The possibility and effectiveness of using an automated zenith telescope to determine selenodetic rotation parameters by computer simulation of observations using a telescope installed on the lunar surface are considered, in particular, modeling of star tracks at an automated zenith telescope and the possibilities of astrophysical research, development of a space observations program.

This work is devoted to the construction of a brightness structural model of the long-period comet Bennett C/1969 Y1. This comet belongs to the comets of the Jupiter family (JF) and has a Tisserand's parameter T > 2. Determining the brightness characteristics of the comet has been one of the most important goals of cometary observations over the past century. The complexity of such studies lies in the fact that we are dealing with extended sources moving relative to background stars. The problem of obtaining reliable estimates of the distribution of brightness parameters (BPs) for long-period comets also remains especially important, because for many of them observations were made back in the days when high-precision methods, such as CCD-matrices and other technical tools, were not available. At the same time, most of the determined stellar magnitudes of long-period comets were related to the gaseous coma surrounding the comet's nucleus, and not to the comet's nucleus itself. At the same time, cosmic ultraviolet observations of comets in the Lyman-alpha hydrogen lines made it possible to obtain very important data for estimating the emission of H2O by the cometary nucleus, as well as other types of molecules (e.g. C2, C3, CN, OH). In the presence of dependencies between the productivity of the H2O cometary nucleus and its brightness characteristics, the determination of BPs of cometary nuclei has acquired a new meaning. However, the dependence of the size of the nucleus on its BPs is not linear, since there is a correlation with the albedo of the surface of the nucleus. In this work, BPs and albedo for comet Bennett C/1969 Y1 are studied. Taking into account the data obtained and the solution of the described problems, we applied the author's isophote method to analyze the structure of the brightness characteristics of Bennett C/1969 Y1.

The work focuses on using the isophote method to construct a 45P/Honda comet model. At the same time, important problems were solved for modeling the physical surface of a comet and studying the structure of the cometary nucleus. This is due to the fact that, on the basis of modern studies of meteoroids, complex internal processes and dynamic phenomena on their surface have been discovered. The study of comet nuclei is of great importance, since, according to the theory of their formation, they were formed from the matter of the protoplanetary disk. Thus, modeling and analysis of the structure of various comets make it possible to create a more accurate theory of their evolution. This made it possible to evaluate the structural parameters more accurately and reliably. This allowed for the evaluation of the structural parameters more accurately and reliably. Isophotes of the nucleus, coma and tail of comet 45P/Honda were determined. Depending on the point where the comet is located on the trajectory of its orbit, one can see structural changes in the comet’s brightness from the nucleus to the peripheral region. Near the cometary nucleus, the isophotes are circular in shape. If in the center of the model the isophotes have a shape close to narrow rings, then elongations in the direction of the cometary tail and thickening of their structure appear towards the peripheral regions. Large and small tail rays can be distinguished, and the nucleus is well marked. In the future, the author’s method for modeling isophotes, developed in this work, will allow studying the structure of various cometary objects, and, based on the results, determine the degree of comet activity. On the other hand, about the development of the theory of dynamic processes and the evolution of the Solar system, one can use the data on changes in cometary activity in the process of its movement around the Sun.

Up to here we have seen the abstract theory, which involves a certain number of operators on H. The choice of H and of these operators fixes the physical model. This section provides some hints on how to do this choice.

This paper aims at considering the issues of regression modeling of the surface of Saturn’s moon Titan and at studying the produced model by means of fractal geometry. The fractal analysis allows studying the structure of complex objects, taking into account their qualitative specifics, for example, the relationship between the structure and the processes of its formation. When constructing a harmonic model of Titan, the method of expansion of topographic information into spherical functions was used. As a result, based on the harmonic analysis of the Cassini mission data, a topographic model of Titan was created. In the final form, the model describing Titan’s surface includes the expansion of the height parameter depending on the spherical coordinates into a slowly converging regression series of spherical harmonics. It should be emphasized that for modeling surface details of the surface on a scale of 1 degree, the order of expansion should be about 180, which requires an analysis of (180+1)2 harmonic expansion coefficients. An overdetermined topographic information system was solved to meet the regression modelling’s conditions. In this case, a number of qualitative stochastic data, such as external measures, were used together with the standard postulation of the harmonic system of the Titan model. As a result of a sampling of self-similar regions (with close values of the self-similarity coefficients) on the surface of Titan, coinciding with the SRGB parameter (characterizes the color fractal dimension), the elements of the moon’s surface were determined, which with a high degree of probability were evolutionarily formed under the influence of the same selenochemical processes.

One of the priority tasks of modern astronomy is the observation and study of transient celestial processes, which also concerns photoelectric observations of lunar occultations of stars. These measurements provide unique and important material both for determining the star diameters from a diffraction curve analysis regarding the change in the brightness of the star occulted by the Moon and for developing a model of the lunar libration zone. This paper is focused on building a digital model of isohypses (DMI) characterizing the position of 40 000 selenocentric radius vectors depending on the position of the lunar limb.

In this work, using multi-parameter harmonic analysis and expansion of altimetry into spherical functions, models of the Moon’s physical surface (digital lunar selenocentric map - DLSM) are built, and a comparison of similarity of chosen local areas of the complex lunar structure is performed. The constructed DLSM have radius-vectors of the surface points in accordance with the space measurements taken. As result, the averaged fractal dimension of the selenocentric surfaces profiles models was found to 1.345. The similarity and difference parameters were determined by the author’s method using fractal similarity coefficients. The analysis of macrosurfaces based on multi-parameter and fractal methods for the selenocentric models built in this work has not been conducted before.

In this work we propose the determination of the astrophysical dynamic coordinate system's orientation in relation to HCRF (Hipparcos Celestial Reference Frame) using photoelectric lunar occultation. The photoelectric method of recording an occultation that allows obtaining occultations moment with the accuracy up to 0.001s (i.e. 100 times more accurate than by visual method) was found to be the most accurate. Apart from the tasks of space geodesy, photoelectric observations allow carrying out other interesting researches, too. These tasks include determination of amendments to orbital longitude and latitude of the Moon and amendments to ephemeris time. The photoelectric observations of occultation are valuable materials for solving some astrophysical tasks. If one records changes in magnitude at the moment when a star is occultated by the Moon, then one may obtain diameter of the occultated star through the spectrum of those changes. Other important problems are detecting double and multiple systems of stars and measuring angular distances between their components.

The present paper focuses on studying the lunar dynamic processes. As selenophysics is a complex system and moonquakes are complex multi-parametric systems too, the analysis of moonquakes and the development of an analytical theory of such processes require the application of robust methods and using multiparametric calculations. Moreover, selenophysics is a more complex system than geophysics. In this connection, the study of lunar processes and determination of moonquakes parameters require reliable estimates of the results obtained and application of the methods of complex system physics. The observations from "Apollo" space mission were used in the study, and the multiparametric correlation method was developed for their processing. Currently, one uses various methods, similar to the ones for the Earth's seismic process investigation, such as seismic interferometry for deep moonquakes, time scales analysis, seismic phenomena magnitude gradient change, solution of the inverse problem of signals reflection on "Apollo" stations. Now, on the basis of moonquakes data, the internal structure of the Moon is being studied. Using the moonquakes data, a model of the lunar tidal parameters had been developed and was later refined by "GRAIL" (gravitation), "LRO" (shape), and "LLR" (rotation) space missions' data. As a result, in the areas where deep moonquakes occurred, the inner layer of the Moon with low viscosity was found. In the present work, the author's method of analyzing moonquakes allowing to conduct multiparametric analysis of seismic time series observations was applied. The method was developed for the investigation of seismic processes occurring on the Earth using the space observations. In order to provide qualitative description of moonquakes dynamical parameters, the special software was developed.

An important area of investigation in astronomy is the relationship between fundamental and dynamical coordinate systems. Valuable material for such studies is provided by photoelectric occultation observations of stars by the Moon, which can provide high precision of detecting rapidly occurring processes and have been carried out over a long time interval. This latter feature is especially important for analyses of the stellar propermotions dynamics. A method has been developed to use photoelectric occultation observations to determine the orientation and rotational parameters of the axes of the coordinate system used for modern star catalogs relative to the coordinate axes of a highly accurate dynamical ephemeris of theMoon. A complete database of photoelectric occultation observations has been created for this purpose, containing data for 57 365 events. The combination of photoelectric occultation observations and other astronomical observations such as lunar laser-ranging data enables the highly accurate determination of parameters of the Moon’s dynamics, such as systematic errors in catalog coordinate systems, including various geodetic reference systems. The parameters of shifts and the rotation of the axes of the Hipparcos Celestial Reference Frame relative to the DE421 dynamical system are obtained. This paper is based on a talk given at the conference “Modern Astrometry 2017,” dedicated to the memory of K.V. Kuimov (Sternberg Astronomical Institute, Moscow State University, October 23–25, 2017).

There is a new approach for the estimation of the position accuracy and proper motions of the stars in astrometric catalogues by comparison of the stars' positions in the researched and Hipparcos catalogues in different periods, but under a standard equinox. To verify this method was carried out the analysis of the star positions and proper motions UCAC2, PPM, ACRS, Tycho-2, ACT, TRC, FON and Tycho catalogues. As a result of this study was obtained that the accuracy of positions and proper motions of the stars in Tycho-2 and UCAC2 catalogues are approximately equal. The results of the comparison are represented graphically.

In this work, the selenocentric dynamic reference net was developed for the first time in the field of selendesy in order to address problems with space navigation. Three tasks were addressed in this research: a) the analysis of the mathematical model of the orthogonal coordinate transformation accuracy; b) the identification of the basic dynamic reference system objects with ones that are contained in reducing catalogues; and c) the extension of the base points net of the basic dynamic reference system. The result was a dynamic coordinate system summary that contains 1 162 objects. The correlation analysis of this net was carried out and was found to coincide with modern dynamic coordinate systems that have been obtained. This selenocentric reference catalogue covers the full visible area of the Moon.