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Journal Articles Celestial Mechanics and Dynamical Astronomy Year : 2022

Comparative study of Mercury's perihelion advance

Abstract

Mercury's motion has been studied using numerical methods in the framework of a model including only the non-relativistic Newtonian gravitational interactions of the solar system: eight major planets and Pluto in translation around the Sun. Since the true trajectory of Mercury is an open, non-planar curve, special attention to the exact definition of the advance of Mercury's perihelion has been given. For this purpose, the concepts of an extended and a geometrical perihelion have been introduced. In addition, for each orbital period, a mean ellipse was fitted to the trajectory of Mercury. I have shown that the perihelion advance of Mercury deduced from the behavior of the Laplace-Runge-Lenz vector, as well as from the extended and geometrical perihelion advance depend on the fitting time interval and for intervals of the order of 1 000 years converge to a value of 532.1 per century. The behavior of the perihelia, either extended or geometrical, is strongly impacted by the influence of Jupiter. The advance of the extended perihelion depends on the time step used in the calculations, while the advance of the geometrical perihelion and that deduced by the rotation of the Laplace-Runge-Lenz vector depends only slightly on it.

Dates and versions

insu-03779391 , version 1 (16-09-2022)

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S. P. Pogossian. Comparative study of Mercury's perihelion advance. Celestial Mechanics and Dynamical Astronomy, 2022, 134, ⟨10.1007/s10569-022-10085-5⟩. ⟨insu-03779391⟩
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