On the Secular Behavior of Irregular Satellites

Ćuk, Matija; Burns, Joseph A.

doi:10.1086/424937

Cited by 66 publications

(60 citation statements)

References 39 publications

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“…Extensive stability surveys of irregular satellites within the Hill sphere of the giant planets have been carried out by Carruba et al (2002) and Nesvorný et al (2003) by recording the lifetimes of irregular satellite test particles in various parameter surveys. Yokoyama et al (2003) studied the region 250 R Jup < r < 370 R Jup for prograde Jovian irregular orbits in the semimajor axis and inclination plane finding evidence for the presence of secular resonances (Whipple & Shelus 1993; Ćuk & Burns 2004; Nesvorný & Beaugé 2007). Stability properties of irregular orbits at the outer regions of the giant planet's Hill sphere and beyond were studied by Shen & Tremaine (2008).…”

Section: Introductionmentioning

confidence: 99%

Application of the MEGNO technique to the dynamics of Jovian irregular satellites

Hinse

Christou

Alvarellos³

et al. 2010

Monthly Notices of the Royal Astronomical Society

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We apply the Mean Exponential Growth Factor of Nearby Orbits (MEGNO) technique to the dynamics of Jovian irregular satellites. The MEGNO indicator is a practical numerical tool to distinguish between quasi‐periodic and chaotic structures in phase space of a given dynamical system. The MEGNO indicator is used to generate a mapping of relevant phase‐space regions occupied by observed Jovian irregular satellites. The construction of MEGNO maps of the Jovian phase‐space region within its Hill‐sphere is addressed and the obtained results are compared with previous studies regarding the dynamical stability of irregular satellites. Since this is the first time the MEGNO technique is applied to study the dynamics of irregular satellites, we provide a review of the MEGNO theory and illustrate basic properties. We consider the elliptic restricted three‐body problem in which Jupiter is orbited by a massless test satellite subject to solar gravitational perturbations. The equations of motion of the system are integrated numerically and the MEGNO indicator computed from the system's variational equations. A large set of initial conditions is studied to generate the MEGNO maps. The chaotic nature of initial conditions is demonstrated by studying a quasi‐periodic orbit and a chaotic orbit. As a result, we establish the existence of several high‐order mean‐motion resonances (MMR) detected for retrograde orbits along with other interesting dynamical features related to various dynamical resonances. The computed MEGNO maps allow us to differentiate qualitatively between chaotic and quasi‐periodic regions of the irregular satellite phase space within a relatively short integration time of 60 000 yr for each orbit. By comparing with previous published results, we can establish a correlation between chaotic regions and corresponding regions of orbital instability. Based on our results, we hypothesize on the possibility of gravitational scattering from high‐order MMR as a dynamical cause to explain the observed orbital velocity dispersion for members of the Pasiphae family.

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Section: Introductionmentioning

confidence: 99%

Application of the MEGNO technique to the dynamics of Jovian irregular satellites

Hinse

Christou

Alvarellos³

et al. 2010

Monthly Notices of the Royal Astronomical Society

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“…where A, B and C are the Moon's principal moments of inertia, andΩ is the rate of precession of the lunar node, which we estimate as 34 :Ω = 3 4…”

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confidence: 99%

Tidal evolution of the Moon from a high-obliquity, high-angular-momentum Earth

Ćuk

Hamilton

Lock

et al. 2016

Nature

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131

103

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In the giant impact hypothesis for lunar origin, the Moon accreted from an equatorial circumterrestrial disk; however the current lunar orbital inclination of 5 • requires a subsequent dynamical process that is still debated [1][2][3] . In addition, the giant impact theory has been challenged by the Moon's unexpectedly Earth-like isotopic composition 4, 5 . Here, we show that tidal dissipation due to lunar obliquity was an important effect during the Moon's tidal evolution, and the past lunar inclination must have been very large, defying theoretical explanations. We present a new tidal evolution model starting with the Moon in an equatorial orbit around an initially fast-spinning, high-obliquity Earth, which is a probable outcome of giant impacts. Using numerical modeling, we show that the solar perturbations on the Moon's orbit naturally induce a large lunar inclination and remove angular momentum from the 1 arXiv:1802.03356v1 [astro-ph.EP] 9 Feb 2018Earth-Moon system. Our tidal evolution model supports recent high-angular momentum giant impact scenarios to explain the Moon's isotopic composition [6][7][8] and provides a new pathway to reach Earth's climatically favorable low obliquity.The leading theory for lunar origin is the giant impact 9, 10 , which explains the Moon's large relative size and small iron core. Here we refer to the giant impact theory in which the Earth-Moon post-impact angular momentum (AM) was the same as it is now (in agreement with classic lunar tidal evolution studies 11, 12 ) as "canonical". In the canonical giant impact model 13 , a Mars-mass body obliquely impacts the proto-Earth near the escape velocity to generate a circum-terrestrial debris disk. The angular momentum of the system is set by the impact, and the Moon accretes from the disk, which is predominantly (> 60 wt%) composed of impactor material. However, Earth and the Moon share nearly identical isotope ratios for a wide range of elements, and this isotopic signature is distinct from all other extraterrestrial materials 4, 5 . Because isotopic variations arise from multiple processes 4 , the Moon must have formed from, or equilibrated with, Earth's mantle 5,14 . Earth-Moon isotopic equilibration in the canonical model has been proposed by Pahlevan and Stevenson 15 , but has been questioned by other researchers 16 , who suggest that the large amount of mass exchange required to homogenize isotopes could lead to the collapse of the proto-lunar disk.Cuk and Stewart 6 proposed a new variant of the giant impact that is based on an initially high AM Earth-Moon system. In this model, a late erosive impact onto a fast-spinning proto-Earth produced a disk that was massive enough to form the Moon, and was composed primarily of material from Earth, potentially satisfying the isotopic observations. Canup 7 presented a variation of a high-2 AM origin in which a slow collision between two similar-mass bodies produces a fast-spinning Earth and disk with Earth-like composition. Subsequently, Lock et al. 8 have argued that a range of hig...

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“…This is indeed an approximation, since these additional perturbations may cause significant orbital variations (e.g. Carruba et al 2004; Ćuk & Burns 2004). In particular, the temporary nature of the ν ⊙ resonance lock of real satellites is due to the gravitational effects of the other planetary bodies.…”

Section: Discussionmentioning

confidence: 99%

“…This imprecision is not restricted to the structure of the phase space in the vicinity of this satellite, but is a general flaw of the averaging process used to obtain the analytical model. As shown by Ćuk & Burns (2004), averaging over short‐period terms must be performed to order higher than unity, to include the effect of second‐ and third‐order secular terms such as evection. These effects cause significant variations in the secular frequencies, thus affecting the long‐term evolution of individual bodies, calculations of including proper elements and the location of the secular resonances in the domain of irregular satellites.…”

Section: Analytical Models For the ν⊙ Resonancementioning

confidence: 99%

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Mapping theν_⊙secular resonance for retrograde irregular satellites

Correa-Otto¹,

Leiva²,

Giuppone³

et al. 2010

Monthly Notices of the Royal Astronomical Society

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Constructing dynamical maps from the filtered output of numerical integrations, we analyse the structure of the ν⊙ secular resonance for fictitious irregular satellites in retrograde orbits. This commensurability is associated with the secular angle θ=ϖ−ϖ⊙, where ϖ is the longitude of the pericentre of the satellite and ϖ⊙ corresponds to the (fixed) planetocentric orbit of the Sun. Our study is performed in the restricted three‐body problem, where the satellites are considered as massless particles around a massive planet and perturbed by the Sun. Depending on the initial conditions, the resonance presents a diversity of possible resonant modes, including librations of θ around 0 (as found for Sinope and Pasiphae) or 180° as well as asymmetric librations (e.g. Narvi). Symmetric modes are present in all giant planets, although each regime appears restricted to certain values of the satellite inclination. Asymmetric solutions, on the other hand, seem absent around Neptune due to its almost circular heliocentric orbit. Simulating the effects of a smooth orbital migration on the satellite, we find that the resonance lock is preserved as long as the induced change in the semimajor axis is much slower compared to the period of the resonant angle (adiabatic limit). However, the librational mode may vary during the process, switching between symmetric and asymmetric oscillations. Finally, we present a simple scaling transformation that allows us to estimate the resonant structure around any giant planet from the results calculated around a single primary mass.

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On the Secular Behavior of Irregular Satellites

Cited by 66 publications

References 39 publications

Application of the MEGNO technique to the dynamics of Jovian irregular satellites

Application of the MEGNO technique to the dynamics of Jovian irregular satellites

Tidal evolution of the Moon from a high-obliquity, high-angular-momentum Earth

Mapping theν_⊙secular resonance for retrograde irregular satellites

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On the Secular Behavior of Irregular Satellites

Cited by 66 publications

References 39 publications

Application of the MEGNO technique to the dynamics of Jovian irregular satellites

Application of the MEGNO technique to the dynamics of Jovian irregular satellites

Tidal evolution of the Moon from a high-obliquity, high-angular-momentum Earth

Mapping theν⊙secular resonance for retrograde irregular satellites

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Mapping theν_⊙secular resonance for retrograde irregular satellites