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

Research in Astronomy and Astrophysics 2019年第9期19卷 3-12页

作者： Nan Wang Zhi-Guo He Ocean College Zhejiang University

We build a conceptual coupled model of the climate and tidal evolution of the Earth-Moon system to find the influence of the former on the latter. An energy balance model is applied to calculate steady-state temperature field from the mean annual insolation as a function of varying astronomical parameters. A harmonic oscillator model is applied to integrate the lunar orbit and 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 Earth’s obliquity ε and the M2 tide, simulations are performed near tidal resonance for 106 yr. It is verified that the climate can influence the tidal evolution via ocean. Compared with the tidal evolution with constant ε, that with varying ε is slowed down;the EarthMoon distance oscillates in phase with ε 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.

关键词： Moon planets and satellites:dynamical evolution and stability planets and satellites:oceans

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Orbital evolution of a planet with tidal dissipation in a restricted three-body system

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Research in Astronomy and Astrophysics 2019年第9期19卷 79-96页

作者： Wen-Lei Wang Xue-Qing Xu Xin-Hao Liao Shanghai Astronomical Observatory Chinese Academy of SciencesShanghai200030China Key Laboratory of Planetary Sciences Shanghai Astronomical ObservatoryChinese Academy of SciencesShanghai200030China University of Chinese Academy of Sciences Beijing100049China

The angle between planetary spin and the normal direction of an orbital plane is supposed to reveal a range of information about the associated planetary formation and evolution. Since the orbit’s eccentricity and inclination oscillate periodically in a hierarchical triple body and tidal friction makes the spin parallel to the normal orientation of the orbital plane with a short timescale in an isolated binary system, we focus on the comprehensive effect of third body perturbation and tidal mechanism on the angle. Firstly, we extend the Hut tidal model(1981) to the general spatial case, adopting the equilibrium tide and weak friction hypothesis with constant delay time, which is suitable for arbitrary eccentricity and any angle ? between the planetary spin and normal orientation of the orbital plane. Furthermore, under the constraint of angular momentum conservation, the equations of orbital and ratational motion are given. Secondly, considering the coupled effects of tidal dissipation and third body perturbation, and adopting the quadrupole approximation as the third body perturbation effect, a comprehensive model is established by this work. Finally, we find that the ultimate evolution depends on the timescales of the third body and tidal friction. When the timescale of the third body is much shorter than that of tidal friction, the angle ? will oscillate for a long time,even over the whole evolution;when the timescale of the third body is observably larger than that of the tidal friction, the system may enter stable states, with the angle ? decaying to zero ultimately, and some cases may have a stable inclination beyond the critical value of Lidov-Kozai resonance. In addition, these dynamical evolutions depend on the initial values of the orbital elements and may aid in understanding the characteristics of the orbits of exoplanets.

关键词： astrometry and celestial mechanics:celestial mechanics planet-star interactions planets and satellites:dynamical evolution and stability

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