Chaotic diffusion of the fundamental frequencies in the Solar System

Vol. 654
10. Planets and planetary systems

Chaotic diffusion of the fundamental frequencies in the Solar System

In 1941 Milutin & Milankovi suggested that major climate changes that have occurred on Earth originated from the long-term variations in its orbital and rotational elements. Several studies employing stratigraphic sequences of sediments have indeed shown a correlation between the astronomical quantities of the Earth and its climates. A difficulty arises from the chaos of the inner Solar System, which deteriorates the accuracy of the determination of the astronomical quantities dating back more than 60 Myr. One way to represent these quantities is to express the fundamental frequencies of the Solar System seen as a dynamical system. These frequencies roughly correspond to orbital periods and the precession periods of the planetary orbits, and they unequivocally give us the mean distances between the Sun and the planets. In this paper, the authors use two statistical tools, kernel density estimation and moving block bootstrap, to estimate the long-term variations in these frequencies and their accuracy. These estimations require the use of tens of thousands of numerical simulations of the evolution of the Solar System, which are facilitated by the use of averaged equations. The authors show the success of their method by comparing their astronomical results with two sets of geological data.