The resonant tidal evolution of the Earth-Moon distance

Ever since the Moon formed close to the Earth, it has been forced by tidal interactions to drift away through orbital angular momentum pumping. Available geological data provide snapshots of the lunar orbital history, the earliest registered to date at ~3.2 Ga. However, a complete theoretical reconstruction of the lunar orbit, which traces its evolution from the present state to a post-impact nosy neighbor at ~4.5 Ga was missing. Namely, previous tidal models attempting this reconstruction are either empirical, or numerically costly, and are always incompatible with the well-constrained lunar age. We undertake a systematic exploration of the time-varying tidal dissipation in the Earth’s oceans and solid interior to provide, for the first time, a history of the lunar orbit that fits the present measurement of its recession and the estimated lunar age. Our work extends a lineage of earlier works on the semi-analytical treatment of fluid tides on varying bounded surfaces, allowing us to mimic the time-varying effect of continentality on Earth. We further couple the oceanic response with solid bodily tidal deformations using an Andrade rheology. The modeled oceanic tidal response is effectively barotropic and is parametrized by only two parameters describing the oceanic thickness and the timescale of dissipation. Our resulting tidal response reconstructs a history of the lunar orbit that is predominantly shepherded by robust resonant excitations in the Earth’s paleo-oceans. This lunar orbital reconstruction is in good agreement with the available geological proxies, which predicates the dominance of long-wavelength flows in controlling the tidal history, instead of the continentality-driven basin modes. The generated tidal resonances caused significant and, relatively, rapid variations in the lunar semi-major axis, the Earth’s length of the day, and the Earth’s obliquity. Consequently, these astronomical features should have driven significant paleo-climatic variations through tidal heating and the changing insolation.