Physics Colloquium with Norman Murray on Why the Day is 24 Hours Long

The length of the day and the month are seen to be increasing, due to gravitational tidal torques. Geologic data suggests, however, that between about 2,000 million years ago (Ma) and 1,000 Ma, the length of day (LOD) was fixed at about 19.5 hours, while the length of the month was increasing. Following a suggestion by Zahnle and Walker in the 1980's, my co-workers and I explore the hypothesis that the fixed LOD results from the Solar thermal atmospheric tide, which was stronger in the past, due in part to a resonance in Earth's atmosphere. Absent this resonance, the LOD today would be around 60 hours. We use two global circulation models (or GCMs), PlaSim and LMD, to estimate the frequencies of normal modes (or free oscilliations) in Earth's atmosphere, finding excellent agreement with recent measurements. Using the GCMs, we show that an atmospheric resonant period of 19.5 hours corresponds to a mean global surface temperature T in the range 40-50 C; the GCMs show that T could have been that high despite the lower Solar flux 2,000 Ma, if the partial pressure of CO2 was of order a tenth of a bar, compared to the present day value of 0.0004 bar. This is at the upper range of estimates 1,500 Ma based on geochemical and paleosoil evidence. Thermal tides are likely to have affected the length of day of many exoplanets.