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Register a new userTidal Evolution of the Evection Resonance/Quasi-Resonance and the Angular Momentum of the Earth-Moon System
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Forming the Moon by a high-angular momentum impact may explain the Earth-Moon isotopic similarities, however, the post-impact angular momentum needs to be reduced by a factor of 2 or more to the current value (1 L_EM) after the Moon forms. Capture into the evection resonance, occurring when the lunar perigee precession period equals one year, could remove the angular momentum excess. However the appropriate angular momentum removal appears sensitive to the tidal model and chosen tidal parameters. In this work, we use a constant-time delay tidal model to explore the Moons orbital evolution through evection. We find that exit from formal evection occurs early and that subsequently, the Moon enters a quasi-resonance regime, in which evection still regulates the lunar eccentricity even though the resonance angle is no longer librating. Although not in resonance proper, during quasi-resonance angular momentum is continuously removed from the Earth-Moon system and transferred to Earths heliocentric orbit. The final angular momentum, set by the timing of quasi-resonance escape, is a function of the ratio of tidal strength in the Moon and Earth and the absolute rate of tidal dissipation in the Earth. We consider a physically-motivated model for tidal dissipation in the Earth as the mantle cools from a molten to a partially molten state. We find that as the mantle solidifies, increased terrestrial dissipation drives the Moon out of quasi-resonance. For post-impact systems that contain >2 L_EM, final angular momentum values after quasi-resonance escape remain significantly higher than the current Earth-Moon value.
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A high-angular momentum giant impact with the Earth can produce a Moon with a silicate isotopic composition nearly identical to that of Earths mantle, consistent with observations of terrestrial and lunar rocks. However, such an event requires subsequent angular momentum removal for consistency with the current Earth-Moon system. The early Moon may have been captured into the evection resonance, occurring when the lunar perigee precession period equals one year. It has been proposed that after a high-angular momentum giant impact, evection removed the angular momentum excess from the Earth-Moon pair and transferred it to Earths orbit about the Sun. However, prior N-body integrations suggest this result depends on the tidal model and chosen tidal parameters. Here we examine the Moons encounter with evection using a complementary analytic description and the Mignard tidal model. While the Moon is in resonance the lunar longitude of perigee librates, and if tidal evolution excites the libration amplitude sufficiently, escape from resonance occurs. The angular momentum drain produced by formal evection depends on how long the resonance is maintained. We estimate that resonant escape occurs early, leading to only a small reduction (~few to 10%) in the Earth-Moon system angular momentum. Moon formation from a high-angular momentum impact would then require other angular momentum removal mechanisms beyond standard libration in evection, as have been suggested previously.
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 Earths 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 Earths 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.
A giant impact origin for the Moon is generally accepted, but many aspects of lunar formation remain poorly understood and debated. Cuk et al. (2016) proposed that an impact that left the Earth-Moon system with high obliquity and angular momentum could explain the Moons orbital inclination and isotopic similarity to Earth. In this scenario, instability during the Laplace Plane transition, when the Moons orbit transitions from the gravitational influence of Earths figure to that of the Sun, would both lower the systems angular momentum to its present-day value and generate the Moons orbital inclination. Recently, Tian and Wisdom (2020) discovered new dynamical constraints on the Laplace Plane transition and concluded that the Earth-Moon system could not have evolved from an initial state with high obliquity. Here we demonstrate that the Earth-Moon system with an initially high obliquity can evolve into the present state, and we identify a spin-orbit secular resonance as a key dynamical mechanism in the later stages of the Laplace Plane transition. Some of the simulations by Tian and Wisdom (2020) did not encounter this late secular resonance, as their model suppressed obliquity tides and the resulting inclination damping. Our results demonstrate that a giant impact that left Earth with high angular momentum and high obliquity ($theta > 61^{circ}$) is a promising scenario for explaining many properties of the Earth-Moon system, including its angular momentum and obliquity, the geochemistry of Earth and the Moon, and the lunar inclination.
The stability of satellites in the solar system is affected by the so-called evection resonance. The moons of Saturn, in particular, exhibit a complex dynamical architecture in which co-orbital configurations occur, especially close to the planet where this resonance is present. We address the dynamics of the evection resonance, with particular focus on the Saturn system, and compare the known behavior of the resonance for a single moon to that of a pair of moons in co-orbital trojan configuration. We developed an analytic expansion of the averaged Hamiltonian of a trojan pair of bodies, including the perturbation from a distant massive body. {The analysis of the corresponding equilibrium points was restricted to the asymmetric apsidal corotation solution of the co-orbital dynamics.} We also performed numerical N-body simulations to construct dynamical maps of the stability of the evection resonance in the Saturn system, and to study the effects of this resonance under the migration of trojan moons caused by tidal dissipation. The structure of the phase space of the evection resonance for trojan satellites is similar to that of a single satellite, differing in that the libration centers are displaced from their standard positions by an angle that depends on the periastron difference $varpi_2-varpi_1$ and on the mass ratio $m_2/m_1$ of the trojan pair. The interaction with the inner evection resonance may have been relevant during the early evolution of the Saturn moons Tethys, Dione, and Rhea. In particular, Rhea may have had trojan companions in the past that were lost when it crossed the evection resonance, while Tethys and Dione may either have retained their trojans or have never crossed the evection. This may help to constrain the dynamical processes that led to the migration of these satellites and to the evection itself.
The giant impact hypothesis is the dominant theory explaining the formation of our Moon. However, its inability to produce an isotopically similar Earth-Moon system with correct angular momentum has cast a shadow on its validity. Computer-generated impacts have been successful in producing virtual systems that possess many of the physical properties we observe. Yet, addressing the isotopic similarities between the Earth and Moon coupled with correct angular momentum has proven to be challenging. Equilibration and evection resonance have been put forth as a means of reconciling the models. However, both were rejected in a meeting at The Royal Society in London. The main concern was that models were multi-staged and too complex. Here, we present initial impact conditions that produce an Earth-Moon system whose angular momentum and isotopic properties are correct. The model is straightforward and the results are a natural consequence of the impact.
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