Reconstruct the evolution of Milankovtich cycle in Paleozoic and Proterozoic and Earth-Moon separation history

At present, it is difficult to obtain numerical astronomy solutions prior to 50 Ma , which should be two reasons for this. First, the solar system's chaotic behavior, namely, small initial disturbances will greatly affect the results of the numerical model of the earth orbit. Second, we do not fully understand the evolution history of the Earth-Moon separation, that is the distance versus time series. Recently, a new method called "TimeOptMCMC" has been successfully applied to invert the paleo-astronomical parameters of Cenozoic (~55Ma) and Proterozoic (~1400Ma). However, only two case studies cannot show the complete evolution process, and there is a lack of suitable way to model and discuss the Earth-Moon separation process. Therefore, in this study, we perform TimeOptMCMC analysis on four well-studied sections’ proxy sequences to enrich the eccentricity and precession estimates in Paleozoic and Proterozoic. At the same time, we innovatively use a simple continuous Markov monotone stochastic process to reconstruct the Earth-Moon separation history from 2465 Ma to present. Meanwhile, based on the reconstructed Earth-Moon separation simulations, we calculate the tidal drag factor which represents the history of tidal dissipation in the Earth-Moon system. Our results improve the estimates of palaeoastronomical parameters in the Paleozoic and Proterozoic, providing results with good constraints for tuning cyclostratigraphy in ancient era. Further, we corroborate the previous inference that the Earth-Moon system has a long-term low tidal dissipation, give the Earth-Moon system’s dissipation history trend with stepwise characteristic at large scale, and provide a comparison with other tidal models.