Updating a simple model of lunar recession

TL;DR

This paper reviews and updates a simple classical model of lunar recession, comparing its predictions with astronomical and paleontological data, and discusses the effects of atmospheric tides and non-tidal processes.

Contribution

It introduces updated parameters and incorporates short-term fluctuations, demonstrating the model's consistency with paleontological data and discussing additional effects.

Findings

Model slightly overestimates EMD and LOD compared to astronomical data.

Predicted EMD and LOD are consistent with paleontological data when short-term fluctuations are included.

The model serves as a useful zeroth-order approximation for lunar recession and LOD evaluation.

Abstract

A classical model of lunar recession is reviewed and updated, where input parameters are taken or inferred from earlier astronomical computation of insolation quantities on Earth back to 0.25 Gyr. Free parameters are (i) the transition age, where mean lunar recession is suddenly lowered, and (ii) the merging age, where Earth-Moon distance (EMD), drops to zero. Predicted mean EMD and length of day (LOD) slightly overstimate their counterparts from the above mentioned astronomical computation. Predicted LOD, where the effect of atmospheric tides and nontidal processes is considered and supposed to be time independent, slightly understimates a linear interpolation from paleontological data related to Phanerozoic, inferred in earlier investigations. If short-period ($\Delta t\approx10^{-3}$ Gyr) EMD fluctuations ($\Delta a\approx\mp0.5R_\oplus$), resulting from the above mentioned astronomical computation back to 0.25 Gyr, occur along the whole evolution of Earth-Moon system (EMS), then the predicted mean EMD is consistent with values inferred from three well studied paleontological data sets: Elatina-Reynella (ER), Big Cottonwood (BC), Weeli Wolli (WW), for a suitable choice of input parameters. The same holds for LOD where, in addition, computed values are consistent with a linear interpolation from paleontological data related to Proterozoic, inferred in earlier investigations. The effect of atmospheric tides and nontidal processes is also discussed. In conclusion, the current model can be considered as a useful zeroth-order approximation to the evaluation of lunar recession and LOD. More accurate paleontological data, expecially in connection with error evaluation, would be desirable in view of improved results and further constraints involving both Astronomy and Paleontology.