On the Dynamics of the Solar System IV: Perihelion and Eccentricity Evolution

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.