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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

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 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 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., Comment: Accepted for the Planetary Science Journal

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

We numerically simulate the past tidal evolution of the five large moons of Uranus (Miranda, Ariel, Umbriel, Titania, and Oberon). We find that the most recent major mean-motion resonance (MMR) between any two moons, the Ariel-Umbriel 5:3 MMR, had a large effect on the whole system. Our results suggest that this resonance is responsible for the current 4.3$^{\circ}$ inclination of Miranda (instead of previously proposed 3:1 Miranda-Umbriel MMR), and that all five moons had their inclinations excited during this resonance. Miranda experienced significant tidal heating during the Ariel-Umbriel 5:3 MMR due to its eccentricity being excited by Ariel's secular perturbations. This tidal heating draws energy from shrinking of Miranda's orbit, rather than Ariel's outward evolution, and can generate heat flows in excess of 100 mW m$^{-2}$, sufficient to produce young coronae on Miranda. We find that this MMR was followed by a sequence of secular resonances, which reshuffled the moons' eccentricities and inclinations. We also find that the precession of Oberon's spin axis is close to a resonance with the precession of Umbriel's orbital plane, and that this spin-orbit resonance was likely excited during the Ariel-Umbriel 5:3 MMR. After the exit from the MMR, subsequent Ariel-Umbriel secular resonance and Oberon-Umbriel spin-orbit resonance may be able to explain the current low inclinations of Ariel and Umbriel. The age of Miranda's surface features tentatively suggests Uranian tidal $Q=15,000-20,000$, which can be further refined in future work., Accepted for Planetary Science Journal

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

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.

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.

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

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