# Near-resonance tidal evolution of the Earth-Moon system influenced by orbital-scale climate change

Research paper by Nan Wang, Zhiguo He

Indexed on: 25 Jun '20Published on: 21 Jul '19Published in: arXiv - Astrophysics - Earth and Planetary Astrophysics

#### Abstract

We build a coupled conceptual model of the climate and the tidal evolution of the Earth-Moon system to find the influence of the former on the latter. Energy balance model is applied to calculate steady temperature field from the mean annual insolation as a function of varying astronomical parameters. Harmonic oscillator model is applied to integrate the lunar orbit and the Earth's rotation with the tidal torque dependent on the dominant natural frequency of ocean. An ocean geometry acts as a bridge between temperature and oceanic frequency. On assumptions of a fixed hemispherical continent and an equatorial circular lunar orbit, considering only the 41 kyr periodicity of the Earth's obliquity $\varepsilon$ and the $M_2$ tide, simulations are performed near tidal resonance for $10^6$ yr. It is verified that the climate can influence the tidal evolution via ocean. Compared with the tidal evolution with constant $\varepsilon$, that with varying $\varepsilon$ is slowed down; the Earth-Moon distance oscillates in phase with $\varepsilon$ before the resonance maximum but exactly out of phase after that; the displacement of the oscillation is in positive correlation with the difference between oceanic frequency and tidal frequency.