4.5 billion years of Earth-Moon evolution from high-level ocean tide and orbital dynamics models: First results

Brian K Arbic1, Houraa Daher1, James G Williams2, Joseph K Ansong3, Dale H. Boggs4, Malte Müller5, Michael Schindelegger6, Alistair Adcroft7, Jacqueline Austermann8, Bruce D Cornuelle9, Eliana Crawford10, Oliver B Fringer11, Harriet C. P. Lau12, Simon James Lock13, Adam C Maloof14, Dimitris Menemenlis15, Jerry X Mitrovica16, Mattias Green17 and Matthew Huber18, (1)University of Michigan Ann Arbor, Ann Arbor, MI, United States, (2)NASA Jet Propulsion Laboratory, Pasadena, CA, United States, (3)Univ of MI-Earth & Environ Sci, Ann Arbor, MI, United States, (4)NASA Jet Propulsion Laboratory, United States, (5)Norwegian Meteorological Institute, Oslo, Norway, (6)University of Bonn, Institute of Geodesy and Geoinformation, Bonn, Germany, (7)Princeton University, Program in Atmospheric and Oceanic Sciences, Princeton, NJ, United States, (8)Lamont-Doherty Earth Observatory of Columbia University, Palisades, United States, (9)University of California San Diego, Scripps Institution of Oceanography, La Jolla, United States, (10)Kenyon College, United States, (11)Stanford University, Stanford, CA, United States, (12)Brown University, Earth, Environmental, and Planetary Sciences, Providence, United States, (13)University of Bristol, Bristol, BS8, United Kingdom, (14)Princeton University, Department of Geosciences, Princeton, NJ, United States, (15)NASA Jet Propulsion Laboratory, Pasadena, United States, (16)Harvard University, Department of Earth and Planetary Sciences, Cambridge, United States, (17)Bangor University, School of Ocean Sciences, Bangor, LL59, United Kingdom, (18)Purdue University, Department of Earth, Atmospheric, and Planetary Sciences, West Lafayette, IN, United States
Abstract:
Over geological time, Earth-Moon orbital parameters undergo profound changes due to tides, which are profoundly affected by the orbital changes. Here we perform a backwards integration of 4.5 billion years of Earth-Moon orbital evolution through coupling of ocean tide and orbital dynamics models that are both ``high-level'', i.e. not idealized. We employ a realistic ocean tide model with four continental geometries--the present-day (PD), 55 Ma, 116 Ma, and 252 Ma. The Love number factor $k sin \chi$ relating tidal dissipation to tidal forcing depends tends to decrease with increasing Earth rotation rate, but is also a strong function of ocean basin geometry. The orbital dynamics model timesteps secular changes in Earth's rotation rate, the semimajor axis and eccentricity of the lunar orbit, the inclination of the Moon's orbit to the ecliptic, and the obliquity of the Earth's spin axis. To mimic the uncertain history of ocean basin geometry, we employ 1000 Monte Carlo simulations, with $k sin \chi$ values randomly selected from ocean tide simulations employing the four geometries. The Monte Carlo results provide a spread of plausible values for all orbital variables, especially lunar inclination. From about 3-4.5 Ga, the inclination, eccentricity, and semimajor axis of the lunar orbit are dominated by effects of tides in the Moon, and the lunar core-mantle boundary, which are included in the orbital dynamics model. The eventual goal of this research is to help constrain lunar formation models. We discuss the additional physics that needs to be included before our confidence in the backwards trajectories is great enough for this purpose.
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