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Modified Method of Round Gaussian Rings. Application to the Two-Planetary Problemстатья
Дата последнего поиска статьи во внешних источниках: 19 июня 2024 г.
- Авторы: Kondratyev B.P., Kornoukhov V.S., Basova E.V.
- Журнал: Moscow University Physics Bulletin
- Том: 78
- Номер: 5
- Год издания: 2023
- Издательство: Allerton Press
- Местоположение издательства: New York, N.Y., United States
- Первая страница: 681
- Последняя страница: 688
- DOI: 10.3103/S0027134923050089
- Аннотация: Abstract—A scheme of the modified method of round Gaussian rings, designed to study the secularevolution of orbits in systems consisting of a central star and two planets, is presented. The reason for the secular evolution of the nodes and inclinations of the orbits of the planets is their mutual gravitational attraction. The orbits of the planets are modeled by homogeneous round Gaussian rings, to which the masses, sizes and angles of inclination of the orbits, as well as orbital angular momenta of the planets, are transferred. The method takes into account the fact that, in general, the ascending nodes of the orbits maynot coincide. The mutual gravitational energy of the rings Wmut is represented as a series in the quadratic approximation in powers of small inclination angles. Using this function Wmut, a closed system of four differential equations describing the secular evolution of the planets’ orbits is composed. The solution to theequations is obtained in finite analytic form, which simplifies the interpretation of the investigated planetary motions. The method was tested on the example of the Sun–Jupiter–Saturn system; for it, in particular, the difference in the longitudes of the nodes of the orbits of Jupiter and Saturn was calculated as a functionof time. New approach is also used to study the precession of nodes in the exoplanetary system K2-36; graphs of all unknown quantities are obtained. It has been established that in the course of evolution the mutual inclination angle of the orbits remains constant, and the librations of the orbits in the inclination angle and in the motion of the nodes occur synchronously.
- Добавил в систему: Кондратьев Борис Петрович
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