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Description
The long-term variations of 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 time scales (e.g. Gradstein & Ogg, 2020, in Geologic Time Scale (Amsterdam: Elsevier), 21). However, the orbital variations beyond 60Myr cannot be reliably predicted because of the A,chaotic dynamics of the planetary orbits in the Solar System (Laskar, 1989Natur.338..237L). Taking into account this dynamical uncertainty is necessary for a complete astronomical calibration of geological records. Our work addresses this problem with a statistical analysis on 120000 orbital solutions of the secular model of the Solar System ranging from 500Myr to 5Gyr. 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. Applicationof our work is illustrated on two geological data: the Newark-Hartford
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