The origin of chaos in the Solar System through computer algebra
Abstract
The discovery of the chaotic motion of the planets in the Solar System dates back more than 30 years. Still, no analytical theory has satisfactorily addressed the origin of chaos so far. Implementing canonical perturbation theory in the computer algebra system TRIP, we systematically retrieve the secular resonances at work along the orbital solution of a forced longterm dynamics of the inner planets. We compare the time statistic of their halfwidths to the ensemble distribution of the maximum Lyapunov exponent and establish dynamical sources of chaos in an unbiased way. New resonances are predicted by the theory and checked against direct integrations of the Solar System. The image of an entangled dynamics of the inner planets emerges.
 Publication:

Astronomy and Astrophysics
 Pub Date:
 June 2022
 DOI:
 10.1051/00046361/202243327
 arXiv:
 arXiv:2205.03298
 Bibcode:
 2022A&A...662L...3M
 Keywords:

 celestial mechanics;
 planets and satellites: dynamical evolution and stability;
 chaos;
 Astrophysics  Earth and Planetary Astrophysics;
 Nonlinear Sciences  Chaotic Dynamics;
 Physics  Classical Physics;
 Physics  Computational Physics
 EPrint:
 16 pages, 8 figures. Astronomy &