Astronomical School’s Report

Journal Information
ISSN / EISSN : 1607-2855 / 2411-6602
Published by: National Aviation University (10.18372)
Total articles ≅ 434
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Ya.I. Zyelyk, L.V. Pidgorodetska, S.V. Chornyy, L.M. Kolos, Yu.R. Dykach
Astronomical School’s Report, Volume 16, pp 48-57; https://doi.org/10.18372/2411-6602.16.08

Abstract:
Climate change studies are based on the data processing of the following time series for number of Ukrainian cities: daily precipitation and air temperature from the site of the European Climate Assessment & Dataset (ECA&D) project and monthly carbon dioxide emissions from fossil fuels in the atmosphere from the area of one geographical degree size from the site of the Carbon Dioxide Information Analysis Center (CDIAC). Assessment of synchronous dynamics and forecasting of the air temperature, precipitation according to the period 1950–2016 and the carbon dioxide concentration in atmosphere according to the period 1951–2013 was performed using two types of models: linear regression and neural network model in the form of perceptron with one hidden neuron layer. These models implementation is based on modern approaches to the Big Data intellectual analysis: Data Mining and Knowledge Discovery in Databases. The program scenarios for processing, intelligent analysis and forecasting of the above mentioned data time series using the constructed forecasting models have been developed and implemented in the unified analytical platform Deductor. The monthly time series of the emission in atmosphere of carbon dioxide from fossil fuels to area of 1 geographical degree in 1951–2013 for number of Ukrainian cities shows clear trend, which is well approximated by the cubic polynomial and does not contain a periodic seasonal component. There is the tendency to increasing CO2 emissions before 1991 and the declining tendency after 1991 with some “plateau” in the period 2000–2009 that are years of relative stability in the economic development of Ukraine. However, there is no correlation between the trend of CO2 emissions and the trend of average monthly temperature in 1951–2013. The predictive model of linear regression was the most acceptable for time series of average monthly temperature in 1950–2016, which are characterized by strong seasonal component with the periodicity of 1 year. Using the predictive model of linear regression [240 × 1], trained on the dataset, constructed by the sliding window method with retrospective depth of 240 months, the consistent forecast of the average monthly temperature time series for Kyiv after 12.01.2016 with the forecast horizon of 60 months was derived. However, the application of the predictive model of linear regression is characterized by a relatively short horizon of consistent forecasting. For the time series of the average monthly temperature for Kyiv city after 12.01.2016, the predictive neural network model [360 × 5 × 1] (number of inputs is equal to the selected prehistory depth of the time series samples that is 360; number of outputs is 1; number of neurons in the hidden layer is 5; activation function type is sigmoid with the given slope 1) provided the consistent forecast with the horizon of 120 months. Low values of the maximum and average relative errors of the neural network model were achieved on the training set (4.45·10-2 and 2.99·10-4, respectively) and on the test set (3.60·10-2 and 5.69·10-3, respectively). Similarly, for the time series of monthly CO2 emissions for the Kyiv city after December 1, 2013, the predictive neural network model [240 × 5 × 1] provided consistent forecast with the horizon of 60 months. In general, the time series of monthly CO2 emission values are characterized by much smaller values of the consistent forecast horizon in comparison with the time series of the average monthly temperature, at least when using predictive neural network models.
M.M. Fys, A.M. Brydun, A.R. Sohor
Astronomical School’s Report, Volume 16, pp 38-42; https://doi.org/10.18372/2411-6602.16.06

Abstract:
The generalization of the formula of a priori accuracy estimation for the case of implicitly given functions is performed. This is based on the classical definition of the root mean square error, which is given as the sum of the squares of the products of partial derivatives of the arguments and the errors of their definition. Differentiation of functions is carried out with the involvement of the theory of implicit functions of many variables, which does not require explicit assignment of the function by an analytical expression. The corresponding derivatives are determined by the differentiation of the equations in which the investigated function appears, according to the corresponding variables, including the function itself. Only the values of the function and arguments for which the accuracy is evaluated are required for the calculations. These values are found in different ways, including approximate methods for solving nonlinear equations (for example, Newton's method, half-division method). This approach is generalized to the case of several functions, which are already determined by a set of nonlinear equations. Their differentiation gives a linear system, which solutions are elements in the formulas for estimating the accuracy of each function. The solution of this system is determined by Cramer's method. Since the matrix of coefficients is the same for all linear systems, it is advisable to use the inverse matrix method to solve it. This significantly reduces the calculations. The values of the functions for which errors are determined are obtained from the set of equations that connect them. Finding them is much more problematic than for one variable. Thus, a strict priori estimate of accuracy is obtained without any restrictions on the studied functions, for example, in the form of their approximate representation by Taylor series or approximate estimates when solving equations. Proposed method is tested on test examples, which include the assessment of accuracy for both one and two variables, and is considered in the first case. The results of the calculations confirm the feasibility of using this technique. Therefore, with the traditional approach, the above algorithm can be used in more complex cases, i.e. for the case of implicit definition of the function.
, , A.F. Steklov, S.M. Pokhvala, I.A. Verlyuk
Astronomical School’s Report, Volume 16, pp 8-15; https://doi.org/10.18372/2411-6602.16.02

Abstract:
This paper presents theoretical developments of some issues in the physics of space intrusions. We report the discovery of a new effect – variations in brightness and “wobbling” in the meteor trail. The frequency of the variations of brightness (fc) and wobbling (fm) that can be measured is important information parameters that allow us to obtain estimates all the characteristics of the meteor if its height and speed are known. Basic two-side intrusion observations automatically determine both the height and speed of the intrusion. We offer a new “tuning technique” that allows determining the meteor characteristics during one-side observations. The essence of a new technique is to fine-tune the initial parameters of the simulation model of intrusion until the calculated and measured frequencies fc, fm coincide. We found that rotation plays an important role in the dynamics of meteors; in particular, they can burst in due to centrifugal forces that exceed the strength of the material. In the case of one-side observations, we construct a grid of intrusion models using the Impact 4A software program on the plane of the primary “mass–speed” meteoroid. As a result of modelling, we find the height at which the frequency ratio fc/fm coincides with the value found from measurements for exploding meteoroid. The paper describes the characteristics of the space intrusion of a meteor in Kyiv on August 12, 2019, 22:52:57 UT. The amplitude of the brightness fluctuations was found about 0.1 magnitudes, the amplitude of the wobbling of about 4 arc seconds. Using the Impact 4A software program the preatmospheric velocity was evaluated ∼40 km/sec; the mass of the meteoroid was evaluated approximately 0.45 kg. This meteoroid reached maximum light at 82.2 km and ablated partially. We find estimates of a residual mass of about 10 grams and a residual speed of about 20 km/s. We found that the radius of the helical path of the meteor at this height is about 1.5 meters. The meteoroid reached a critical value of the speed of rotation on the surface. At this moment, a meteoroid exploded and destroyed.
A.R. Sohor, M.M. Fys, A.M. Brydun, M.A. Sohor
Astronomical School’s Report, Volume 16, pp 33-37; https://doi.org/10.18372/2411-6602.16.05

Abstract:
The ecological status of the surface waters of the Lviv region is influenced by closely related various factors, namely: soil pollution, atmosphere, change of landscape structure and technogenic congestion of the territory, inefficient work of sewage and treatment facilities, failure of the mapping of coastal water protection and marsh, as well as their non-observance, especially in settlements, pollution and clogging of rivers with household and other wastes, trellising of forests along streams in mountainous terrain. Another important problem that leads to surface water pollution in the region is the lack of water protection zones and coastal protection strips of water bodies in the territory of the region. Absence of planning and mapping materials and uncertainty on the terrain boundaries of water protection zones and coastal protection strips lead to violations of land and water legislation when using them. At present, the state of water bodies in Ukraine, and in particular in the Lviv region is at an unsatisfactory level. The main problems in this area are the progressive nature of the negative impact on the environmental and human health. As at present there is no cartographic material that can visualize the problem of surface water pollution in Lviv region, the main purpose of this work was to create an interactive map of surface water pollution. To achieve this goal, we collected and systematized geospatial statistical mapping materials on the ecological status of the surface waters of the Lviv region. The necessary software for the development of the interactive map is identified and its possibilities are examined. An algorithm for loading geospatial data into the created web resource has been developed. The application template for the creation of web-maps of the monitoring network of the surface water of the Lviv region and the discharge of sewage for 2017–2018 in ArcGIS Online environment was selected. Thus, two interactive maps of ecological pollution of Lviv region's surface water in ArcGIS Online were developed.
, A.A. Berezhnoy, S.F. Velichko,
Astronomical School’s Report, Volume 16, pp 16-21; https://doi.org/10.18372/2411-6602.16.03

Abstract:
Detailed description of the original pointing software used for spectral observations of the lunar exosphere is given. The software allows to point the spectrograph of 2-m telescope of Terskol Observatory inside and outside the lunar disk with accuracy of about 2″. Observations of Na lines in the exosphere of the Moon on January 8 and October 7, 2017, do not reveal quick variability of Na lines at time scales of about 20 minutes. On January 8, 2017, the intensity of Na lines above the south pole of the Moon was stronger than that above the north pole of the Moon.
Astronomical School’s Report, Volume 16, pp 22-32; https://doi.org/10.18372/2411-6602.16.04

Abstract:
Saturn's equatorial plane has an inclination of 26.75° to the plane of its orbit. Therefore, its atmosphere is characterized by seasonal changes. Because of the eccentricity of 0.056 orbit, the southern hemisphere receives 25% more energy from the sun than the northern one, because the aphelion of Saturn occurs in the summer in the northern hemisphere, and perihelion in the summer in the southern. At the moments of equinox, the planet is at an average distance to the Sun. We digitized up to 200 images of Saturn obtained by different observers at the equinoxes of 1966, 1980, 1995, 2010, and prepared brightness distributions along several latitudinal belts and along the central meridian in the spectral range of 300...890 nm. Using the available photometric and polarimetric data, we calculated the intensities of radiation diffusely reflected from the atmosphere within the framework of a two-layer model. In it, the upper layer is an optically thin gas layer, the lower one is a semi-infinite gas-aerosol layer. The atmospheric parameters were obtained by comparing the observational data with the calculated values. Analysis of the distributions of methane and ultraviolet (UV) absorption over the disk for the period 1964–2020. showed seasonal variations in the levels of formation of visible clouds and above-cloud fog. Meridional course of absorptions at equinoxes in 1966 and 1995 is the opposite of the course of changes obtained from observations at the 1980 equinox. But the expected difference in the course of absorption between the hemispheres of Saturn in 2010, and as that obtained in 1980, did not occur. Although all the orbital and physical characteristics on Saturn are repeated at the moments of the four equinoxes, the response of the atmosphere to them was different. The available seasonal models of Saturn's climate change are in good agreement with seasonal changes in methane and UV absorption in its atmosphere at the equinoxes of 1966, 1980, 1995. But the data from observations of the planet's hemispheres at the 2010 equinox showed a significantly different result. A study of observations from Voyagers and Cassini showed that at tropopause levels, the tropical regions of Saturn's atmosphere warmed by more than 10 K in one year (from 1980 to 2010). Such warming in the tropopause has significantly altered atmospheric stratification, stability, and influenced the large-scale dynamics of the upper troposphere. At the minimum of solar activity in 2010, atmospheric convection also significantly decreased.
L.V. Zadorozhna, A.V. Tugay, S.Yu. Shevchenko
Astronomical School’s Report, Volume 16, pp 1-7; https://doi.org/10.18372/2411-6602.16.01

Abstract:
Extra-galactic X-ray research with the launch of XMM-Newton has become the forefront of X-ray astronomy. X-ray sources outside our galaxy are the other galaxies – normal galaxies, radio galaxies, quasars, blazars, Seyfert galaxies, as well as extended sources in galaxy clusters – the glow of cluster's halo. X-ray space observatory's equipment reach a high level of angular separation that allow to discern the individual sources within the galaxies nearest to us. The observations have shown that X-rays from galaxies are mainly the radiation of the central region – the active nucleus of the galaxy, which, according to generally accepted theory, is the radiation from the central supermassive black hole, and the set of X-ray sources in the galaxy's disk. Such sources could be the areas of star formation, the populations of X-ray binaries, etc. We cross-correlate the 4XMM-DR9 catalog and the HyperLeda galaxy database. The 4XMM-DR9 catalog contains 550124 unique sources covering 2.85% of the sky. As a result, we received 1207 galaxies with an X-ray flux exceeding 10-13 erg/(сm2·s). This range was chosen, since a spectrum could be constructed for such sources; therefore, they are of particular interest. About 600 galaxies from our sample were identified and classified. The leading place is occupied by galaxies whose optical angular sizes are in the range exceed 60″, total number of such galaxies is 364. Among them, 19 galaxies are in clusters with a bright X-ray halo; 20 galaxies without an X-ray nucleus; 13 galaxies don't have X-ray radiation within a specified range. Most galaxies have an extended core with a visible surface distribution of brightness, which decreases from the center to the periphery. With more than one X-ray source, we have 184 galaxies. In future, it will be interesting to obtain spectra and light curves of the discrete X-ray sources in galaxies for a more detailed study of their radiation's nature.
, , A.F. Steklov
Astronomical School’s Report, Volume 16, pp 43-47; https://doi.org/10.18372/2411-6602.16.07

Abstract:
This paper presents an example of the application of theoretical developments on some issues of physics of space invasion. The effect of brightness oscillations and “wobbling” in the meteor trail, which we discovered, allows us to obtain estimates of some characteristics of the meteor by measuring the frequency of changes in the brightness in the trace (fc) and meteoroid oscillations (fm), if its velocity and altitude are known. Based on the proposed “tuning technique”, it is possible to determine the characteristics of the meteor at one-sided observations. To do this, we set the initial parameters for the model of meteoroid dynamics by the coincidence of the calculated and measured values of the frequencies fc and fm. Our simulation allows us to find the altitude at which the ratio of frequencies fc/fm coincides with the value found in the explosion of a meteoroid. Using this “tuning technique” and assuming the mineral composition for the meteor, we found estimates of the initial velocity of 21 km/s and the mass of 850 kg of the meteoroid, which reached a critical value of surface speed at an altitude of about 20.9 km in about 7.9 s with a residual mass of about 13.9 kg and a residual speed of about 10.9 km/s. At that moment, the meteoroid exploded.
V.N. Krivodubskij
Astronomical School’s Report, Volume 15, pp 25-32; https://doi.org/10.18372/2411-6602.15.05

Abstract:
The processes of restructuring of the deep toroidal magnetic field, which is excited by radial differential rotation in a stable radiant zone filled with the primary (relic) poloidal magnetic field, are analyzed. According to the data of helioseismological experiments on the internal rotation of the Sun, the radial angular velocity gradient covers layers of the ray zone deeper than the solar convective zone (SCZ). We believe that this radial angular velocity gradient acts on the primary diploid type poloidal field and thus excites a toroidal field (Ω-effect) of a time-constant direction, which will be pushed out of the generation zone due to magnetic buoyancy. From the steady state condition, when the Ω-effect compensates for the field losses caused by magnetic buoyancy, we derived a formula for estimating the maximum value of a stationary toroidal field, which can be maintained in the radiating zone for a long time. Taking into account the intensity of the relict radial field in the radiant zone Br≈ 0,1...10 G, the radial angular velocity gradient (∂Ω/∂r ≈ 7⋅10-18 rad/s⋅cm) determined from helioseismological measurements is capable of generating a sufficiently strong deep toroidal magnetic field BT≈106...108 G. Toroidal fields, the magnitude of which outweighs these steady-state values, are gradually removed from the radiant zone due to magnetic buoyancy into the higher layers of the SCZ where the αΩ-dynamo mechanism operates. In view of this, the total toroidal field in the SCZ will consist of two components: variable and stationary. The first magnetic component is excited by the dynamo process and so it changes its direction (polarity) with a period of 11 years. At the same time, the second component of permanent orientation, which penetrates into the SCZ from below (from the radiant zone), cannot be the cause of cyclicity. However, it will be affect the amplitude of neighboring cycles of solar activity. In one cycle, the total toroidal field, when the directions of the two components of the field coincide, will have a greater intensity than in the neighboring cycle, when the directions of these components are opposite. Since the intensity of the sunspots formation is determined by the floating up to the solar surface of the total toroidal field, this should ultimately lead to the observed alternation of the amplitude of the neighboring 11-year cycles of solar activity.
G.A. Frolov, V.Yu. Belenok
Astronomical School’s Report, Volume 15, pp 7-10; https://doi.org/10.18372/2411-6602.15.02

Abstract:
The temporal changes in the level of the Black Sea were studied using statistical analysis of Black Sea surface level anomalies measurements. Off-season variations of Black Sea level were shown. Three maxima of the sea level temporal curve were found in 2010, 2013 and 2016. Correlation analysis was performed as well as a linear regression graph was plotted for average sea level anomalies and average sea surface temperature over the observation period (2008–2017). The spatial correlation between SLA and SST was found earlier. Using spatio-temporal data, we study the temporal correlation here. A weak temporal correlation is revealed.
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