La2010: a new orbital solution for the long-term motion of the Earth^⋆

¹ ASD, IMCCE-CNRS UMR8028, Observatoire de Paris, UPMC, 77 Av. Denfert-Rochereau, 75014 Paris, France
e-mail: laskar@imcce.fr
² Observatoire de Besançon–CNRS UMR6213, 41bis Av. de l’Observatoire, 25000 Besançon, France

Received: 5 March 2011
Accepted: 3 May 2011

Abstract

We present here a new solution for the astronomical computation of the orbital motion of the Earth spanning from 0 to  −250 Myr. The main improvement with respect to our previous numerical solution La2004 is an improved adjustment of the parameters and initial conditions through a fit over 1 Myr to a special version of the highly accurate numerical ephemeris INPOP08 (Intégration Numérique Planétaire de l’Observatoire de Paris). The precession equations have also been entirely revised and are no longer averaged over the orbital motion of the Earth and Moon. This new orbital solution is now valid over more than 50 Myr in the past or into the future with proper phases of the eccentricity variations. Owing to the chaotic behavior, the precision of the solution decreases rapidly beyond this time span, and we discuss the behavior of various solutions beyond 50 Myr. For paleoclimate calibrations, we provide several different solutions that are all compatible with the most precise planetary ephemeris. We have thus reached the time where geological data are now required to discriminate between planetary orbital solutions beyond 50 Myr.