| Issue |
A&A
Volume 654, October 2021
|
|
|---|---|---|
| Article Number | A156 | |
| Number of page(s) | 18 | |
| Section | Planets and planetary systems | |
| DOI | https://doi.org/10.1051/0004-6361/202140989 | |
| Published online | 25 October 2021 | |
Chaotic diffusion of the fundamental frequencies in the Solar System★
Astronomie et Systèmes Dynamiques, Institut de Mécanique Céleste et de Calcul des Éphémérides, CNRS UMR 8028, Observatoire de Paris, Université PSL, Sorbonne Université,
77 Avenue Denfert-Rochereau,
75014
Paris,
France
e-mail: nam.hoang-hoai@obspm.fr
Received:
2
April
2021
Accepted:
4
May
2021
The long-term variations in the orbit of the Earth govern the insolation on its surface and hence its climate. The use of the astronomical signal, whose imprint has been recovered in the geological records, has revolutionized the determination of the geological timescales. However, the orbital variations beyond 60 Myr cannot be reliably predicted because of the chaotic dynamics of the planetary orbits in the Solar System. Taking this dynamical uncertainty to account is necessary for a complete astronomical calibration of geological records. Our work addresses this problem with a statistical analysis of 120 000 orbital solutions of the secular model of the Solar System ranging from 500 Myr to 5 Gyr. We obtain the marginal probability density functions of the fundamental secular frequencies using kernel density estimation. The uncertainty of the density estimation is also obtained here in the form of confidence intervals determined by the moving block bootstrap method. The results of the secular model are shown to be in good agreement with those of the direct integrations of a comprehensive model of the Solar System. Application of our work is illustrated on two geological data sets: the Newark-Hartford records and the Libsack core.
Key words: chaos / diffusion / celestial mechanics / methods: statistical
The density estimation of the fundamental frequencies and their combinations are only available at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/cat/J/A+A/654/A156
© N. H. Hoang et al. 2021
Open Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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