A long-term numerical solution for the insolation quantities of the Earth

A long-term numerical solution for the insolation quantities of the Earth

Received 23 May 2004 / Accepted 11 August 2004 | J. Laskar, P. Robutel, F. Joutel, M. Gastineau, A. C. M. Correia, and B. Levrard
This paper presents a new numerical solution for the astronomical computation of insolation quantities on Earth over a 250 million-year period, improving upon the La93 solution by using direct integration of gravitational equations and enhancing dissipative contributions, particularly in the Earth-Moon system. The solution is expected to be useful for age calibrations of paleoclimatic data over 40 to 50 million years, and potentially over the full Palaeogene period (65 million years). The most significant feature of the obliquity solution is a secular global increase due to tidal dissipation, accompanied by a strong decrease of about 0.38 degrees due to the crossing of the $s_6 + g_5 - g_6$ resonance. For the calibration of the Mesozoic time scale, the term of largest amplitude in the eccentricity, related to $g_2 - g_5$, with a fixed frequency of 3.200 arcseconds per year, is proposed. The uncertainty of this time scale over 100 million years is estimated to be about 0.1%, and 0.2% over the full Mesozoic era. The paper also discusses the numerical model, including the orbital and rotational dynamics, and the numerical integrator used. It compares the new solution with the DE406 ephemeris and the La93 solution, showing that the differences are within acceptable limits. The secular frequencies and analytical approximations for orbital motion, obliquity, and precession are provided, offering practical tools for paleoclimatic studies.This paper presents a new numerical solution for the astronomical computation of insolation quantities on Earth over a 250 million-year period, improving upon the La93 solution by using direct integration of gravitational equations and enhancing dissipative contributions, particularly in the Earth-Moon system. The solution is expected to be useful for age calibrations of paleoclimatic data over 40 to 50 million years, and potentially over the full Palaeogene period (65 million years). The most significant feature of the obliquity solution is a secular global increase due to tidal dissipation, accompanied by a strong decrease of about 0.38 degrees due to the crossing of the $s_6 + g_5 - g_6$ resonance. For the calibration of the Mesozoic time scale, the term of largest amplitude in the eccentricity, related to $g_2 - g_5$, with a fixed frequency of 3.200 arcseconds per year, is proposed. The uncertainty of this time scale over 100 million years is estimated to be about 0.1%, and 0.2% over the full Mesozoic era. The paper also discusses the numerical model, including the orbital and rotational dynamics, and the numerical integrator used. It compares the new solution with the DE406 ephemeris and the La93 solution, showing that the differences are within acceptable limits. The secular frequencies and analytical approximations for orbital motion, obliquity, and precession are provided, offering practical tools for paleoclimatic studies.
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