Misfit surfaces of χ² for the three studied geometric models. The past dynamical evolution of the Earth-Moon system is reconstructed for the shown ranges of our two free model parameters H and σ_R. The misfit is established using the currently measured lunar recession rate via LLR, and the lunar age (Appendix C). The three models differ in the imposed geometry of the oceanic shell over the geological history, with the combined model featuring more physical realism that the other two. The numerical results of this analysis are summarized in (Table C.1). The dynamical evolution associated with each of the misfit minima is plotted in terms of: the lunar semi-major axis in Fig. 3, length of the day in Fig. 5, and obliquity and precession frequency in Fig. 6.