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Register a new userModeling the evection resonance for trojan satellites: application to the Saturn system
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Added by
Cristian Andr\\'es Giuppone
Publication date
2018
fields
Physics
and research's language is
English
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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.
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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.
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 present thermal model fits for 11 Jovian and 3 Saturnian irregular satellites based on measurements from the WISE/NEOWISE dataset. Our fits confirm spacecraft-measured diameters for the objects with in situ observations (Himalia and Phoebe) and provide diameters and albedo for 12 previously unmeasured objects, 10 Jovian and 2 Saturnian irregular satellites. The best-fit thermal model beaming parameters are comparable to what is observed for other small bodies in the outer Solar System, while the visible, W1, and W2 albedos trace the taxonomic classifications previously established in the literature. Reflectance properties for the irregular satellites measured are similar to the Jovian Trojan and Hilda Populations, implying common origins.
Constructing dynamical maps from the filtered output of numerical integrations, we analyze the structure of the $ u_odot$ secular resonance for fictitious irregular satellites in retrograde orbits. This commensurability is associated to the secular angle $theta = varpi - varpi_odot$, where $varpi$ is the longitude of pericenter of the satellite and $varpi_odot$ 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 $theta$ around zero (as found for Sinope and Pasiphae) or 180 degrees, 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 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 to estimate the resonant structure around any giant planet from the results calculated around a single primary mass.
The one-meter telescope-reflector `Saturn (D=1 m, F = 4 m) was partially renovated at the Pulkovo observatory at the end of 2014. The telescope was equipped by CCD camera S2C with 14x14 arcmin field of view and 824 mas per pix scale. The observations of outer Jovian satellites have been performed in a test mode since January 2015. The exposure time of 30 seconds allows us to obtain images of stars up to magnitude 19.5 with the present state of the mirror and the equipment. The observations of outer Jovian satellites have been performed during testing period. These objects are interesting targets because their astrometric observations required to improve ephemeris and dynamic studies. Satellites positions have been determined on the basis of CCD images obtained within 6 nights. Astrometric reduction is performed by linear method using HCRF/UCAC4 and HCRF/URAT1. Internal accuracy of satellites positions has been estimated as 20 - 100 mas. The absolute values of residuals O-C do not exceed 100 mas in most cases. The independent tests have been carried out by the direct comparison with the results of observations of the Jovian satellite Himalia performed simultaneously by the Normal astrograph (the largest difference was 113 mas). This work has been partially supported by RFBR (12-02-00675-a) and the 22 Program of RAS Praesidium.
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