and Computational Methods

doi: 10.18698/2309-3684-2015-1-8393

We have analysed and presented observations of artificial celestial body 43096. We obtained the observations in 2006–2012 within the project “Scientific Network of Optic Instruments for Astrometric and Photometric Observations” (ISON). We have determined the Kepler orbit elements and state vector as of 1 hour 55 minutes 50,76 seconds, November 24, 2006 UTC (1:55:50,76 November 24,2006 UTC). We have performed numerical integration of the motion equations, taking into account the perturbations from the polar compression of the Earth, the Moon, the Sun and the solar radiation pressure. We propose a method for deorbiting artificial celestial bodies in high altitude orbits. The method is based on a numerical model of motion in circumterrestrial space, which takes into account only the largest perturbations. For the first time ever we have obtained such a great amount of data on objects with a large area of surface to mass ratio over long time spans. The data allowed us to study the objects and reveal their peculiar properties.

Bazey A., Bazey N., Borovin G., Zolotov V., Kashuba V., Kashuba S., Kupriyanov V., Molotov I. Evolution of the orbit of a passive fragment with a large area of surface in high Earth orbit. Маthematical Modeling and Coтputational Methods, 2015, №1 (5), pp. 83-93

doi: 10.18698/2309-3684-2019-4-6990

A statistical model of space debris is proposed. The model is based on the catalog of orbits of space objects, constructed using domestic and foreign sources. To build this model, the cataloged objects are clustering using criterion of closeness in a 4d space of orbital parameters characterizing the semimajor axis, eccentricity and position of the plane of the satellite orbits composing a cluster. The distribution of objects in each cluster is determined by the mathematical expectation and the covariance matrix of the spread of the orbital parameters of the cluster.

Боровин Г.К., Захваткин М.В., Степаньянц В.А., Усовик И.В. Статистическая модель распределения космических объектов в пространстве орбитальных параметров. Математическое моделирование и численные методы, 2019, № 4, с. 69–90.

doi: 10.18698/2309-3684-2023-4-6473

One of the types of gravitational scattering in the Solar System within the framework of the circular restricted three-body problem (CR3BP) are the gravity assist maneuvers of "particles of insignificant mass" (spacecraft, asteroids, comets, etc.). For their description, a physical analogy with the scattering of beams of charged alpha-particles in the Coulomb field is useful. However, unlike the scattering of charged particles, there are external restrictions on the ability to perform gravity assists associated with the limited size of the spheres of influence of the planet. At the same time, internal limitations on the possibility of performing gravity assists are known from the literature on CR3BP, estimated by the effective radii of planets (including gravitational capture by a planet falling into it). They depend on the asymptotic velocity of the particle relative to the planet. For obvious reasons, their influence makes it impossible to effectively use gravity assist maneuvers. The paper presents generalized estimates of the sizes of near-planetary regions (flat "perturbation rings" or "perturbation hollow spheres" rotating synchronously with a small body in the three-dimensional case), falling into which is a necessary condition for the implementation of gravity assists. A detailed analysis shows that Neptune and Saturn have characteristic of perturbation hollow spheres of the largest size in the Solar System, and Jupiter occupies only the fourth place in this list

Боровин Г.К., Голубев Ю.Ф., Грушевский А.В., Тучин А.Г. Моделирование пертурбационных оболочек для гравитационных маневров в Солнечной системе.Математическое моделирование и численные методы, 2023, № 4, с. 64–73.