Why the day is 24 hours long: The history of Earth’s atmospheric thermal tide, composition, and mean temperature

The Sun drives a semidiurnal (12-hour) thermal tide in Earth’s atmosphere. Zahnle and Walker suggested that an atmospheric oscillation with period P(res) ≈ 10.5 hours resonated with the Solar driving ≈600 million years ago (Ma), when the length of day (lod) was ≈21 hours. They argued that the enhanced torque balanced the Lunar tidal torque, fixing the lod. We explore this hypothesis using two different global circulation models (GCMs), finding P(res) = 11.4 and 11.5 hours today, in excellent agreement with a recent measurement. We quantify the relation between P(res), mean surface temperature [Formula: see text] , composition, and Solar luminosity. We use geologic data, a dynamical model, and a Monte Carlo sampler to find possible histories for the Earth-Moon system. In the most likely model, the lod was fixed at ≈19.5 hours between 2200 and 600 Ma ago, with sustained high [Formula: see text] and an increase in the angular momentum L(EM) of the Earth-Moon system of ≈5%.