2024 On the Dynamics of the Solar System IV: Perihelion and Eccentricity Evolution
Ramon Gonz\'alez Calvet
J. Geom. Symmetry Phys. 67: 1-46 (2024). DOI: 10.7546/jgsp-67-2024-1-46

Abstract

The perihelion precession rate and the time derivative of the orbitaleccentricity are joined into the derivative of a complex variable beingrepresentative of the Runge-Lenz vector. The integration of the lineardifferential equation system so obtained yields the evolution of theperihelion and the eccentricity of all the planets. Each eccentricityreaches a maximum, and in the case of giant planets also a minimum.The variation of each semimajor axis is shown to be very small.Since the semimajor axes are bounded and the planetary orbits neverintersect, the stability of the solar system is proven.

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Ramon Gonz\'alez Calvet. "On the Dynamics of the Solar System IV: Perihelion and Eccentricity Evolution." J. Geom. Symmetry Phys. 67 1 - 46, 2024. https://doi.org/10.7546/jgsp-67-2024-1-46

Information

Published: 2024
First available in Project Euclid: 27 May 2024

Digital Object Identifier: 10.7546/jgsp-67-2024-1-46

Rights: Copyright © 2024 Bulgarian Academy of Sciences, Institute of Mechanics

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