Constraints on Moon's Orbit 3.2 Billion Years Ago From Tidal Bundle Data

The angular momentum of the Earth‐Moon system was initially dominated by Earth's rotation with a short solar day of around 5 hr duration. Since then, Earth gradually transferred angular momentum through tidal friction to the orbit of the Moon, resulting in an increasing orbital radius and a deceleration of Earth's rotation. Geologic observations of tidal deposits can be used to verify and constrain models of lunar orbital evolution. In this work we reexamine the oldest tidal record suitable for analysis from the Moodies Group, South Africa, with an age of 3.22 billion years. Time frequency analysis of the series of thicknesses of the sandstone‐shale layers yields a periodicity of 15.0 layers, taking into account the possibility of missing laminae. Assuming a mixed tidal system, the duration of two neap‐spring‐neap cycles was 30.0 lunar days for dominant semidiurnal or 30.0 sidereal days for dominant diurnal tides. We derive the relationship between this observation and the past Earth‐Moon distance and re‐visit related published work. We find that the Earth‐Moon distance 3.2 billion years ago was about 70% of today's value. The Archean solar day was around 13 hr long. The ratio of solar to lunar tide‐raising torque controls the leakage of angular momentum from the Earth‐Moon system, but deviation from the assumed ratio of 0.211 results in only moderate changes. A duration of a postulated 21‐hr atmospheric resonance shorter than 200 million years would be consistent with our observation; it would significantly alter the Earth‐Moon distance. Plain Language Summary After its formation 4.5 billion years ago, the Moon circled Earth in a low orbit while Earth rotated faster than today around its axis. In the course of time, the Moon gradually evolved to a higher orbit while the rotation of Earth slowed due to the frictional effect of tides. Theoretical models can describe the evolution of the distance between Earth and the Moon with time until today. Counting the thickness of thin sandstone‐shale couplets of known age, which are layered due to tides, can constrain these models. In this work we reexamine the oldest of these geological records in the Moodies Group of South Africa, with an age of 3.2 billion years. The thickness of layers changes with a periodicity of 15 layers which is assumed to originate from varying strengths of currents between successive spring tides. Kepler's third law and the law of conservation of angular momentum allow us to derive the par