The Modified Technique for the Identification and Study of Secular Resonances in the Dynamics of Nearplanetary Objects

The modified method for calculating secular frequencies is presented that reveals and investigates secular apsidal-nodal resonances in the dynamics of artificial Earth satellites (AES) and other near-planetary objects (NPO).Представлена модифицированная в части вычисления вековых частот методика выявления и исследования вековых апсидально-нодальных резонансов в динамике искусственных спутников Земли (ИСЗ) и других околопланетных объектов (ОПО).Работа выполнена при финансовой поддержке РНФ в рамках научного проекта № 19-72-10022 от 07.08.2019

Study of the dynamic structure of the near-lunar orbital space

The knowledge of the dynamic features of the near-lunar space is necessary for its optimal mastering. This work is devoted to a study of the special features of the dynamics of the artificial Moon satellites (AMS) with intermediate and high orbits in the range of semimajor axes from 2500 to 26000 km

Features of rejection of positional and photometric measurements when determining dynamic parameters of space debris objects

В работе представлены результаты численного эксперимента по выбору и обоснованию критериев отбраковки позиционных и фотометрических измерений.The paper presents the results of a numerical experiment on the selection and justification of criteria for rejecting positional and photometric measurements

Numerical Models of Motion of Artificial Satellites of the Earth and the Moon. Latest Version

A description of the latest versions of the numerical models of the motion of artificial satellites of the Earth (AES) and the Moon (AMS) developed at the RIAMM NRTSU is presented and the possibilities of their use in solving problems of satellite dynamics are descussed.Представлено описание последних версий разработанных в НИПММ НИТГУ численных моделей движения искусственных спутников Земли (ИСЗ) и Луны (ИСЛ) и показаны возможности их использования в решении задач спутниковой динамики.Работа выполнена при финансовой поддержке РНФ в рамках научного проекта № 19-72-10022 от 07.08.2019

Numerical Model of the Motion of Artificial Earth Satellite Systems. Latest Version

В работе представлено описание последней версии численной модели движения систем искусственных спутников Земли (ИСЗ), разработанной в НИИ ПММ ТГУ. Представленное программное математическое обеспечение (ПМО) позволяет прогнозировать движение ИСЗ, исследовать хаотичность движения околоземных объектов, вычислять резонансные характеристики для изучения влияния вековых резонансов на динамику ИСЗ. Программный комплекс реализован в двух версиях: для персонального компьютера (ПК) и в среде параллельных вычислений «СКИФ Cyberia» ТГУ. Для удобства ПМО дополнено пользовательским интерфейсом.The paper presents a description of the latest version of the numerical model of the motion of artificial Earth satellites (AES) systems developed at the Research Institute of Applied Mathematics and Mechanics of Tomsk State University. The presented mathematical software (MO) makes it possible to predict the motion of the satellite, to investigate the chaotic character of the motion of AES, to calculate resonant characteristics to study the influence of secular resonances on the dynamics of the satellite. The software package is realized in two versions: for a personal computer and in the environment of parallel computing “SKIF Cyberia” TSU. For convenience, the MO is supplemented with a user interface.Исследование выполнено за счет гранта Российского научного фонда № 19-72-10022, https://rscf.ru/project/19-72-10022/

Determination of area-to-mass ratio of geosynchronous objects using positional observations obtained at Terskol pike

Представлены результаты совместного определения элементов орбит и параметра парусности объекта γ = A/m для группы геосинхронных фрагментов космического мусора на основании позиционных наблюдений, полученных на уникальной научной установке «Цейсс-2000» на Терскольской обсерватории Института астрономии РАН в период 11—25 сентября 2020 г.The results of the joint determination of the orbital elements and the area-to-mass ratio of the object γ = A/m for a group of geosynchronous fragments of space debris based on positional observations obtained at the unique scientific installation Zeiss-2000 at the Terskol Observatory of the Institute of Astronomy of the Russian Academy of Sciences during September 11—25, 2020 are presented.Работа выполнена в рамках государственного задания Министерства науки и высшего образования Российской Федерации (тема № 0721-2020-0049)

Numerical simulation and visualization in problems of studying space debris dynamics

We present a description of the application SDVEApp designed to conduct research on the dynamic evolution of near-Earth space objects, namely, for calculation and visualization of the near-Earth object characteristics frequently used in research. In addition, the application makes it easier to work with a number of well-known catalogs of space objects. We demonstrate the results of application of the developed software to a set of objects from the NORAD and ESA Classification of geosynchronous objects catalogs, as well as objects, data on which were obtained from observations made by the employees of the Department of Celestial Mechanics and Astrometry of the Research Institute of PMM TSU

To the substantiation of a numerical-analytical method for revealing secular resonances

Results of the substantiation of a numerical-analytical method for determining secular frequencies in the process of revealing secular resonances in the dynamics of circumplanetary objects are presented. The presented method combines two approaches: the traditional analytical approach and the numerical one. Each of the approaches has its own special features. The analytical approach is not suitable for large eccentricities, since it uses formulas obtained for small eccentricities, and the formulas that implement the numerical approach have irremovable singularities for small eccentricities and orbital inclinations. Since a special feature of the influence of secular resonances is the increase in the eccentricities from zero values to values close to unity, combining these two approaches makes it possible to obtain reliable results. This is confirmed by examples of investigation of the influence of secular resonances on the dynamics of circumlunar objects