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Saturn has a dynamically rich satellite system, which includes at least three orbital resonances between three pairs of moons: Mimas-Tethys 4:2, Enceladus-Dione 2:1, and Titan-Hyperion 4:3 mean-motion resonances. Studies of the orbital history of Saturn's moons usually assume that their past dynamics was also dominated solely by two-body resonances. Using direct numerical integrations, we find that three-body resonances among Saturnian satellites were quite common in the past, and could result in a relatively long-term, but finite capture time (10 Myr or longer). We find that these three-body resonances are invariably of the eccentricity type, and do not appear to affect the moons' inclinations. While some three-body resonances are located close to two-body resonances (but involve the orbital precession of the third body), others are isolated, with no two-body arguments being near resonance. We conclude that future studies of the system's past must take full account of three-body resonances, which have been overlooked in the past work., Comment: Accepted for ApJL

Some of the small inner moons of Uranus have very closely-spaced orbits. Multiple numerical studies have found that the moons Cressida and Desdemona, within the Portia sub-group, are likely to collide in less than 100 Myr. The subsequent discovery of three new moons (Cupid, Perdita, and Mab) made the system even more crowded. In particular, it has been suggested that the Belinda group (Cupid, Belinda, and Perdita) will become unstable in as little as 10$^5$ years. Here we revisit the issue of the stability of the inner moons of Uranus using updated orbital elements and considering tidal dissipation. We find that the Belinda group can be stable on $10^8$-year timescales due to an orbital resonance between Belinda and Perdita. We find that tidal evolution cannot form the Belinda-Perdita resonance, but convergent migration could contribute to the long-term instability of the Portia group. We propose that Belinda captured Perdita into the resonance during the last episode of disruption and re-accretion among the inner moons, possibly hundreds of Myr ago., Comment: 11 pages, 4 figures, accepted for AJ

The Moon is known to have a small liquid core, and it is thought that in the distant past the core may have produced strong magnetic fields recorded in lunar samples. Here we implement a numerical model of lunar orbital and rotational dynamics that includes the effects of a liquid core. In agreement with previous work, we find that the lunar core is dynamically decoupled from the lunar mantle, and that this decoupling happened very early in lunar history. Our model predicts that the lunar core rotates sub-synchronously, and the difference between the core and the mantle rotational rates was significant when the Moon had a high forced obliquity during and after the Cassini State transition. We find that the presence of the lunar liquid core further destabilizes synchronous rotation of the mantle for a wide range of semimajor axes centered around the Cassini State transition. CMB torques make it even more likely that the Moon experienced large-scale inclination damping during the Cassini State transition. We present estimates for the mutual core-mantle obliquity as a function of Earth-Moon distance, and we discuss plausible absolute time-lines for this evolution. We conclude that our results are consistent with the hypothesis of a precession-driven early lunar dynamo and may explain the variability of the inferred orientation of the past lunar dynamo., Accepted for JGR:Planets

The NASA Double Asteroid Redirection Test (DART) mission is a planetary defense-driven test of a kinetic impactor on Dimorphos, the satellite of the binary asteroid 65803 Didymos. DART will intercept Dimorphos at a relative speed of ${\sim}6.5 \text{ km s}^{-1}$, perturbing Dimorphos's orbital velocity and changing the binary orbital period. We present three independent methods (one analytic and two numerical) to investigate the post-impact attitude stability of Dimorphos as a function of its axial ratios, $a/b$ and $b/c$ ($a \ge b \ge c$), and the momentum transfer efficiency $\beta$. The first method uses a novel analytic approach in which we assume a circular orbit and a point-mass primary that identifies four fundamental frequencies of motion corresponding to the secondary's mean motion, libration, precession, and nutation frequencies. At resonance locations among these four frequencies, we find that attitude instabilities are possible. Using two independent numerical codes, we recover many of the resonances predicted by the analytic model and indeed show attitude instability. With one code, we use fast Lyapunov indicators to show that the secondary's attitude can evolve chaotically near the resonance locations. Then, using a high-fidelity numerical model, we find that Dimorphos enters a chaotic tumbling state near the resonance locations and is especially prone to unstable rotation about its long axis, which can be confirmed by ESA's Hera mission arriving at Didymos in late 2026. We also show that a fully coupled treatment of the spin and orbital evolution of both bodies is crucial to accurately model the long-term evolution of the secondary's spin state and libration amplitude. Finally, we discuss the implications of a post-impact tumbling or rolling state, including the possibility of terminating BYORP evolution if Dimorphos is no longer in synchronous rotation., Comment: 38 pages, 13 figures, Accepted for publication in Icarus

Most close-in planetary satellites are in synchronous rotation, which is usully the stable end-point of tidal despinning. Saturn's moon Hyperion is a notable exception by having a chaotic rotation. Hyperion's dynamical state is a consequence of its high eccentricity and its highly prolate shape (Wisdom et al. 1984). As many binary asteroids also have elongated secondaries, chaotic rotation is expected for moons in eccentric binaries (Cuk & Nesvorny 2010), and a minority of asteroidal secondaries may be in that state (Pravec et al. 2016). The question of the secondary's rotation is importrant for the action of the BYORP effect, which can quickly evolve orbits of synchrnous (but not non-synchronous) secondaries (Cuk & Burns 2005). Here we report preliminary numerical simulations which indicate that in binary systems with a large secondary and significant spin-orbit coupling a different kind of non-synchronous rotation may arise. In this "barrel instability" the secondary slowly rolls along its long axis, while the longest diameter is staying largelly aligned with the primary-secondary line. This behavior may be more difficult to detect through lightcurves than a fully chaotic rotation, but would likewise shut down BYORP. Unlike fully chaotic rotation, barrel instability can happen even at low eccentricties. In our presentation we will discuss our theoretical results and their implications for the evolution of binary asteroids, such as the Didymos-Dimorphos pair.

Climate change is a major impending threat to the future of humanity. According to the International Panel on Climate Change (IPCC), our emissions are estimated to have caused 0.8 deg C-1.2 deg C of anthropogenic global warming (AGW) above pre-industrial levels. AGW is likely to reach 1.5 degrees C between 2030 and 2052 if it continues to increase at the current rate. As the climate change is driven by the release of carbon dioxide and other greenhouse gases (GHG) into the atmosphere, there is a broad consensus that the mitigation of climate change requires transition to low GHG emission energy sources, technologies and practices. Implementing such changes systematically from individual to community-wide scales together with the resulting cultural changes and leadership towards environmental consciousness and responsibility are crucial to mitigate the looming damage of AGW. Given planetary scientists' wide recognition of the realities of climate change, and the need for us to maintain credibility by leading by example, it is appropriate to make own professional behavior more environmentally responsible. While scientists are few in numbers, and planetary scientists far fewer, high volumes of academic travel to conferences, panels, colloquia, and research collaboration visits together with extensive use of large, energetically demanding infrastructures make the "carbon footprint" of scientists much higher than that of an average citizen. This White Paper focuses on how modifying our activities, particularly associated with academic travel, can affect the carbon footprint of the planetary science community, and it makes recommendations on how the community and the funding agencies could best participate in the cultural change required to mitigate the damage that AGW will cause., Planetary Science and Astrobiology Decadal Survey 2023-2032 White Paper. Asking for endorsements

In the giant impact hypothesis for lunar origin, the Moon accreted from an equatorial circum-terrestrial disk; however the current lunar orbital inclination of 5 degrees requires a subsequent dynamical process that is still debated. In addition, the giant impact theory has been challenged by the Moon's unexpectedly Earth-like isotopic composition. 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 Earth-Moon system. Our tidal evolution model supports recent high-angular momentum giant impact scenarios to explain the Moon's isotopic composition and provides a new pathway to reach Earth's climatically favorable low obliquity., Preprint version of Nature vol. 539, pp-402-406 (2016)

We numerically explore the possibility that the large orbital inclination of the martian satellite Deimos originated in an orbital resonance with an ancient inner satellite of Mars more massive than Phobos. We find that Deimos's inclination can be reliably generated by outward evolution of a martian satellite that is about 20 times more massive than Phobos through the 3:1 mean-motion resonance with Deimos at 3.3 Mars radii. This outward migration, in the opposite direction from tidal evolution within the synchronous radius, requires interaction with a past massive ring of Mars. Our results therefore strongly support the cyclic martian ring-satellite hypothesis of Hesselbrock and Minton (2017). Our findings, combined with the model of Hesselbrock and Minton (2017), suggest that the age of the surface of Deimos is about 3.5-4 Gyr, and require Phobos to be significantly younger., Comment: Accepted for ApJL

Quantifying the energy budget of Earth in the first few million years following the Moon-forming giant impact is vital to understanding Earth's initial thermal state and the dynamics of lunar tidal evolution. After the impact, the body was substantially vaporized and rotating rapidly, very different from the planet we know today. The subsequent evolution of Earth's energy budget, as the body cooled and angular momentum was transferred during lunar tidal recession, has not been accurately calculated with all relevant energy components included. Here, we use giant impact simulations and planetary structure models to calculate the energy budget at stages in Earth's evolution. We show that the figure and internal structure of Earth changed substantially during its post-impact evolution and that changes in kinetic, potential, and internal energy were all significant. These changes have important implications for the dynamics of tidal recession and the thermal structure of early Earth., Comment: 23 pages, 13 figures. Accepted in Earth and Planetary Science Letters

Using numerical integrations, we find that the orbital eccentricity of Saturn's moon Iapetus undergoes prominent multi-Myr oscillations. We identify the responsible resonant argument to be $\varpi-\varpi_{g5}+\Omega-\Omega_{eq}$, with the terms being the longitudes of pericenter of Iapetus and planetary secular mode $g_5$, Iapetus's longitude of the node and Saturn's equinox. We find that this argument currently (on a $10^7$~yr timescale) appears to librate with a very large amplitude. On longer timescales, the behavior of this resonant angle is strongly dependent on the resonant interaction between Saturn's spin axis and the planetary mode $f_8$, with long-term secular resonance being possible if Saturn's equinox is librating relative to the node of the $f_8$ eigenmode. We present analytical estimates of the dependence of the resonant argument on the orbital elements of Iapetus. We find that this Iapetus-$g_5$ secular resonance could have been established only after the passage of Iapetus through the 5:1 mean-motion resonance with Titan, possibly in the last Gyr. Using numerical simulations, we show that the capture into the secular resonance appears to be a low-probability event. While the Iapetus-$g_5$ secular resonance can potentially help us put new constraints on the past dynamics of the Saturnian system, uncertainties in both the spin axis dynamics of Saturn and the tidal evolution rate of Titan make it impossible to make any firm conclusions about the resonance's longevity and origin., Comment: Accepted for MNRAS

The giant impact hypothesis remains the leading theory for lunar origin. However, current models struggle to explain the Moon's composition and isotopic similarity with Earth. Here we present a new lunar origin model. High-energy, high-angular momentum giant impacts can create a post-impact structure that exceeds the corotation limit (CoRoL), which defines the hottest thermal state and angular momentum possible for a corotating body. In a typical super-CoRoL body, traditional definitions of mantle, atmosphere and disk are not appropriate, and the body forms a new type of planetary structure, named a synestia. Using simulations of cooling synestias combined with dynamic, thermodynamic and geochemical calculations, we show that satellite formation from a synestia can produce the main features of our Moon. We find that cooling drives mixing of the structure, and condensation generates moonlets that orbit within the synestia, surrounded by tens of bars of bulk silicate Earth (BSE) vapor. The moonlets and growing moon are heated by the vapor until the first major element (Si) begins to vaporize and buffer the temperature. Moonlets equilibrate with BSE vapor at the temperature of silicate vaporization and the pressure of the structure, establishing the lunar isotopic composition and pattern of moderately volatile elements. Eventually, the cooling synestia recedes within the lunar orbit, terminating the main stage of lunar accretion. Our model shifts the paradigm for lunar origin from specifying a certain impact scenario to achieving a Moon-forming synestia. Giant impacts that produce potential Moon-forming synestias were common at the end of terrestrial planet formation., Accepted for publication in Journal of Geophysical Research: Planets. Main text: 44 pages, 24 figures. Supplement: 16 pages, 5 figures, 3 tables

Out of nine known stable Mars Trojans, seven appear to be members of an orbital grouping including the largest Trojan, Eureka. In order to test if this could be a genetic family, we simulated the long term evolution of a tight orbital cluster centered on Eureka. We explored two cases: cluster dispersal through planetary gravity alone over 1 Gyr, and a 1 Gyr evolution due to both gravity and the Yarkovsky effect. We find that the dispersal of the cluster in eccentricity is primarily due to dynamical chaos, while the inclinations and libration amplitudes are primarily changed by the Yarkovsky effect. Current distribution of the cluster members orbits are indicative of an initially tight orbital grouping that was affected by a negative acceleration (i.e. one against the orbital motion) consistent with the thermal Yarkovsky effect. We conclude that the cluster is a genetic family formed either in a collision or through multiple rotational fissions. The cluster's age is on the order of 1 Gyr, and its long-term orbital evolution is likely dominated by the seasonal, rather than diurnal, Yarkovsky effect. If confirmed, Gyr-scale dominance of the seasonal Yarkovsky effect may indicate suppression of the diurnal Yarkovsky drift by the related YORP effect. Further study of Mars Trojans is essential for understanding the long-term orbital and rotational dynamics of small bodies in the absence of frequent collisions., Submitted to Icarus

The Hungaria asteroid group is located interior to the main asteroid belt, with semimajor axes between 1.8 and 2 AU, low eccentricities and inclinations of 16-35 degrees. Recently, it has been proposed that Hungaria asteroids are a secularly declining population that may be related to the Late Heavy Bombardment (LHB) impactors (\'Cuk et al. 2012, Bottke et al. 2012). While \'Cuk et al. (2012) and Bottke et al. (2012) have reproduced a Hungaria-like population that declined exponentially, the real Hungarias were never confirmed to be unstable to the same degree. Here we find that the stability of Hungarias is strongly dependent on the evolution of the eccentricity of Mars, which is chaotic and unpredictable on Gyr timescales. We find that the high Martian eccentricity chiefly affects Hungarias through close approaches with Mars, rather than planetary secular modes. However, current minimum perihelia of Hungarias (over Myr timescales) are not diagnostic of their long-term stability due to a number of secular and mean motion resonances affecting the Hungaria region (Milani et al. 2010). We conclude that planetary chaos makes it impossible to determine the effective lifetimes of observed Hungarias. Furthermore, long-term changes of Martian eccentricity could lead to variable Hungaria loss over time. We speculate that some of the most stable Hungarias may have been placed in their present orbit when the eccentricity of Mars was significantly higher than today., Comment: Accepted for Icarus special issue on asteroids

The Hungaria asteroids are interior to the main asteroid belt, with semimajor axes between 1.8 and 2 AU, low eccentricities and inclinations of 16-35 degrees. Small asteroids in the Hungaria region are dominated by a collisional family associated with (434) Hungaria. The dominant spectral type of the Hungaria group is the E or X-type (Warner et al, 2009), mostly due to the E-type composition of Hungaria and its genetic family. It is widely believed the E-type asteroids are related to the aubrite meteorites, also known as enstatite achondrites (Gaffey et al, 1992). Here we explore the hypothesis that aubrites originate in the Hungaria family. In order to test this connection, we compare model Cosmic Ray Exposure ages from orbital integrations of model meteoroids with those of aubrites. We show that long CRE ages of aubrites (longest among stony meteorite groups) reflect the delivery route of meteoroids from Hungarias to Earth being different than those from main-belt asteroids. We find that the meteoroids from Hungarias predominantly reach Earth by Yarkovsky-drifting across the orbit of Mars, with no assistance from orbital resonances. We conclude that the CRE ages of aubrites are fully consistent with a dominant source at the inner boundary of the Hungaria family at 1.7 AU. From here, meteoroids reach Earth through the Mars-crossing region, with relatively quick delivery times favored due to collisions (with Hungarias and the inner main-belt objects). We find that, after Vesta, (434) Hungaria is the best candidate for an asteroidal source of an achondrite group., Comment: Accepted for Icarus

1I/`Oumuamua is the first known interstellar small body, probably being only about 100~m in size. Against expectations based on comets, `Oumuamua does not show any activity and has a very elongated figure, and also exhibits undamped rotational tumbling. In contrast, `Oumuamua's trajectory indicates that it was moving with the local stars, as expected from a low-velocity ejection from a relatively nearby system. Here I assume that `Oumuamua is typical of 100-m interstellar objects, and speculate on its origins. I find that giant planets are relatively inefficient at ejecting small bodies from inner solar systems of main-sequence stars, and that binary systems offer a much better opportunity for ejections of non-volatile bodies. I also conclude that `Oumuamua is not a member of a collisional population, which could explain its dramatic difference from small asteroids. I observe that 100-m small bodies are expected to carry little mass in realistic collisional populations, and that occasional events when whole planets are disrupted in catastrophic encounters may dominate interstellar population of 100-m fragments. Unlike the Sun or Jupiter, red dwarf stars are very dense and are capable of thoroughly tidally disrupting terrestrial planets. I conclude that the origin of `Oumuamua as a fragment from a planet that was tidally disrupted and then ejected by a dense member of a binary system could explain its peculiarities., Comment: Revised for ApJL

Unlike Trojans, horseshoe coorbitals are not generally considered to be long-term stable (Dermott and Murray, 1981; Murray and Dermott, 1999). As the lifetime of Earth's and Venus's horseshoe coorbitals is expected to be about a Gyr, we investigated the possible contribution of late-escaping inner planet coorbitals to the lunar Late Heavy Bombardment. Contrary to analytical estimates, we do not find many horseshoe objects escaping after first 100 Myr. In order to understand this behaviour, we ran a second set of simulations featuring idealized planets on circular orbits with a range of masses. We find that horseshoe coorbitals are generally long lived (and potentially stable) for systems with primary-to-secondary mass ratios larger than about 1200. This is consistent with results of Laughlin and Chambers (2002) for equal-mass pairs or coorbital planets and the instability of Jupiter's horseshoe companions (Stacey and Connors, 2008). Horseshoe orbits at smaller mass ratios are unstable because they must approach within 5 Hill radii of the secondary. In contrast, tadpole orbits are more robust and can remain stable even when approaching within 4 Hill radii of the secondary.

The Hungarias are a stable asteroid group orbiting between Mars and the main asteroid belt, with high inclinations (16–30), low eccentricities (e < 0.18), and a narrow range of semi-major axes (1.78– 2.06 AU). In order to explore the significance of thermally-induced Yarkovsky drift on the population, we conducted three orbital simulations of a 1000-particle grid in Hungaria a–e–i space. The three simulations included asteroid radii of 0.2, 1.0, and 5.0 km, respectively, with run times of 200 Myr. The results show that mean motion resonances—martian ones in particular—play a significant role in the destabilization of asteroids in the region. We conclude that either the initial Hungaria population was enormous, or, more likely, Hungarias must be replenished through collisional or dynamical means. To test the latter possibility, we conducted three more simulations of the same radii, this time in nearby Mars-crossing space. We find that certain Mars crossers can be trapped in martian resonances, and by a combination of chaotic diffusion and the Yarkovsky effect, can be stabilized by them. Therefore, some Hungarias (around 5% of non-family members with absolute magnitudes H < 15.5 and 10% for H < 17) may represent previously transient Mars crossers that have been adopted in this manner.

We calculate the current spatial distribution of projectile delivery to the Earth and Moon using numerical orbital dynamics simulations of candidate impactors drawn from a debiased Near-Earth Object (NEO) model. We examine the latitude distribution of impactor sites and find that for both the Earth and Moon there is a small deficiency of time-averaged impact rates at the poles. The ratio between deliveries within 30° of the pole to that of a 30° band centered on the equator is small for Earth ( 0.958 ± 0.001 ) and somewhat greater for the Moon (∼10%) ( 0.903 ± 0.005 ). The terrestrial arrival results are examined to determine the degree of AM/PM asymmetry to compare with the PM excess shown in meteorite fall times. We find that the average lunar impact velocity is 20 km/s, which has ramifications in converting observed crater densities to impactor size distributions. We determine that current crater production on the leading hemisphere of the Moon is 1.28 ± 0.01 that of the trailing when considering the ratio of craters within 30° of the apex to those within 30° of the antapex and that there is virtually no nearside–farside asymmetry, in agreement with observations of rayed craters. As expected, the degree of leading–trailing asymmetry increases when the Moon's orbital distance is decreased.

Multiple large impact basins on the lunar nearside formed in a relatively-short interval around 3.8–3.9 Gyr ago, in what is known as the Lunar Cataclysm (LC; also known as Late Heavy Bombardment). It is widely thought that this impact bombardment has affected the whole Solar System or at least all the inner planets. But with non-lunar evidence for the cataclysm being relatively weak, a geocentric cause of the Lunar Cataclysm cannot yet be completely ruled out [Ryder, G., 1990. Eos 71, 313, 322–323]. In principle, late destabilization of an additional Earth satellite could result in its tidal disruption during a close lunar encounter (cf. [Asphaug, E., Agnor, C.B., Williams, Q., 2006. Nature 439, 155–160] ). If the lost satellite had D > 500 km , the resulting debris can form multiple impact basins in a relatively short time, possibly explaining the LC. Canup et al. [Canup, R.M., Levison, H.F., Stewart, G.R., 1999. Astron. J. 117, 603–620] have shown that any additional satellites of Earth formed together with (and external to) the Moon would be unable to survive the rapid initial tidally-driven expansion of lunar orbit. Here we explore the fate of objects trapped in the lunar Trojan points, and find that small lunar Trojans can survive the Moon's orbital evolution until they and the Moon reach 38 Earth radii, at which point they are destabilized by a strong solar resonance. However, the dynamics of Trojans containing enough mass to cause the LC (diameters >150 km) is more complex; we find that such objects do not survive the passage through a weaker solar resonance at 27 Earth radii. This distance was very likely reached by the Moon long before the LC, which seems to rule out the disruption of lunar Trojans as a cause of the LC.

We explore the past evolution of Saturn's moons using direct numerical integrations. We find that the past Tethys-Dione 3:2 orbital resonance predicted in standard models likely did not occur, implying that the system is less evolved than previously thought. On the other hand, the orbital inclinations of Tethys, Dione and Rhea suggest that the system did cross the Dione-Rhea 5:3 resonance, which is closely followed by a Tethys-Dione secular resonance. A clear implication is that either the moons are significantly younger than the planet, or that their tidal evolution must be extremely slow (Q > 80,000). As an extremely slow-evolving system is incompatible with intense tidal heating of Enceladus, we conclude that the moons interior to Titan are not primordial, and we present a plausible scenario for the system's recent formation. We propose that the mid-sized moons re-accreted from a disk about 100 Myr ago, during which time Titan acquired its significant orbital eccentricity. We speculate that this disk has formed through orbital instability and massive collisions involving the previous generation of Saturn's mid-sized moons. We identify the solar evection resonance perturbing a pair of mid-sized moons as the most likely trigger of such an instability. This scenario implies that most craters on the moons interior to Titan must have been formed by planetocentric impactors., To appear in The Astrophysical Journal on March 24, 2016

Our understanding of binary asteroids is currently undergoing major revisions. Until recently, all known small binaries (primary diameters 1 km) were near-Earth asteroids (NEAs), making it plausible that they originate in close encounters with terrestrial planets, and were not to be found among the main belt asteroids (MBAs). First simulations of tidal disruption have produced incidence of binaries that roughly matched the observed fraction of binary NEAs. Thermal-radiation effects, most notably YORP (Yarkovsky-O'Keefe-Radzievskii-Paddack), were not needed to explain the life cycle of binary asteroids, despite some theoretical arguments in favor of significant YORP evolution. Recent discovery of abundant small MBA binaries and a more self-consistent reassessment of effects of planetary encounters have put the primacy of planetary encounters in doubt and shown a need for new theoretical explanations. Here I show that the mass loss from the primary's surface due to YORP could explain the formation of kilometer-sized binary NEAs. I also suggest that the small-separation NEA binaries' observed properties are consistent with evolution through "binary YORP," rather than tidal stripping during planetary passages (when the pairs evolve beyond ~10 primary radii, encounters become important). Such a life cycle implies not only the extreme youth of small binary asteroids (

The passage of Jupiter and Saturn through mutual 1:2 mean-motion resonance has recently been put forward as explanation for their relatively high eccentricities [Tsiganis, K., Gomes, R., Morbidelli, A., Levison, H.F., 2005. Nature 435, 459–461] and the origin of Jupiter's Trojans [Morbidelli, A., Levison, H.F., Tsiganis, K., Gomes, R., 2005. Nature 435, 462–465]. Additional constraints on this event based on other small-body populations would be highly desirable. Since some outer satellite orbits are known to be strongly affected by the near-resonance of Jupiter and Saturn (“the Great Inequality”; Cuk, M., Burns, J.A., 2004b. Astron. J. 128, 2518–2541), the irregular satellites are natural candidates for such a connection. In order to explore this scenario, we have integrated 9200 test particles around both Jupiter and Saturn while they went through a resonance-crossing event similar to that described by Tsiganis et al. [Tsiganis, K., Gomes, R., Morbidelli, A., Levison, H.F., 2005. Nature 435, 459–461]. The test particles were positioned on a grid in semimajor axes and inclinations, while their initial pericenters were put at just 0.01 AU from their parent planets. The goal of the experiment was to find out if short-lived bodies, spiraling into the planet due to gas drag (or alternatively on orbits crossing those of the regular satellites), could have their pericenters raised by the resonant perturbations. We found that about 3% of the particles had their pericenters raised above 0.03 AU (i.e. beyond Iapetus) at Saturn, but the same happened for only 0.1% of the particles at Jupiter. The distribution of surviving particles at Saturn has strong similarities to that of the known irregular satellites. If saturnian irregular satellites had their origin during the 1:2 resonance crossing, they present an excellent probe into the early Solar System's evolution. We also explore the applicability of this mechanism for Uranus, and find that only some of the uranian irregular satellites have orbits consistent with resonant pericenter lifting. In particular, the more distant and eccentric satellites like Sycorax could be stabilized by this process, while closer-in moons with lower eccentricity orbits like Caliban probably did not evolve by this process alone.

The Yarkovsky force, produced when thermal radiation is re-emitted asymmetrically, causes significant orbital evolution of asteroids in the 10 m–10 km size range. When acting on a non-spherical body, the momentum carried by this radiation generally produces a torque, called the YORP effect, which may be important in re-orienting asteroidal spins. Here we explore a related effect, the “binary YORP” (BYORP), that can modify the orbit of a synchronously rotating secondary in a binary system. It arises because a locked secondary is effectively an asymmetric appendage of the primary. It should be particularly important for Near-Earth Asteroids (NEAs) owing to their small sizes, proximity to the Sun, and benign collisional environment. To estimate BYORP's strength, we subjected 100 random Gaussian spheroids to the thermal radiation model of Rubincam (2000, Radiative spin-up and spin-down of small asteroids, Icarus, 148, 2–11). For most shapes, a significant torque arose on the secondary's orbit, typically modifying the orbit's size, eccentricity and inclination in less than 10 5 years, for components of 1 and 0.3 km radii, separated by 2 km, at 1 AU, each of density 1750 kg m −3 . Together YORP and BYORP are capable of synchronizing secondaries and circularizing orbits, making tidal dissipation unnecessary to explain the evolved state of observed NEA pairs. However, BYORP's rapid timescale poses a problem for the abundance of observed NEA binaries, since their formation rate is thought to be much slower. We consider and reject the following resolutions of this quandary: (i) the approximation using Gaussian spheroids inadequately models YORP; (ii) most secondaries are not synchronous, but inhabit other spin-orbit resonances (very unlikely); (iii) tidal dissipation is much more efficient than previously estimated, and thus capable of stabilizing observed systems; and (iv) moderately close encounters with planets can re-orient secondaries, turning BYORP into a slower, random-walk process. Finally, we speculate that most observed binary NEAs are in a stable state in which the obliquity-changing torques of YORP (acting on the primary) and BYORP cancel out, and that those systems must be close to 55° inclination, where the momentum-changing torques of both YORP and BYORP tend to be very small. Some retrograde systems might develop such that the nodes precess at a Sun-synchronous rate, while some prograde ones might move into the “evection” resonance. All three of these hypotheses can be tested directly by comparison with the i , Ω and ϖ observed for NEA binaries.

2003 VB $_{12}$ (Sedna) is as much distinguished by its considerable size as by its extremely unusual orbit, which has perihelion at about $q=76$ AU with semi-major axis $a=533$ AU (Brown et al . 2004, JPL Horizons). Thus it is effectively decoupled from both Neptune and the Galactic tide (Fernandez 1997). Brown et al . (2004) and Morbidelli & Levison (2004) maintain that only scattering by a so-far-unobserved “Planet X” or by an errant star could produce such a high-perihelion orbit for a scattered-disk KBO. While a close encounter is plausible, given the Sun's likely birth in an open cluster, such an interaction would profoundly disturb the Oort cloud and would require fundamental revision to the present theories of its formation. Although the planets cannot significantly affect VB $_{12}$ 's orbit through close approaches, resonant perturbations could conceivably produce secular effects on it. To explore this possibility, we have numerically integrated test particles with $480 AU and a fixed $q=76$ AU. Including the four giant planets, but ignoring the Kuiper Belt and the inner Oort Cloud, as well as the Galactic tide, we find multiple resonances, some of which perturb significantly the test particles' eccentricity more strongly than the leading secular terms. We identify these resonances as variants of the very high-order ( $n_N > 60 \n$ ) mean-motion commensurabilities between Neptune and VB $_{12}$ . Although unprecedented, these extremely high-order resonances can be significant due to VB $_{12}$ 's very high eccentricity ( $e=0.86$ ). Even powers of eccentricity beyond sixty are still on the order of $10^{-4}$ , which is comparable to the strength of low-order resonances involving near-circular orbits. We extrapolate the possible long-term drift rate and estimate the likelihood of such resonances producing an “inner Oort cloud” population consistent with VB $_{12}$ over the age of the Solar System. Finally we discuss how planetary migration and the Kuiper-Belt's depletion might have affected VB $_{12}$ 's putative resonance. To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

To elucidate the capture of Jupiter's outer moons, we reverse-evolve satellites from their present orbits to their original heliocentric paths in the presence of Jupiter's primordial circumplanetary disk (Lubow et al., 1999, Astrophys. J. 526, 1001–1012; Canup and Ward, 2003, Astron. J. 124, 3404–3423). Our orbital histories use a symplectic integrator that allows dissipation. We assume that the present satellites Himalia, Elara, Lysithea, Leda, and S/2000 J11 are collisional fragments of a single parent. Our simulations show that this “prograde-cluster progenitor” (PCP) could be derived from objects with heliocentric orbits like those of the Hilda asteroid group. We show analytically that this capture is energetically possible. We also compare the spectroscopic characteristics of the prograde cluster members (Grav et al., 2003, Icarus, submitted for publication) with those of the Hildas, and conclude that the surface color of the prograde-cluster progenitor is consistent with an origin within the Hilda group. Accordingly, gas drag in the primordial jovian nebula is found to offer a plausible explanation for the origin of the prograde cluster. A similar capture mechanism is proposed for Saturn's Phoebe.

The dwarf planet Haumea has two large satellites, Namaka and Hi'iaka, which orbit at relatively large separations. Both moons have significant eccentricities and inclinations, in a pattern that is consistent with a past orbital resonance (Ragozzine and Brown, 2009). Based on our analysis, we find that the present system is not consistent with satellite formation close to the primary and tidal evolution though mean-motion resonances. We propose that Namaka experienced only limited tidal evolution, leading to the mutual 8:3 mean-motion resonance which redistributed eccentricities and inclinations between the moons. This scenario requires that the original orbit of Hi'iaka was mildly eccentric; we propose that this eccentricity was either primordial or acquired though encounters with other TNOs. Both dynamical stability and our preferred tidal evolution model imply that the moons' masses are only about one half of previously estimated values, suggesting high albedos and low densities. As the present orbits of the moons strongly suggest formation from a flat disk close to their present locations, we conclude that Hi'iaka and Namaka may be second-generation moons, formed after the breakup of a past large moon, previously proposed as the parent body of the Haumea family (Schlichting and Sari, 2009). We derive plausible parameters of that moon, consistent with the current models of Haumea's formation (Leinhardt et al, 2010). An interesting implication of this hypothesis is that Hi'iaka and Namaka may orbit retrograde with respect to Haumea's spin. Retrograde orbits of Haumea's moons would be in full agreement with available observations and our dynamical analysis, and could provide a unique confirmation the "disrupted satellite" scenario for the origin of the family., Comment: Accepted for The Astronomical Journal

The origin of the Moon's nonnegligible orbital eccentricity of 0.053 has no theoretical explanation. Lunar laser ranging indicates that tides on Earth are currently increasing the Moon's eccentricity. However, ocean tides were likely much weaker during the first billion years, allowing lunar tides to damp any primordial lunar eccentricity very early on. During the tidally driven expansion of its orbit, the Moon must have been affected by two substantial resonances related to Jupiter and Venus, passage through which may have generated today's lunar eccentricity.

We present simulations of Triton's post-capture orbit that confirm the importance of Kozai-type oscillations in its orbital elements. In the context of the tidal orbital evolution model, these variations require average pericenter distances much higher than previously published, and the timescale for the tidal orbital evolution of Triton becomes longer than the age of the Solar System. Recently-discovered irregular satellites present a new constraint on Triton's orbital history. Our numerical integrations of test particles indicate a timescale for Triton's orbital evolution to be less than $10^5$ yrs for a reasonable number of distant satellites to survive Triton's passage. This timescale is inconsistent with the exclusively tidal evolution (time scale of $>10^8$ yrs), but consistent with the interestion with the debris from satellite-satellite collisions. Any major regular satellites will quickly collide among themselves after being perturbed by Triton, and the resulting debris disk would eventually be swept up by Triton; given that the total mass of the Uranian satellite system is 40% of that of Triton, large scale evolution is possible. This scenario could have followed either collisional or the recently-discussed three-body-interaction-based capture., 10 pages, 4 figures, accepted for ApJL

Among the many new irregular satellites that have been discovered in the last five years, at least six are in the so-called Kozai resonance. Due to solar perturbations, the argument of pericenter of a satellite usually precesses from 0 to 360 degrees. However, at inclinations higher than 39.3 degrees and lower than 140.7 degrees a new kind of behavior occurs for which the argument of pericenter oscillates around +/-90 degrees. In this work we will concentrate on the orbital history of the saturnian satellite S/2000 S5 Kiviuq, one of the satellites currently known to be in such resonance Kiviuq's orbit is very close to the separatrix of the Kozai resonance. Due to perturbations from the other jovian planets, it is expected that orbits near the Kozai separatrix may show significant chaotic behavior. This is important because chaotic diffusion may transfer orbits from libration to circulation, and vice versa. To identify chaotic orbits we used two well-known methods: the Frequency Analysis Method (Laskar 1990) and Maximum Lyapunov Exponents (Benettin et al. 1980). Our results show that the Kozai resonance is crossed by a web of secondary resonances, whose arguments involve combinations of the argument of pericenter, the argument of the Great Inequality, longitude of the node, and other terms related to the secular frequencies g5, g6, and s6. Many test orbits whose precession period is close to the period of the Great Inequality (883 yrs), or some of its harmonics, are trapped by these secondary resonances, and show significant chaotic behavior. Planetary migration, by moving the locations of these secondary resonances, may have depleted an original population of Kozai resonators., Comment: 47 pages, 18 figures, submitted to the Astronomical Journal

Although analytical studies on the secular motion of the irregular satellites have been published recently, these theories have not yet been satisfactorily reconciled with the results of direct numerical integrations. These discrepancies occur because in secular theories the disturbing function is averaged over orbital motions, whereas instead one should take into account some large periodic terms, most notably the so-called ``evection''. We demonstrate that such terms can be incorporated into the Kozai formalism, and that our synthetic approach produces much better agreement with results from symplectic integrations. Using this method, we plot the locations of secular resonances in the orbital-element space, and we note that the distribution of irregular satellite clusters appears to be non-random. We find that the large majority of irregular-satellite groups cluster close to the secular resonances, with several objects having practically stationary pericenters. None of the largest satellites belong to this class, so we argue that this dichotomy implies that the smaller near-resonant satellites might have been captured differently than the largest irregulars., Comment: 56 pages, 24 figures, accepted for publication in The Astronomical Journal

Mercury's spin and its orbit around the Sun are tied to each other in a unique arrangement. According to a set of calculations, random asteroid impacts may have aided the planet's evolution into the current spin-orbit pattern.

Asteroids with satellites are natural laboratories to constrain the formation and evolution of our solar system. The binary Trojan asteroid (624) Hektor is the only known Trojan asteroid to possess a small satellite. Based on W.M. Keck adaptive optics observations, we found a unique and stable orbital solution, which is uncommon in comparison to the orbits of other large multiple asteroid systems studied so far. From lightcurve observations recorded since 1957, we showed that because the large Req=125-km primary may be made of two joint lobes, the moon could be ejecta of the low-velocity encounter, which formed the system. The inferred density of Hektor's system is comparable to the L5 Trojan doublet (617) Patroclus but due to their difference in physical properties and in reflectance spectra, both captured Trojan asteroids could have a different composition and origin., 13 pages, 3 figures, 2 tables