Constraints on astronomical parameters from the geological record for the last 25 Myr

We develop a new method, based on interference patterns between the precession and obliquity components of geological data from Ocean Drilling Program (ODP) Leg 154 and astronomical solutions, to extract small changes in the precession constant p due to tidal dissipation over the last 25 million years and to put numerical constraints on the parameters for tidal dissipation and the dynamical ellipticity of the Earth. We show that these parameters have remained close to the present day values over the last 25 million years. The best fitting astronomical solution we obtained gives rise to a value of 0.9999 times the current day dynamical ellipticity, and 1.004 times the current day tidal dissipation value as used in the algorithm of Laskar (1993). Our range of uncertainty is 0.9996–1.0001 for the dynamical ellipticity of the Earth and 0.945–1.025 for the tidal dissipation. Our model does not require changes in these parameters over the last 25 Ma and we show that using the solution of Laskar (1993) with present day values for dynamical ellipticity and tidal dissipation as a tuning target does not introduce large errors during astronomical tuning. Our results indicate that the Earth has not crossed into resonance with Saturn and Jupiter during the last few million years. Our conclusions depend on the assumption of a correct initial tuning of the ODP Leg 154 data.