Vertical angular momentum constraint on lunar formation and orbital history

Tian, Zhengkun; Wisdom, Jack

doi:10.1073/pnas.2003496117

Cited by 15 publications

(34 citation statements)

References 29 publications

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“…So where does all this leave us? Well, the last major generalization of Laplace's work ushered a stream of applications, mainly to extra solar settings (Muñoz & Lai 2015;Zanazzi & Lai 2016), but also to scenarios of Lunar formation which argue for an initially steeply oblique and fast spinning Earth (Ćuk et al 2016;Tian & Wisdom 2020;Ćuk et al 2021). We can foresee the same for our renewed focus on the foundations of the Laplace Surface itself, and for the rich structure of equilibria we have identified, with applications ranging from man made satellites, to exo-moons around planets on Kozai-Lidov cycles, then debris disks with enclosed planets, the whole perturbed by a wide eccentric binary.…”

Section: Discussionmentioning

confidence: 99%

“…The circle was recently closed back onto the solar system, when it was realized that origin around a fast spinning and oblique Earth, which is favored on geochemical grounds, could generate a Moon whose Laplace plane may very well be prone to TTN's eccentricity instability! (Ćuk et al 2016;Tian & Wisdom 2020;Ćuk et al 2021) The present work begins where TTN left the Laplace Surface, and relaxes yet another assumption in the original Laplace story by explicitly accounting for an eccentric binary companion, thus effectively breaking the hitherto assumed axisymmetry of the outer perturber. This level of generality is again demanded by exo-planetary systems, the disks that generate them, remnant debris disks, all in the presence of a massive wide binary companion on an eccentric (and inclined) orbit.…”

Section: Introductionmentioning

confidence: 99%

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Laplace surface dynamics, revisited: satellites, exo-planets and debris with distant, eccentric companions

Farhat,

Touma

2021

Preprint

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To date, studies of Laplace Surface dynamics have concerned themselves with test particle orbits of fixed shape and orientation in the combined field of an oblate central body (to which the particle is bound) and a distant, inclined, companion which is captured to quadrupolar order. While amply sufficient for satellites around planets on near-circular orbits, the quadrupolar approximation fails to capture essential dynamical features induced by a wide binary companion (be it a star, a planet or a black hole) on a fairly eccentric orbit. With similar such astronomical settings in mind, we extend the classical Laplace framework to higher multipoles, and map out the backbone of stationary orbits, now complexified by the broken axial symmetry. Eccentric and inclined Laplace equilibria, which had been presaged in systems of large enough mutual inclination, are here delineated over a broad range of mutually inclined perturbations. We recover them for test particles in the field of a hot Jupiter and a wide eccentric stellar binary, highlighting their relevance for the architecture of multi-planet systems in binaries. We then extend and deploy our machinery closer to home, as we consider the secular dynamics of Trans-Neptunian Objects (TNOs) in the presence of a putative ninth planet. We show how generalized Laplace equilibria seed islands for Trans-Neptunian objects to be sheltered around, islands within chaotic seas which we capture via Poincaré sections, while highlighting a beautiful interplay between Laplace and Kozai-Lidov secular dynamical structures. An eminently classical tale revived for the exo-planetary 21st century!

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Laplace surface dynamics, revisited: satellites, exo-planets and debris with distant, eccentric companions

Farhat,

Touma

2021

Preprint

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“…During the instability, Earth's spin decreases and AM is transferred to Earth's orbit (Ćuk et al., 2016). However, Tian and Wisdom (2020) argue that such an evolution cannot reproduce the current Earth‐Moon system, because the needed initial high‐obliquity state is inconsistent with the component of the current Earth‐Moon angular momentum that is perpendicular to the ecliptic plane.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Tidal Evolution of the Evection Resonance/Quasi‐Resonance and the Angular Momentum of the Earth‐Moon System

Rufu

Canup

2020

JGR Planets

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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 LEM) after the Moon forms. Capture into the evection resonance, occurring when the lunar perigee precession period equals 1 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 Moon's 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 Earth's 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 LEM, final angular momentum values after quasi‐resonance escape remain significantly higher than the current Earth‐Moon value.

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“…Recently, Tian & Wisdom (2020) have shown that the Laplace Plane instability, like other solar interactions with the Earth-Moon system, should conserve the component of the AM vector of the system that is perpendicular to the ecliptic (referred to by Tian & Wisdom (2020) as the "vertical AM" but which we will refer to as "ecliptic AM"). The simulations of Ćuk et al (2016) did not conserve this quantity, casting serious doubt on the results of Ćuk et al (2016), including the Earth-Moon system AM loss through the LPT.…”

Section: Introductionmentioning

confidence: 99%

“…The simulations of Ćuk et al (2016) did not conserve this quantity, casting serious doubt on the results of Ćuk et al (2016), including the Earth-Moon system AM loss through the LPT. Beyond the issue of ecliptic AM conservation, Tian & Wisdom (2020) stated that evolution through the Laplace Plane instability cannot result in the current Earth-Moon system regardless of the tidal parameters assumed for the system. Tian & Wisdom (2020) found that all high-obliquity Earth-Moon pairs with the correct ecliptic AM led to systems with too much AM and too high an obliquity for Earth at the end of the LPT.…”

Section: Introductionmentioning

confidence: 99%

Tidal Evolution of the Earth-Moon System with a High Initial Obliquity

Ćuk¹,

Lock²,

Stewart³

et al. 2021

Preprint

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A giant impact origin for the Moon is generally accepted, but many aspects of lunar formation remain poorly understood and debated. Ćuk et al. (2016) proposed that an impact that left the Earth-Moon system with high obliquity and angular momentum could explain the Moon's orbital inclination and isotopic similarity to Earth. In this scenario, instability during the Laplace Plane transition, when the Moon's orbit transitions from the gravitational influence of Earth's figure to that of the Sun, would both lower the system's angular momentum to its present-day value and generate the Moon's orbital inclination. Recently, Tian & 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 & 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 (θ > 61 • ) 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.

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Vertical angular momentum constraint on lunar formation and orbital history

Cited by 15 publications

References 29 publications

Laplace surface dynamics, revisited: satellites, exo-planets and debris with distant, eccentric companions

Laplace surface dynamics, revisited: satellites, exo-planets and debris with distant, eccentric companions

Tidal Evolution of the Evection Resonance/Quasi‐Resonance and the Angular Momentum of the Earth‐Moon System

Tidal Evolution of the Earth-Moon System with a High Initial Obliquity

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