditionally separated into precession, nutation, the polar motion, and rotation about the Earth’s axis. Existing theoretical models do not describe variations in the Earth-orientation parameters with the required accuracy, so that the current polar coordinates and duration of the day must be determined from observations. To improve theoretical models for the time dependence of the coordinates of the Earth’s pole, we examine the possible excitation of the Chandler wobble due to internal properties of the Earth-Moon system. A differential equation describing the parametric resonance in the Earth-Moon system is obtained for the first region of the parametric excitation. The solution of this equation analytically describes the finite amplitudes of the nonlinear conservative system. The theoretical results are compared with the empirical laws of Melchior deduced from observational data on the coordinates of the Earth’s pole.     

Dynamics of Natural Satellites of Planets Based on Observations

There is wide interest in the results of studies of the dynamics of satellites of planets. Such data are needed to determine the physical properties of celestial bodies, and they may be able to provide information about the origins and evolution of the solar system. The general approach to studying the dynamics of satellites involves developing models for the motion and ephemerides based on observational data. Ephemerides are required to prepare and launch space missions to other planets and help discover new celestial bodies. High-precision astrometric coordinates of the principal satellites of Jupiter, Saturn, and Uranus are derived from photometric observations of occultations and eclipses of these satellites. To this end, worldwide observing campaigns have been organized. Enhancement in the precision of ephemerides can be obtained not only by increasing the accuracy of observations, but also by expanding the time interval covered by the observations. Many new, distant satellites of the major planets were discovered in the early 21st century. However, observations of these satellites are scarce and were obtained over short time intervals; as a result, some of these satellites were lost. To date, 179 natural satellites are known. This paper is based on a presentation made at the conference “Modern Astrometry 2017,” dedicated to the memory of K.V. Kuimov (Sternberg Astronomical Institute, Moscow State University, October 23–25, 2017).

     

Perspectives for Distributed Observations of Near-Earth Space Using a Russian–Cuban Observatory

The creation of a specialized network of large, wide-angle telescopes for distributed observations of near-Earth space using a Russian–Cuban Observatory is considered. An extremely important goal of routine monitoring of near-Earth and near-Sun space is warding off threats with both natural and technogenic origins. Natural threats are associated with asteroids or comets, and technogenic threats with man-made debris in near-Earth space. A modern network of ground-based optical instruments designed to ward off such threats must: (a) have a global and, if possible, uniform geographic distribution, (b) be suitable for wide-angle, high-accuracy precision survey observations, and (c) be created and operated within a single network-oriented framework. Experience at the Institute of Astronomy on the development of one-meter-class wide-angle telescopes and elements of a super-wide-angle telescope cluster is applied to determine preferences for the composition of each node of such a network. The efficiency of distributed observations in attaining maximally accurate predictions of the motions of potentially dangerous celestial bodies as they approach the Earth and in observations of space debris and man-made satellites is estimated. The first estimates of astroclimatic conditions at the proposed site of the future Russian–Cuban Observatory in the mountains of the Sierra del Rosario Biosphere Reserve are obtained. Special attention is given to the possible use of the network to carry out a wide range of astrophysical studies, including optical support for the localization of gravitational waves and other transient events.     

Numerical modeling of the motion of rigid ellipsoidal objects in slow viscous flows: A new approach

A simple algorithm for modeling the rotation of rigid ellipsoidal objects in viscous flows based on Jeffery's (1922, Proceedings of the Royal Society of London A102, 161–179) theory is presented and is implemented in a fully graphic mathematics application Mathcad^® (http://www.mathsoft.com). The orientation of ellipsoidal objects is specified in terms of polar coordinate angles that can be easily converted to the trend and plunge angles of the three principal axes rather than the Euler angles. With the Mathcad worksheets presented in the supplementary data associated with this paper, modeling the rotation paths of individual rigid objects, the development of inclusion trail geometry within syn-kinematic porphyroblasts, and the development of preferred orientation and shape fabrics for a population of rigid objects becomes as easy a task as using a spreadsheet. The shape and preferred orientation fabrics for a population of rigid objects can be presented in both a three-dimensional form and a two-dimensional form, allowing easy comparison between field data and model predictions. The modeler can customize the type and format of the output to best fit the purpose of the investigation and to facilitate the comparison of model predictions with geological observations. Application examples are presented for various types of modeling involving rigid objects.     

Long-Period Variations in Oscillations of the Earth’s Pole due to Lunar Perturbations

A numerical–analytical approach is used to investigate irregular effects in oscillations of the Earth’s pole related to variations in the Chandler and annual components. An approach to studying oscillations in the motion of the Earth’s pole based on a joint analysis of the Chandler and annual components of this motion is proposed. A transformation to a new coordinate system in which the motion of the pole is synchronous with the precession of the lunar orbit can be found in this approach. Estimates of the precision of predictions of the coordinates of the Earth’s pole taking into account additional terms due to lunar perturbations are presented.

     

Effects of instability of the Earth and celestial coordinate systems on Earth orientation parameters

Unknown secular and long-term changes in the Earth orientation parameters attributed to instability (possible rotation) of both the Earth and celestial coordinate systems (ECS and CCS) are studied. Rotation of the CCS due to changes in the coordinates of extragalactic sources resulting from gravitational lensing can lead to errors of the order of several microarcseconds in the orientation parameters. The rotation of the ECS due to the crust pressing on the mantle diminishes the tidal retardation of the Earth's rotation and produces long-term variations in the duration of the day (with a period of about 1500 years) and in the motion of the pole relative to the Earth's surface.     

Modeling intraday oscillations of the Earth’s pole

An amplitude-frequency analysis of a few-parameter model for intraday oscillations of the Earth’s pole induced by gravitational-tidal torques exerted by the Sun and the Moon is presented. The characteristic features of the intraday oscillations in the polar coordinates are found using the dynamical Euler-Liouville equations, taking into account irregular perturbations. The modeling results for the polar motion are compared with high-accuracy VLBI observations over short time intervals. An amplitude-frequency analysis of the polar oscillations and the second zonal harmonic c ₂₀ of the geopotential is presented.     

Principles for selecting a list of reference radio sources for a celestial coordinate system

Time series of the coordinates of radio sources defining the celestial coordinate frame are analyzed. Methods for selecting such sources so as to enhance the stability of the frame are considered. Some of these sources, including so-called “defining” sources, demonstrate significant proper motions. Since the stability of the celestial coordinate frame is determined by an absence of global rotation relative to the defining sources (no net rotation), variation in their coordinates will lead to a rotation of the axes of the celestial coordinate frame. The parameters of this rotation are calculated for two physical models for the motions of extragalactic radio sources. The motions displayed by the first group of sources are linear and uniform. Since the apparent speeds of radio sources are often close to, and sometimes exceed, the speed of light, it is supposed that such radio sources have relativistic jets or plasma clouds that move with speeds roughly equal to the speed of light. The observed uniform, linear motion can then be explained by precession of the jet. The second group of sources display non-linear motions, interpreted as a manifestation of the acceleration of matter by the jet. It is assumed that a cloud of particles that moves into the path of the jet is accelerated to relativistic speeds by the jet. A list of sources that should form a very stable coordinate system for several decades into the future is composed based on these two models.     

Orbits of the visual binaries ADS 8814 and ADS 8065 from observations along a short arc

The orbits of the visual binaries ADS 8814 and ADS 8065 are determined for the first time. The orbits were calculated using the parameters of the apparent motion, based on position observations along short arcs obtained on the 26-inch refrector of the Pulkovo Observatory, supplemented with radial-velocity observations for the stellar components in both pairs obtained on the 1-m telescope of the Simeiz Section of the Crimean Astrophysical Observatory. All previous visual and photographic observations of these stars after 1832 were also taken into account. The orbit of ADS 8814 was refined using the differential-correction method. The orbital periods of these two stars are about 800 and 6000 years, respectively. The mass estimates derived for the known parallaxes from the Hipparcos catalog correspond to the spectral types of these stars. The polar vectors of the obtained orbits in Galactic coordinates are also given.     

A gravitational-tidal mechanism for the Earth’s polar oscillations

Perturbed, rotational-oscillational motions of the Earth induced by the gravitational torques exerted by the Sun and Moon are studied using a linear mechanical model for a viscoelastic rigid body. A tidal mechanism is identified for the excitation of polar oscillations, i.e., for oscillations of the angular-velocity vector specified in a fixed coordinate frame, attributed to the rotational-progressive motion of the barycenter of the Earth-Moon “binary planet” about the Sun. The main features of the oscillations remain stable and do not change considerably over time intervals significantly exceeding the precessional period of the Earth’s axis. A simple mathematical model containing two frequencies, namely, the Chandler and annual frequencies, is constructed using the methods of celestial mechanics. This model is adequate to the astrometric measurements performed by the International Earth Rotation Service (IERS). The parameters of the model are identified via least-squares fitting and a spectral analysis of the IERS data. Statistically valid interpolations of the data for time intervals covering from several months to 15–20 yr are obtained. High-accuracy forecasting of the polar motions for 0.5–1 yr and reasonably trustworthy forecasting for 1–3 yr demonstrated by observations over the last few years are presented for the first time. The results obtained are of theoretical interest for dynamical astronomy, geodynamics, and celestial mechanics, and are also important for astrometrical, navigational, and geophysical applications.     

The Hamiltonian in the planetary or satellite problem as a d’Alembertian function

This completes a series of three articles establishing the d’Alembertian properties of key functions in celestial mechanics. The first two presented the concept of a d’Alembertian function of a pair of complex variables specified within an infinitely long bottle with a narrowing neck. The main properties of d’Alembertian functions were demonstrated, and it was shown that the main functions in celestial mechanics belong to this class, including Cartesian coordinates. The d’Alembertian radii of these functions were found and their moduli estimated, in many cases exactly. The current paper demonstrates the d’Alembertian nature of the perturbing function—or equivalently, the Hamiltonian—in the planetary or satellite problem. The d’Alembertian radius of this function is estimated.     

Automated forecasting of volcanic ash dispersion utilizing Virtual Globes

There are over 100 active volcanoes in the North Pacific (NOPAC) region, most of which are located in sparsely populated areas. Dispersion models play an important role in forecasting the movement of volcanic ash clouds by complementing both remote sensing data and visual observations from the ground and aircraft. Puff is a three-dimensional dispersion model, primarily designed for forecasting volcanic ash dispersion, used by the Alaska Volcano Observatory and other agencies. Since early 2007, the model is in an automated mode to predict the movement of airborne volcanic ash at multiple elevated alert status volcanoes worldwide to provide immediate information when an eruption occurs. Twelve of the predictions are within the NOPAC region, nine more within the southern section of the Pacific ring of fire and the others are in Europe and the Caribbean. Model forecasts are made for initial ash plumes ranging from 4 to 20 km altitude above sea level and for a 24-h forecast period. This information is made available via the Puff model website. Model results can be displayed in Virtual Globes for three-dimensional visualization. Here, we show operational Puff predictions in two and three-dimensions in Google Earth^®, both as iso-surfaces and particles, and study past eruptions to illustrate the capabilities that the Virtual Globes can provide. In addition, we show the opportunity that Google Maps^® provides in displaying Puff operational predictions via an application programming web interface and how radiosonde data (vertical soundings) and numerical weather prediction vertical profiles can be displayed in Virtual Globes for assisting in estimating ash cloud heights.     

基于卫星高度计的全球大洋潮汐模式的准确度评估

依据152个深海验潮站与大洋岛屿地面验潮站观测得到的8个主要分潮(M2、S2、K1、O1、N2、K2、P1及Q1)调和常数,对现有7个全球大洋潮汐模式的准确度进行了检验,结果显示各模式在深海大洋区域均达到了比较高的准确度:M2分潮的潮高均方根偏差在1.0～1.3cm之间;8个分潮的和方根偏差在2.1～2.3cm之间,与早期的模式相比,准确度又有了进一步提高。还依据中国近海18个岛屿的调和常数对其中的5个大洋潮汐模式的准确度进行了检验,结果表明,M2分潮均方根偏差在4.4～10cm,明显高于大洋的均方根偏差。其中日本国家天文台的潮汐模式NAO99在中国近海的结果相对较准确。     

The maser source S140-H2O as a protoplanetary disk

We present the observations of the H₂O maser in S140 with the 22-m radio telescope of the Pushchino Radio Astronomy Observatory in 1992–1999. The H₂O maser emission is mainly concentrated in three symmetrically placed narrow radial-velocity intervals. In contrast to our earlier observations (1981–1991), we did not detect emission simultaneously in all three intervals; instead, the emission appeared successively in each. We discuss possible origins for this behavior. To explain the flux variability and radial-velocity drift of the main components, we propose a model with Keplerian orbital motion of clumps (protoplanets) and calculate their orbital parameters.     

Chandler wobble of the poles as part of the nutation of the atmosphere-ocean-Earth system

The paper presents calculated spectra of El Niño Southern oscillation (ENSO) indices. The ENSO spectra have components with periods that are multiples of the Earth’s free (1.2 years) and forced (18.6 years) nutation periods. Analysis of a 41-year series of exciting functions for the atmospheric angular momentum confirms the existence of such periodicity. Nutation waves responsible for the El Niño phenomena in the ocean, the Southern oscillation in the atmosphere, and the presence of subharmonics of the Chandler period (1.2 years) and superharmonics of the lunar period (18.6 years) in the ENSO spectra are described. A model for the nonlinear nutation of the Earth-ocean-atmosphere system is constructed. In this model, the ENSO, acting at frequencies of combinational resonances, excites the Chandler wobble of the Earth’s poles. At the same time, this wobble interacts with the nutation motions of the atmosphere and World Ocean.     

Optical observations of the gravitational lens SBS1 520+530 at the Ma $$\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} $$ danak Observatory

Observations of the gravitationally lensed quasar SBS 1520+530 obtained in 2000–2001 on the 1.5-m telescope of the Ma $\overset{\lower0.5em\hbox{$\overset{\lower0.5em\hbox{ danak Observatory (Uzbekistan) are presented. The photometric algorithms used to observe the components of SBS 1520+530 are discussed. The images have a resolution of 0.5″–0.6″, enabling us to detect the lensing galaxy in the R and I bands and to measure its luminosity and coordinates. The results of photometric observations of components A and B of SBS 1520+530 are presented; the light curves show variability on various time scales from a few weeks to a year. A gravitational-lens model for SBS 1520+530 is constructed utilizing all currently available data.     

On the accuracy of the theory of precession and nutation

Corrections to the IAU 2000/2006 parameters of the theory of precession and nutation are calculated using five different series—two individual series and three combined series that have been used in the literature for this purpose. A comparison of the sets of corrections obtained using the different datasets indicates significance systematic differences between them, which often substantially exceed the corresponding random errors. At the same time, existing studies have usually used data obtained from one or two series chosen by the authors without special justification. When refining the theory of precession and nutation, it is necessary to consider and compare various available series of VLBI data if one wishes to reduce the systematic errors in an improved model.     

公转轴应力场星球说——地球、火星南南西应力场四组三维构造系

介绍了对地球构造格局,运动方式及其动力源问题研究取得的新成果。它不同于流行已久的以地球自转轴旋转和以软流圈带动岩石圈漂移以及随机的地幔柱（流）为构造动力源的观点,而是与黄赤交角相关的沿公转轴方向的统一应力场,认为中国西部ＮＷＷ向压性,ＮＥＥ与ＮＮＷ是与黄赤交角相关的沿公转轴方向的统一应力场。认为中国西部ＮＷＷ向压性,ＮＥＥ与ＮＮＷ向两组共轭扭性及ＮＮＥ向张性带交接,为来自全球ＳＳＷ主压应力场形成的