The slow evolution of the circular orbit in a model of the viscoelastic Mercury under the influence of Venus


Аuthors

Barkin M. Y.*, Gorbachevskaya A. P.**

Bauman Moscow State Technical University, MSTU, 5, bldg. 1, 2-nd Baumanskaya str., Moscow, 105005, Russia

*e-mail: barkin@yandex.ru
**e-mail: gorbachevskayaap@student.bmstu.ru

Abstract

The article discusses the evolution of the translational and rotational motion of the planet Mercury under the influence of the gravitational attraction of the Sun and Venus. The primary focus is on analyzing Mercury's dynamics using Deleon-Andoyer variables, which allows for a more accurate description of its orbital motion and rotation. To solve the system of equations describing this motion, the method of separation of motions proposed by V.G. Vilke is applied. The study examines two main scenarios: the first includes the influence of perturbations caused by Venus's gravitational field on Mercury's dynamics, while the second considers the situation where the attraction of Venus is deemed negligible. Analyzing these cases helps to identify key aspects affecting the evolution of Mercury's orbital motion and its rotation, as well as to assess the degree of influence that neighboring planets have on its dynamics. It has been shown that the stationary motion of Mercury in the gravitational field of the Sun corresponds to the movement of its center of mass along a circle and rotation around the center of mass with an angular velocity coinciding with the orbital angular velocity. Next, a study was conducted on the slow evolution of Mercury's circular orbit under the influence of disturbances from Venus. It has been shown that the angular momentum of Mercury decreases and with it the radius of the orbit decreases. Modern spacecraft such as the Mercury exploration missions, including MESSENGER and BepiColombo, use sophisticated mathematical models and numerical methods to calculate orbits and maneuvers that take into account a variety of factors, including gravitational interactions with other planets. Previously known methods, such as Laplace's method or Kepler's method, provided simpler approaches that could not always account for dynamic changes in the system. Thus, the results of our research can be useful for further improvement of models used in space technology, as well as for improving the accuracy of calculations necessary for the successful completion of complex space missions. The results of the research may be useful for a deeper understanding of the mechanisms governing the motion of planets in the solar system, as well as for developing more accurate models used in celestial mechanics. This work also has practical significance for planning space missions related to the study of Mercury and its interactions with other bodies in the solar system. Thus, the article represents a significant contribution to the study of celestial dynamics and opens new perspectives for further research in the field of celestial mechanics.

Keywords:

Deleon-Andoyer, Mercury, circular orbit, planet, Venus, method of separation of motions, Sun

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