- PII
- S3034517025100068-1
- DOI
- 10.7868/S3034517025100068
- Publication type
- Article
- Status
- Published
- Authors
- Volume/ Edition
- Volume 102 / Issue number 10
- Pages
- 940-949
- Abstract
- By a new method we study the actual variant of the two-planet problem on the secular evolution of planetary orbits with small eccentricities and mutual inclination, having arbitrary orientation with respect to the main (picture) plane. A model has been developed that describes a wide class of exoplanetary systems with an orbital inclination angle different from π / 2. The orbits of the planets are modeled by Gaussian rings, the perturbing function is represented by the mutual gravitational energy of these rings in the form of a series up to terms of second order of smallness. To describe the evolution of orbits, instead of osculating Keplerian elements, a new set of variables is introduced: the unit vector R of normal to the plane of the ring and two Poincaré variables (p,q); for eight independent variables, a system of differential equations is obtained and analytically solved. The method is applied to study the secular evolution of the two-planet system Kepler-117 (KOI-209) with non-resonant orbits of exoplanets. It has been established that in this system the oscillations of the components of the orientation vector R of the same name for each of the orbits, as well as the values (e,i,Ω), occur strictly in the opposite phase. The eccentricities of both orbits oscillate with a period of Tk = 182.3 years, and the inclinations of the orbits and the longitudes of the ascending nodes change in the libration mode with the same period Tg = 174.5 years. The lines of the orbital angles rotate unevenly counterclockwise with periods of secular rotation Tg2 = 178.3 years (for a light planet), and Tg1 = 8140 years (for a more massive planet).
- Keywords
- экзопланеты двупланетные системы кольца Гаусса и их взаимная энергия вектор нормали к орбите переменные Пуанкаре прецессия и вековая эволюция нерезонансных орбит
- Date of publication
- 10.03.2026
- Year of publication
- 2026
- Number of purchasers
- 0
- Views
- 22
References
- 1. K. Moppeti, C. Дермонт Динамика Солнечной системы (2009).
- 2. K.B. Хамисвиков, Э.Д. Кузнецов, Астрономический Вестник 41, № 4, 291 (2007).
- 3. Б.П. Кондратьев, Астрономический Вестник 48, № 5? 366 (2014).
- 4. Б.П. Кондратьев, В.С. Корноухов, Астрон. Журн. 97, № 5, 408–420 (2020).
- 5. Б.П. Кондратьев, В.С. Корноухов, Астрон. Журн. 100, № 6, 524–534 (2023).
- 6. Б.П. Кондратьев, В.С. Корноухов, Е.В. Басова, Вестник Московского университета. Серия 3: Физика, астрономия. 78, № 5, 1–8 (2023).
- 7. https:exoplanetarchive.ipae.caltech.edu.
- 8. S. Hinkley, S. Lacour, G.-D. Marleau et al., Astron. and Astrophys. 671, L5 (2023).
- 9. R. Mastrolanni, Ch. Efthymiopoulos, Proceedings IAU Symposium No. 364 (2022).
- 10. Б.П. Кондратьев, В.С. Корноухов, Е.Н. Киреева, Вестник Московского университета. Серия 3: Физика, астрономия 80, № 2, 1–8 (2025).
- 11. М.Ф. Субботинг Введение в теоретическую астрономию (1968).
- 12. Г.Н. Дубошин Небесная механика. Основные задачи и методы (1975).
- 13. Б.П. Кондратьев Теория потенциала и фигуры равновесия (Москва-Ижевск: РХД, 2003).
- 14. G. Bruno, J.-M. Almenara, S.C.C. Barros et al., Astron. and Astrophys. 573, A124 (2015).
- 15. J.M. Almenara et al., Monthly Not. Roy. Astron. Soc. 453, 2644–2652 (2015).
- 16. N. Bailey, D. Fabrycky, Astron. J. 159, id. 217 (2020).
- 17. Y. Judkovsky et al., Astron. J. 163, id. 91 (2022).
- 18. A. Ofir et al., Astron. J. 169, id. 90 (2025).
- 19. Б.П. Кондратьев, Астрофизика 21, № 3, 499 (1984).
