The construction of averaged planetary motion theory by means of computer algebra system Piranha

Abstract

The application of computer algebra system Piranha to the investigation of the planetary problem is described in this work. Piranha is an echeloned Poisson series processor authored by F. Biscani from Max Planck Institute for Astronomy in Heidelberg. Using Piranha the averaged semi-analytical motion theory of four-planetary system is constructed up to the second degree of planetary masses. In this work we use the algorithm of the Hamiltonian expansion into the Poisson series in only orbital elements without other variables. The motion equations are obtained analytically in time-averaged elements by Hori-Deprit method. Piranha showed high-performance of analytical manipulations. Different properties of obtained series are discussed. The numerical integration of the motion equations is performed by Everhart method for the Solar system's giant-planets and some exoplanetary systems.

arXiv comment14 pages, 4 figures, 7 tables, the conference Applications of Computer Algebra (ACA-2017), Special Issue of Mathematics in Computer Science

References in corpus (6)

• Chaotic diffusion in the Solar System
• The Origin of Chaos in the Outer Solar System
• Kolmogorov and Nekhoroshev theory for the problem of three bodies
• Secular dynamics of a planar model of the Sun-Jupiter-Saturn-Uranus system; effective stability into the light of Kolmogorov and Nekhoroshev theories
• A Semi-Analytic Algorithm for Constructing Lower Dimensional Elliptic Tori in Planetary Systems
• The Piranha algebraic manipulator