Celestial Bodies Research Articles

Mitigation of the Collision Risk of a Virtual Impactor Based on the 2011 AG5 Asteroid Using a Kinetic Impactor

In recent years, the escalating risk of natural disasters caused by Near-Earth Objects (NEOs) has garnered heightened scrutiny, particularly in the aftermath of the 2013 Chelyabinsk event. This has prompted increased interest from governmental and supranational entities, leading to the formulation of various measures and strategies aimed at mitigating the potential threat posed by NEOs. This paper delves into the analysis of the 2011 AG5 asteroid within the context of small celestial bodies (e.g., asteroids, comets, or meteoroids) exhibiting resonant orbits with Earth’s heliocentric revolution. Initial observations in 2011 raised alarms regarding the asteroid’s orbital parameters, indicating a significant risk of Earth impact during its resonant encounter in 2040. Subsequent observations, however, mitigated these concerns. Here, we manipulate the orbital elements of the 2011 AG5 asteroid to simulate its behavior as a virtual impactor (a virtual asteroid whose orbit could impact Earth). This modification facilitates the assessment of impact mitigation resulting from a deflection maneuver utilizing a kinetic impactor. The deflection maneuver, characterized as an impulsive change in the asteroid’s momentum, is executed during a resonant encounter occurring approximately two decades before the potential impact date. The paper systematically evaluates the dependence of the deflection maneuver’s efficacy on critical parameters, including the position along the orbit, epoch, and momentum enhancement factor.

Scribal Revelations in Ancient Judaism

Revelations, visions and their interpretations create in themselves authority. In early Jewish Aramaic tradition, however, this is increased by the role of writing. Enoch receives revelations of the secrets of heaven from heavenly tablets by the Holy Watchers. The Fallen Watchers teach the earthly women magic and sorcery from tablets stolen from the heaven. Scribalism in Second Temple period Judaism and Enoch is becoming more and more researched. As is known, Enoch has a Mesopotamian scholarly tradition behind it, which saw the movement of the celestial bodies as a heavenly writing, the transmission of the will of the gods. Enochic scribes had a good familiarity with the Mesopotamian scribal tradition that took place in the sanctuaries from the Persian period onwards and whose purpose was to record astronomical observations, write diaries, prepare astronomical tables and produce almanacs recording events. Scholarly texts were considered as “secret” or “exclusive” knowledge. The omen list Enūma Anu Enlil, based on a 360-day calendar, was the pinnacle of the scribal tradition and the basis of Mesopotamian astral magic. The Mesopotamian revelatory form in Enoch serves to assert the authority of a calendrical system of its own, the 364-day year and the Holy Watchers and other angelic beings who govern it. The scribal form of revelation is known in Daniel 7 (also in Aramaic), in which the books opened in heaven contain a revelation about the fate of the fourth empire. The book-revelation of cyclic and linear time is present together in the book of Jubilees, whose chronology is based on the 364-day year, and in which Enoch keeps a record of earthly events on heavenly tablets.

Autonomous imaging scheduling networks of small celestial bodies flyby based on deep reinforcement learning

AbstractDuring the flyby mission of small celestial bodies in deep space, it is hard for spacecraft to take photos at proper positions only rely on ground-based scheduling, due to the long communication delay and environment uncertainties. Aimed at imaging properly, an autonomous imaging policy generated by the scheduling networks that based on deep reinforcement learning is proposed in this paper. A novel reward function with relative distance variation in consideration is designed to guide the scheduling networks to obtain higher reward. A new part is introduced to the reward function to improve the performance of the networks. The robustness and adaptability of the proposed networks are verified in simulation with different imaging missions. Compared with the results of genetic algorithm (GA), Deep Q-network (DQN) and proximal policy optimization (PPO), the reward obtained by the trained scheduling networks is higher than DQN and PPO in most imaging missions and is equivalent to that of GA but, the decision time of the proposed networks after training is about six orders of magnitude less than that of GA, with less than 1e−4 s. The simulation and analysis results indicate that the proposed scheduling networks have great potential in further onboard application.

Status of the natural resources of celestial bodies: novelties of the practice of states

The absence of clauses on the legal regime of the natural resources of celestial bodies in the Outer Space Treaty, together with the development by the United States with its partner states of favourable legal conditions for their legal entities and individuals for the mining of space resources on celestial bodies, has highlighted the need for scientific proposals on the relevant Russian legal response. The article after analysing the legislative and treaty acts of the United States in the general context of International Space Law makes such initial proposals.

PIONEERS: a 6DoF motion sensor to measure rotation and tides in the Solar System

Observation of rotation variations and tides provides constraints on the interior properties of celestial bodies. Both can be precisely measured with a 6DoF (Degrees of Freedom) motion sensor placed on their surface. This type of instrument measures rotation rates and linear accelerations in a large frequency band, which includes the frequencies involved in the tides and rotation variations. A novel sensor under development aims to measure rates and accelerations with an amplitude spectral density of 2μrads-1Hz-1/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${2}\\,\\upmu \ extrm{rad}\\, \ extrm{s}^{-1} \ extrm{H}\ extrm{z}^{-1/2}$$\\end{document} and 20μms-2Hz-1/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${20}\\,\\upmu \ extrm{m}\\,\ extrm{s}^{-2} \ extrm{H}\ extrm{z}^{-1/2}$$\\end{document} respectively in its compact version and three orders of magnitude better (5nrads-1Hz-1/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${5}\\,\ extrm{nrad}\\, \ extrm{s}^{-1} \ extrm{H}\ extrm{z}^{-1/2}$$\\end{document} and 10pms-2Hz-1/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${10}\\,\ extrm{pm}\\,\ extrm{s}^{-2} \ extrm{H}\ extrm{z}^{-1/2}$$\\end{document}, respectively) with its high-performance version. Here, we compare these instrument performances with the precision required to measure rotation and tides in order to improve our knowledge of the interior of nine celestial bodies identified as targets for future space missions: Dimorphos, Phobos, Europa, Io, Titan, Enceladus, Triton, the Moon and Mars. Results indicate that Phobos, the Moon, and Mars cannot be investigated with the compact model, but that the interior of the other bodies can be constrained through measurements of rotation rate, and/or centrifugal acceleration, and/or tidal acceleration. We also find that the high-performance prototype instrument is suitable for acceleration measurements for all nine bodies, but not adequate for inferring interior constraints from rotation rate measurements for Triton, the Moon, and Mars. The signatures of the interior in the rotation rate and centrifugal and tidal accelerations also provide scientific requirements for future developments of 6DoF motion sensors for these nine bodies.Graphical

Using the eccentric version of the restricted three-body problem to model exosolar systems

The eccentric version of the restricted three-body problem is applied for obtaining the taxonomy of trajectories in exosolar systems. Our analysis is sufficient enough for the test particles to represent a variety of celestial bodies, such as terrestrial-mass exoplanets, exoasteroids, exocomets, or exomoons. Moreover, our results specifically identify allowed orbits for exomoons. Through the systematic classification of trajectories, we manage to distinguish between the different types of motion and therefore reveal how both the total orbital energy and the eccentricity affect the dynamical properties of trajectories of the test particles.

CAUSAL PHYSICS: CROSS-SECTIONAL AREA INSTEAD OF MASS

A review and analysis on the topic of mass and physical interaction within the framework of causal physics is presented. Mass is considered as a special case of a quantity that is proportional to the cross-sectional area of physical objects. Replacing the mass with this quantity allows further development of the kinetic theory of gravity by Le Sage. Physical interaction is considered as a result of mutual shielding of elementary mass–forming elements - nucleons and systems consisting of them - atomic nuclei in the path of movement of cosmic ether particles. It is shown that the applied approach makes it possible to create a visual and causal picture of physical interaction, both in the microcosm and in the macrocosm, leading to completely new results. The existence of gravitational shielding is substantiated, a visual picture of the mass defect is created, the presence of hidden mass in massive celestial bodies is revealed, the reason for the precession of the perihelion of Mercury and artificial Earth satellites is indicated, semi-daily behavior in the diurnal variation of gravity is described and interpreted, features in the manifestation of tidal processes are described. The applied approach allows to consider the issues of interaction in the micro and macrocosm from a single mechanism.

Enhancing Planetary Exploration through Digital Twins: A Tool for Virtual Prototyping and HUMS Design

In recent times, the demand for resilient space rovers has surged, which has been driven by the amplified exploration of celestial bodies such as the Moon and Mars. Recognising the limitations of direct human intervention in such environments, these rovers have gained a great deal of importance. Our proposal introduces a digital twin for space exploration rovers that seamlessly integrates intricate geometric, kinematic, and dynamic models, along with sensor and control systems. It faithfully emulates genuine real-world scenarios, providing an authentic testing ground for rover prototypes and the development of damage detection algorithms. Its flexibility in replicating diverse terrains, environmental conditions, and operational scenarios significantly expedites rover development. The digital twin serves as a valuable tool in the perfecting of damage detection systems, allowing engineers to efficiently craft diagnostic algorithms. This innovative approach not only conserves valuable resources but also ensures the robustness of space mission systems, thus enhancing the overall success and safety of planetary exploration endeavours.

The effects of the velocity distribution of impact generated water ice ejecta on exospheric escape from airless bodies

We explore the velocity distribution of impact generated water ice ejecta from planetary surface. We show that the ejecta velocity distribution should be modeled by a mixed Maxwellian distribution, rather than the commonly used single Maxwellian distribution, in order to better capture the outcome of the different emission processes and the dynamics of the clustered water molecules in the ejecta. We find that, comparing to the mixed Maxwellian distribution, the single Maxwellian distribution may lead to a significant underestimation of the impact-ejected water molecules that stay gravitationally bound for exosphere models. While the relative difference is within 10% for celestial bodies with a large escape velocity such as Mercury, it can be about 1000% for celestial bodies with a small escape velocity such as Enceladus.

A volcanic inventory of the Moon

The volcanic and magmatic activity of the Moon is intimately tied to its internal thermal and geodynamic evolution through time. While the extrusive nearside maria dominate the volcanic record, little is known regarding their underlying structure and the details of their emplacement. Intrusive activity is even more enigmatic, with most intrusions expressing little to no surface signature. Although prior studies have provided insights into the local igneous activity, no global compilation has been conducted. Here, we present a volumetric inventory of extrusive and intrusive activity. Gravity and topography data are inverted using a two-layer loading model to constrain mare and cryptomare thickness. The mean thickness of mare units is found to be 2.8 km, though with substantial lateral variations, with average values of 7.9 km within large mare basins compared to 1.6 km outside of these basins. This substantial variation in mare thickness associated with minimal change in the surface topography may be explained by some combination of long-distance transport of low viscosity mare and/or a buoyancy control limiting mare eruptions to a constant level surface. Our preferred volumes of mare and cryptomare are 18.2×106 km3 and 2.2×106 km3, respectively. Crustal intrusions associated with linear gravity anomalies, floor-fractured craters, ring dikes, graben, and beneath volcanic constructs, are investigated and yield a total volume of 9.1×106 km3. Our inventory reveals that intrusive activity dominates in the farside (intrusive:extrusive ratio of 5:2), whereas extrusive volcanism is more pronounced in the nearside (1:5). The combined volume of intrusives and extrusives is found to be 3 times greater in the nearside than in the farside. Both are related to the lunar asymmetry in which the thinner crust and warmer subsurface beneath the Procellarum KREEP terrane enables enhanced melting and magma ascent. These observations may have implications for the interpretation of the thermal and geodynamic history of other celestial bodies, where intrusive volcanism remains poorly constrained.

Modeling Development of a Diamagnetically Stabilized Magnetically Levitated Gravimeter.

The aim of this work is to create a new type of gravimeter that can function effectively in the challenging conditions of space, specifically on the surfaces of planets and moons. The proposed device, called a diamagnetically stabilized magnetically levitated gravimeter (DSMLG), uses magnetic forces to balance a test mass against the force of gravity, allowing for accurate measurements. A diamagnetically stabilized levitation structure comprises a floating magnet, diamagnetic material, and a lifting magnet. The floating magnet levitates between two diamagnetic plates without the need for external energy input due to the interaction between the magnetic forces of the floating magnet and the stabilizing force of the diamagnetic material. This structure allows for stable levitation of the floating magnet without requiring additional energy. The goal is to design a gravimeter that is lightweight, requires minimal power, can withstand extreme temperatures and shocks, and has a low data rate. The authors envision this gravimeter being used on various robotic spacecraft, such as landers and rovers, to study the interiors of rocky and icy celestial bodies. This paper reports on the results of a finite element model analysis of the DSMLG and the strength of the resulting diamagnetic spring. The findings contribute to the understanding of the levitation characteristics of diamagnetically stabilized structures and provide valuable insights for their practical applications, including in the development of the proposed DSMLG.

Views of The Scholar-Polymath Beruni on The Secrets of The Universe

Objectives: This section outlines the specific goals and aims of the article, focusing on the exploration of Beruni's profound insights and philosophical perspectives regarding the secrets of the universe. It highlights the scholar-polymath's contributions to various fields, emphasizing the overarching objective of delving into his unique perspectives on the nature of the cosmos, its origins, and its underlying principles.
 
 Methods: Here, the article discusses the approach taken to achieve the stated objectives. It details the methods employed to analyze Beruni's extensive research and writings, providing a framework for examining his contributions to astronomy, physics, mathematics, and philosophy. The methods section establishes the groundwork for the subsequent exploration of Beruni's thoughts on celestial bodies, planetary motion, and the interconnectedness of the universe.
 
 Results: This section presents the findings and insights derived from the analysis of Beruni's works. It discusses the scholar's exploration of celestial bodies, planetary motion, and the interplay between celestial phenomena and earthly events. Additionally, it elucidates Beruni's perspectives on the interconnectedness of the universe, the concept of time, and the existence of parallel worlds. The results section aims to provide a comprehensive overview of the key ideas and discoveries uncovered through the examination of Beruni's intellectual pursuits.
 
 Conclusion: The conclusion synthesizes the key findings and discusses their significance in the context of contemporary scientific and philosophical discourse. It reflects on the enduring relevance of Beruni's ideas and the impact of his contributions to our understanding of the secrets of the universe. This section serves as a culmination of the article, summarizing the insights gained from exploring Beruni's profound perspectives and acknowledging their broader implications.

Ultra-broadband infrared metamaterial absorber based on MDMDM structure for optical sensing

Infrared observation is a crucial tool in the study of astronomical celestial bodies. Metamaterials have a vast prospect for applications in the field of optics due to their unique electromagnetic tunable characteristics. In order to obtain an ultra-broadband high absorption material in the infrared region, we proposed a metal-dielectric-metal-dielectric-metal (MDMDM) metamaterial absorber using a titanium (Ti) nano-cross layer based on surface plasmon polariton (SPP) resonance and magnetic resonance cavity principles. The geometrical parameters of each layer have been examined carefully. The influence of incident angle from 0° to 60° is investigated for transverse electric and transverse magnetic plane-waves. Near-perfect absorption performance is achieved from near-infrared to mid-infrared region. The average absorption reaches as high as 97.41% from 2.05 to 6.08 μm. The absorber exhibits polarization-sensitive characteristics. The absorption peaks are 99.50% and 99.80% at 2.55 and 5.24 μm, respectively. The proposed material has potential applications in astronomical imaging, volcano and fire detection, remote sensing, biological monitoring, and other optical devices.

A promising method for breaking the logjam of time-frequency analysis in astronomy

Abstract Time-frequency analysis could provide detailed dynamic information of celestial bodies and is critical for comprehension of astronomical phenomena. However, it is far from being well-developed in astronomy. Hilbert–Huang transform (HHT) is an advanced time-frequency method but has two problems in analysing astronomical signals. One is that many astronomical signals may be composed of multiple components with various amplitudes and frequencies, while HHT uses assisted noises with the same amplitude to extract all components. The other is that HHT is an empirical method requiring tunable parameters to be optimized using experimental results or known facts, which are challenging to obtain in astronomy and it is therefore hard to determine whether the signal decomposition is right or not. In this study, we adjust the noise amplitude to optimize the decomposition based on the orthogonality of the obtained components and discard the decompositions with non-physical results. Three experiments show that this new extension of HHT is an effective method suitable for high-resolution time-frequency analysis in astronomy. It can be used to dig out valuable pieces of information which are inaccessible with other methods, and thus has the potential to open up new avenues for astronomy research.

Connection Between Gravity and Quantum World

Gravity is the most important force in cosmology. A lot of research deals with it, but we only know its perceptible properties. Two basic descriptions of gravity are accepted today. One is based on classical physics based on Newton\’s theory. The other is the theory of gravity described by Einstein. However, another description of gravity is also possible. Gravitation can also be described in other ways using the equations of Kepler, Newton, Coulomb, and Maxwell. Using their equations, it can be deduced that: The magnitude of the gravitational force field is not determined only by mass. It depends on the speed of the mass. It depends on the size of the gravitational field in which the mass moves Newton\’s and Coulomb\’s laws are equivalent. This has already been determined by several researchers. It was also conducted by Constantin Meis. Newton\’s, Coulomb\’s, Maxwell\’s law can be used to determine a new cosmic constant. It can be counted on in the Solar System, but also in the Milky Way. Denote by μ_2 and √ (μ_2) This constant connects the macro world and the micro or quantum world. This constant can also be calculated using Coulomb\’s and Maxwell\’s equations Maxwell\’s and Coulomb\’s equation can be used to determine the resultant of the associated vibrating charges for each mass and celestial body. Coulomb\’s law can also be used to accurately determine the force effect between masses. Even the force effect between celestial bodies can be determined with it. This is exactly the same as the force effect calculated by Newton\’s law. For a mass of 1 kg, we get exactly Cavendish\’s measurement result with Coulomb\’s law. Already in the 20th century, it was suggested that there is a connection between gravity and the electromagnetic field. This has already been conducted by Constantin Meis and Takaaki Musha and B. Ivanov. Gravitational constant can not only be measured, but also calculated in several ways. This has already been determined by several researchers. The gravitational constant can also be calculated using the mass and its speed. But it can also be calculated using the Coulomb constant and μ_2 The gravitational force field for a given mass or celestial body can be calculated using √(μ_2) and the charge of the mass. The speed of a given planet can be calculated using its charge and √ (μ_2) Based on the derivations, gravity is a force field that has an electric force field component. Therefore, it can be the carrier medium of electromagnetic waves. And so is the carrier of light If we assume that the gravitational force field is a very high frequency electromagnetic wave, then we also understand that gravity is unipolar.

Space Mining

The Outer Space Treaty, the leading source of law for activities in space, has laid out various limitations and regulations regarding actions in space and how space can be used. One of these limitations is commonly referred to as the “non-appropriation principle.” The non-appropriation principle prohibits nations from making claims of sovereignty over celestial bodies in space. This presents a problem as the space industry continues to progress because it causes uncertainty regarding the meaning of appropriation, what is classified as a celestial body, what acts are allowed, and who specifically is prohibited from acting. This Comment identifies these problems and their potential solutions, specifically with the proposition of space mining in mind.

The Uniqueverse, Natural selection as the unique model of evolutionary development of the Universe

The cosmological theories proposed so far do not postulate a common way of creation that can guide the entire line of growth of the universe, from elementary particles to living beings. But everything consists of the same basic components, combined and regulated differently: elementary particles, atoms and molecules make up celestial bodies, solar systems, single and pluricellular organisms, plants and animals. Common constituents are compatible with a common origin and with an incremental and selective development method. One possible common mode is that the Universe was formed according to an evolutionary method based on natural selection, the same process which then allowed the differentiation of biological species. This unique process may have guided from the beginning the development of the fundamental constituents of matter in the primitive universe and then created the other cosmic structures through the evolution of those elementary particles, up to organic molecules and biological beings. A process of this kind is a slow and gradual process, not based on a sudden event but on the progressive increase in the complexity of the structures present in the Universe, regulated by the selection of the most suitable and stable forms. For the relativistic relationship between energy, mass and velocity, we can think that the Universe was formed at the same time as the formation of elementary structures, slowly in a spacetime that was created in parallel: elementary particles created an initial infinitesimal spacetime system that then grew as more matter formed. The incremental creation of the cosmos would also concern forces and physical laws, which may have undergone the same evolutionary process from the most primordial and simple forms to the present, in proportion to the development of the whole system. This modality could justify the current simultaneous presence of quantum and relativistic laws at different levels (atomic and gravitational), as well as the coexistence of different species in different environments. This evolutionary modality is reflected in the fact that atoms, celestial bodies, chemical compounds, the general structure of the universe, physical laws and biological beings show the presence of stable entities selected among the many theoretically possible or unstable.

Sediments and morphology of deep lakes of Central Tunguska Plateau (Krasnoyarsk krai, Evenkia): on the problem of the Tunguska Event at 1908

The shape of the bottom and the thickness of sediments of small lakes Zapovednoye and Peyungda, located 50-60 km from the supposed epicenter of the “Tunguska Event” of 1908, were studied using echo-sounding and seisimo-acoustic profiling, and their age was estimated using 137Cs, 210Pb, 14C. It was revealed that both lakes have funnel shape with a depth of 60 and 34 m, respectively, and are similar in shape and size to Lake Cheko, which, according to some researchers, is an impact crater formed by a celestial body as a result of the “Tunguska Event 1908”. The examples of lakes Zapovednoye and Peyungda show that the shape of Lake Cheko is not unique to this area. The age of the bottom sediments of lakes Zapovednoye and Peyungda exceeds several thousand years. In the sediments of lakes Zapovednoe and Peyungda, a layer with a high content of terrigenous elements was identified, presumably formed due to the input of disturbed soil layer as a result of the massive fall of trees after the “Tunguska 1908”. Thus, the presence of two deep funnel-shaped lakes near the epicenter of the “Tunguska 1908” much older than 1908, casts doubt on the uniqueness of Lake Cheko, and therefore its impact origin. In addition, according to our estimate, the age of Lake Cheko is no less than 300 years, which contradicts the hypothesis of its origin as a result of the “Tunguska 1908”.

On the Co-orbital Motion of Any Inclination

The co-orbital motion occurs when a celestial body (e.g. an asteroid) shares the same semimajor axis with the perturbing object (e.g. a planet), and thus they are in a 1:1 mean motion resonance. Trojan asteroids in the tadpole orbits around planets in the Solar System are these co-orbital objects. The motion and origin of some Trojan asteroids, particularly those on high-inclination orbits, are still not fully understood. In this paper, a newly developed perturbation function expansion, which is applicable to the 1:1 resonance, is used to investigate the co-orbital motion in three-dimensional space. The position of the resonance center and the resonance width are calculated for different initial orbital elements, and the relationship between the orbital types and the initial orbital elements is analyzed. The results obtained by the analytical method are compared with and verified by the results from numerical simulations. A panorama of the co-orbital motion in the wide orbital elements space is obtained.

SUBSTANTIATION OF THE RESULTS OF THE LASER LOCATION OF THE TRAJECTORY OF THE MOON MOVING AWAY FROM THE EARTH

Progress in astronomical measurements of the trajectories of the movement of celestial bodies reveals new effects that require justification. In particular, it refers to the slight drift of the Moon from the Earth. A solution to this problem is possible only based on an adequate mathematical model. To perform this, it was adapted Newton's law of universal gravitation to the case of moving masses in flat space and physical time. At the same time, the final speed of propagation of the gravitational field can be considered. The differential equations of motion of the three-mass Sun-Earth-Moon cosmic system are obtained. In the heliocentric coordinate system, transient processes of the movement of the named celestial bodies are simulated, which testify to the presence of the Moon moving away from the Earth and the influence of the effects of movement on its course. The significant dependence of the final result on numerical methods of integration, computer calculation tools, and the values of space-velocity initial conditions is shown. The results of the simulation of transient processes are attached.