Surfaces of minimal energy and their singular points in the problem of stellar approaches toward the solar system

Authors

  • Azad Hidayat Mammadli

Abstract

Planetary motion during stellar approaches toward the Solar System is examined in the framework of the three-dimensional restricted three-body problem. The exact expression of the force function without a series expansion is used. Regions of possible motion of a planet are determined. Surfaces of minimal energy, which are generalizations of surfaces of zero velocity, are plotted. Singular (exceptional) points of these surfaces are determined, and their type and Lyapunov stability are ascertained. The results thus obtained are shown in the form of figures and tables. Refs 5. Figs 2. Table 1.

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References

1. Маммадли А.Г. Устойчивость движения планет по Хиллу при звездных сближениях // Вестник С-Петерб. ун-та. Сер. 1. 2016. Т. 3(61). Вып. 3. С. 498-505.

2. Дубошин Г.Н. Небесная механика. Аналитические и качественные методы. М.: Наука, 1964.

3. Лукьянов Л.Г. Аналог поверхностей нулевой скорости в ограниченной эллиптической, параболической и гиперболической задачах трех тел // Письма в Астрон. журн. 2010. Т. 36, №11. С. 869-880.

4. Себехей В. Теория орбит. Ограниченная задача трех тел. М.: Наука, 1982.

5. Корн Г., Корн Т. Справочник по математике. М.: Наука, 1984.

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Published

2020-08-20

How to Cite

Mammadli , A. H. (2020). Surfaces of minimal energy and their singular points in the problem of stellar approaches toward the solar system. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 4(2), 336–344. Retrieved from https://math-mech-astr-journal.spbu.ru/article/view/8606

Issue

Vol. 4 No. 2 (2017)

Section

Astronomy

License

Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.