Tidal evolution of Mimas, Enceladus, and Dione

The tidal evolution through several resonances involving Mimas, Enceladus, and/or Dione is studied numerically with an averaged resonance model. We find that, in the Enceladus-Dione 2:1 e-Enceladus type resonance, Enceladus evolves chaotically in the future for some values of k₂/Q. Past evolution of the system is marked by temporary capture into the Enceladus-Dione 4:2 ee^′-mixed resonance. We find that the free libration of the Enceladus-Dione 2:1 e-Enceladus resonance angle of 1.5° can be explained by a recent passage of the system through a secondary resonance. In simulations with passage through the secondary resonance, the system enters the current Enceladus-Dione resonance close to tidal equilibrium and thus the equilibrium value of tidal heating of 1.1(18,000/QS) GW applies. We find that the current anomalously large eccentricity of Mimas can be explained by passage through several past resonances. In all cases, escape from the resonance occurs by unstable growth of the libration angle, sometimes with the help of a secondary resonance. Explanation of the current eccentricity of Mimas by evolution through these resonances implies that the Q of Saturn is below 100,000. Though the eccentricity of Enceladus can be excited to moderate values by capture in the Mimas-Enceladus 3:2 e-Enceladus resonance, the libration amplitude damps and the system does not escape. Thus past occupancy of this resonance and consequent tidal heating of Enceladus is excluded. The construction of a coherent history places constraints on the allowed values of k₂/Q for the satellites.     

Tidal heating in Enceladus

The heating in Enceladus in an equilibrium resonant configuration with other saturnian satellites can be estimated independently of the physical properties of Enceladus. We find that equilibrium tidal heating cannot account for the heat that is observed to be coming from Enceladus. Equilibrium heating in possible past resonances likewise cannot explain prior resurfacing events.     

Episodic volcanism on Enceladus: Application of the Ojakangas-Stevenson model

The main equations in the paper “Episodic volcanism of tidally heated satellites with application to Io” by Ojakangas and Stevenson [Icarus 66, 341-358] are presented; numerical integration of these equations confirms the results of Ojakangas and Stevenson [Icarus 66, 341-358] for Io. Application to Enceladus is considered. It is shown that Enceladus does not oscillate about the tidal equilibrium in this model by both new nonlinear stability analysis and numerical integration of the model equations.     

Thermal inertia and bolometric Bond albedo values for Mimas, Enceladus, Tethys, Dione, Rhea and Iapetus as derived from Cassini/CIRS measurements

Spectra taken by Cassini’s Composite Infrared Spectrometer (CIRS) between 10 and 600 cm⁻¹ (17-1000 μm) of surface thermal emission of Mimas, Enceladus, Tethys, Dione, Rhea and Iapetus have been used to derive the thermal inertia and bolometric Bond albedo values. Only an upper limit for the bolometric Bond albedo of Iapetus’ dark leading side could be determined due to the insensitivity of the thermal model to albedo when albedos are very low. The thermal inertia in this region however is better constrained. The CIRS coverage of Enceladus is extensive enough that the latitudinal variation in these values from 60°S to 70°N has been determined in 10° wide bins. The bolometric Bond albedos determined here are consistent with literature values which show the surface of the saturnian icy moons to be covered in ice contaminated to varying degrees. The thermal inertia of the moons is shown to be in the range 9-, approximately 2-6 times lower than that of the Galilean satellites, implying a less well consolidated and more porous surface. The thermal inertias of Iapetus and Phoebe are somewhat higher, suggesting that the very low thermal inertias of satellites from Rhea inwards may be related to their probable coating of E-ring material. Latitudinal variations on the surface of Enceladus show that the bolometric Bond albedo and thermal inertia increase towards the active plume source at the south pole.     

Tidal dynamical considerations constrain the state of an ocean on Enceladus

In previous work, solutions to the non-dissipative Laplace Tidal Equations (LTE) were used to provide bounds on the heat generated by the response of a subsurface ocean on Enceladus to an obliquity component of tidal forces. Here we improve these bounds using solutions from the LTE with a generic dissipation term explicitly added. We find solutions for a wider range of ocean tidal responses that include both unstratified (barotropic) and stratified (baroclinic) flow responses to obliquity as well as eccentricity components of the tidal forces. We consolidate the results in three ocean tidal scenarios on Enceladus that can explain the high heat fluxes (∼7 mW/m² globally averaged) inferred from measurements by the Cassini spacecraft: (1) a deep (1-50 km) barotropic ocean responding to obliquity tidal forces, where obliquity is at least 0.1°; (2) a shallow (∼360 m) barotropic ocean responding to eccentricity tidal forces; (3) a stratified (baroclinic) ocean responding to eccentricity tidal forces where the density-weighted “equivalent depth” (typically much smaller than the ocean’s physical depth) is near 360 m. The ocean is assumed to be global, but extensions for a semi-global case are also described. A more general result which is independent of the specific scenarios proposed is that an ocean attempting to freeze (with an associated decrease in its liquid depth, which affects the ocean’s dynamical response to the tidal forcing) must first pass through resonant configurations with a greatly increased generation of ocean tidal heat (exceeding 1 W/m² to 1 kW/m²) that would act to halt further freezing and stagnate the ocean state in this configuration so long as there is still orbital energy to provide the tidal forces. With an additional assumption that the ocean has evolved from a more energetic state where the depth of the liquid ocean was greater, we obtain the three scenarios proposed.     

Obliquity tides do not significantly heat Enceladus

Recently, Tyler [Tyler, R.H., 2009. Geophys. Res. Lett. 36, L15205; Tyler, R., 2011. Icarus, 211, 770-779] proposed that the tide due to an obliquity of greater than 0.1° might drive resonant flow in a liquid ocean at Enceladus, and that dissipation of the ocean’s kinetic energy may be an alternate source for the observed global heat flux. While there is currently no measurement of Enceladus’ obliquity, dissipation is expected to drive the spin pole to a Cassini state. Under this assumption, we find that Enceladus should occupy Cassini state 1 and that the obliquity of Enceladus should be less than 0.0015° for values of the degree-2 gravity coefficient C_2,2 between 1.0 × 10⁻³ and 2.5 × 10⁻³. Unless there is a significant free obliquity or the gravity coefficient C_2,2 has been significantly overestimated, it is unlikely that obliquity-driven flow in a subsurface ocean is the source of the extreme heat on Enceladus.     

Dynamics of Enceladus and Dione inside the 2:1 mean-motion resonance under tidal dissipation

In a previous work (Callegari and Yokoyama, Celest. Mech. Dyn. Astr. 98:5–30, 2007), the main features of the motion of the pair Enceladus–Dione were analyzed in the frozen regime, i.e., without considering the tidal evolution. Here, the results of a great deal of numerical simulations of a pair of satellites similar to Enceladus and Dione crossing the 2:1 mean-motion resonance are shown. The resonance crossing is modeled with a linear tidal theory, considering a two-degrees-of-freedom model written in the framework of the general three-body planar problem. The main regimes of motion of the system during the passage through resonance are studied in detail. We discuss our results comparing them with classical scenarios of tidal evolution of the system. We show new scenarios of evolution of the Enceladus–Dione system through resonance not shown in previous approaches of the problem.     

Arecibo radar observations of Rhea, Dione, Tethys, and Enceladus

We have measured the bulk radar reflectance properties of the mid-size saturnian satellites Rhea, Dione, Tethys, and Enceladus with the Arecibo Observatory's 13 cm wavelength radar system during the 2004 through 2007 oppositions of the Saturn system. Comparing to the better studied icy Galilean satellites, we find that the total reflectivities of Rhea and Tethys are most similar to Ganymede while Dione is most similar to Callisto. Enceladus' reflectivity falls between those of Ganymede and Europa. The mean circular polarization ratios of the saturnian satellites range from ∼0.8 to 1.2, and are on average lower than those of the icy Galilean satellites at this wavelength although still larger than expected for single reflections off the surface. The ratio for the trailing hemisphere of Enceladus may be the exception with a value ?0.56. The 13 cm wavelength radar albedos and polarization ratios may be systematically lower than similar results from the Cassini orbiter's RADAR instrument at 2.2 cm wavelength [Ostro, S.J., and 19 colleagues, 2006. Icarus 183, 479-490]. Overall, these reflectivities and polarization properties, together with the shapes of the echo spectra, suggest subsurface multiple scattering to be the dominant reflection mechanism although operating less efficiently than on the large icy moons of Jupiter. All these saturnian moons and icy jovian moons are atmosphere-less, low temperature water ice surfaces, and any differences in radar properties may be indicative of differences in composition or the effects of various processes that modify the regolith structure. The degree of variation in radar properties with wavelength on each satellite may constrain the thickness and efficiency of the scattering layer.     

Astrometry and dynamics of Anthe (S/2007 S 4), a new satellite of Saturn

We describe the astrometry and dynamics of Anthe (S/2007 S 4), a new satellite of Saturn discovered in images obtained using the Imaging Science Subsystem (ISS) of the Cassini spacecraft. Included are details of 63 observations, of which 28 were obtained with Cassini's narrow-angle camera (NAC) and 35 using its wide-angle camera (WAC), covering an observation time-span of approximately 3 years. We estimate the diameter of Anthe to be ∼1.8 km. Orbit modeling based on a numerical integration of the full equations of motion fitted to the observations show that Anthe is in a first-order 11:10 mean motion resonance with Mimas. Two resonant arguments are librating: ?₁=11λ^′−10λ−? and ?₂=11λ^′−10λ−?^′−Ω^′+Ω, where λ, ? and Ω refer to the mean longitude, longitude of pericenter and longitude of ascending node of Mimas and Anthe, with the primed quantities corresponding to Anthe. These resonances cause periodic variations in the orbital elements. The semi-major axis varies by ±26 km over a 913-day period. Anthe is also close to a second-order eccentricity-type mean motion resonant relationship of the form 77:75 with Methone. Since Methone is also in a first-order resonance with Mimas [Spitale, J.N., Jacobson, R.A., Porco, C.C., Owen, W.M., 2006. Astron. J. 132, 692-710], an additional indirect perturbation exists between Methone and Anthe via Mimas. Neither effect is detectable in the orbit fitting and the short-term dynamical evolution of Anthe is dominated by the Mimas-Anthe resonances alone. The expected modulation effect from the Mimas-Tethys 4:2 inclination resonance is also insignificant over this time period. By including Cassini ISS observations of Mimas in the numerical integration fit, we estimate the GM of Mimas to be , consistent with Jacobson et al. [Jacobson, R.A., Spitale, J., Porco, C.C., Owen, W.M., 2006. Astron. J. 132, 711-713].     

Enceladus: The likely dominant nitrogen source in Saturn's magnetosphere

The spatial distribution of N⁺ in Saturn's magnetosphere obtained from Cassini Plasma Spectrometer (CAPS) data can be used to determine the spatial distribution and relative importance of the nitrogen sources for Saturn's magnetosphere. We first summarize CAPS data from 15 orbits showing the spatial and energy distribution of the nitrogen component of the plasma. This analysis re-enforces our earlier discovery [Smith, H.T., Shappirio, M., Sittler, E.C., Reisenfeld, D., Johnson, R.E., Baragiola, R.A., Crary, F.J., McComas, D.J., Young, D.T., 2005. Geophys. Res. Lett. 32 (14). L14S03] that Enceladus is likely the dominant nitrogen source for Saturn's inner magnetosphere. We also find a sharp enhancement in the nitrogen ion to water ion ratio near the orbit of Enceladus which, we show, is consistent with the presence of a narrow Enceladus torus as described in [Johnson, R.E., Liu, M., Sittler Jr., E.C., 2005. Geophys. Res. Lett. 32. L24201]. The CAPS data and the model described below indicate that N⁺ ions are a significant fraction of the plasma in this narrow torus. We then simulated the combined Enceladus and Titan nitrogen sources using the CAPS data as a constraint. This simulation is an extension of the model we employed earlier to describe the neutral tori produced by the loss of nitrogen from Titan [Smith, H.T., Johnson, R.E., Shematovich, V.I., 2004. Geophys. Res. Lett. 31 (16). L16804]. We show that Enceladus is the principal nitrogen source in the inner magnetosphere but Titan might account for a fraction of the observed nitrogen ions at the largest distances discussed. We also show that the CAPS data is consistent with Enceladus being a molecular nitrogen source with a nitrogen to water ratio roughly consistent with INMS [Waite, J.H., and 13 colleagues, 2006. Science 311 (5766), 1419-1422], but out-gassing of other nitrogen-containing species, such as ammonia, cannot be ruled out.     

The ultraviolet reflectance of Enceladus: Implications for surface composition

The reflectance of Saturn’s moon Enceladus has been measured at far ultraviolet (FUV) wavelengths (115-190 nm) by Cassini’s Ultraviolet Imaging Spectrograph (UVIS). At visible and near infrared (VNIR) wavelengths Enceladus’ reflectance spectrum is very bright, consistent with a surface composed primarily of H₂O ice. At FUV wavelengths, however, Enceladus is surprisingly dark - darker than would be expected for pure water ice. Previous analyses have focused on the VNIR spectrum, comparing it to pure water ice (Cruikshank, D.P., Owen, T.C., Dalle Ore, C., Geballe, T.R., Roush, T.L., de Bergh, C., Sandford, S.A., Poulet, F., Benedix, G.K., Emery, J.P. [2005] Icarus, 175, 268-283) or pure water ice plus a small amount of NH₃ (Emery, J.P., Burr, D.M., Cruikshank, D.P., Brown, R.H., Dalton, J.B. [2005] Astron. Astrophys., 435, 353-362) or NH₃ hydrate (Verbiscer, A.J., Peterson, D.E., Skrutskie, M.F., Cushing, M., Helfenstein, P., Nelson, M.J., Smith, J.D., Wilson, J.C. [2006] Icarus, 182, 211-223). We compare Enceladus’ FUV spectrum to existing laboratory measurements of the reflectance spectra of candidate species, and to spectral models. We find that the low FUV reflectance of Enceladus can be explained by the presence of a small amount of NH₃ and a small amount of a tholin in addition to H₂O ice on the surface. The presence of these three species (H₂O, NH₃, and a tholin) appears to satisfy not only the low FUV reflectance and spectral shape, but also the middle-ultraviolet to visible wavelength brightness and spectral shape. We expect that ammonia in the Enceladus plume is transported across the surface to provide a global coating.     

Orbital resonances in the inner neptunian system: II. Resonant history of Proteus, Larissa, Galatea, and Despina

We investigate the orbital history of the small neptunian satellites discovered by Voyager 2. Over the age of the Solar System, tidal forces have caused the satellites to migrate radially, bringing them through mean-motion resonances with one another. In this paper, we extend our study of the largest satellites Proteus and Larissa [Zhang, K., Hamilton, D.P., 2007. Icarus 188, 386-399] by adding in mid-sized Galatea and Despina. We test the hypothesis that these moons all formed with zero inclinations, and that orbital resonances excited their tilts during tidal migration. We find that the current orbital inclinations of Proteus, Galatea, and Despina are consistent with resonant excitation if they have a common density . Larissa's inclination, however, is too large to have been caused by resonant kicks between these four satellites; we suggest that a prior resonant capture event involving either Naiad or Thalassa is responsible. Our solution requires at least three past resonances with Proteus, which helps constrain the tidal migration timescale and thus Neptune's tidal quality factor: 9000<QN<36,000. We also improve our determination of Qs for Proteus and Larissa, finding 36<QP<700 and 18<QL<200. Finally, we derive a more general resonant capture condition, and work out a resonant overlap criterion relevant to satellite orbital evolution around an oblate primary.     

The oxidation state of hydrothermal systems on early Enceladus

The discovery of CO₂, CH₄, and N₂ in a plume at Enceladus provides useful clues about the chemistry and evolution of this moon of Saturn. Here, we use chemical equilibrium and kinetic calculations to estimate the oxidation state of hydrothermal systems on early Enceladus, with the assumption that the plume's composition was inherited from early hydrothermal fluids. Chemical equilibrium calculations are performed using the CO₂/CH₄ ratio in the plume, and kinetic calculations are conducted using equations from fluid dynamics and chemical kinetics. Our results suggest that chemical equilibrium between CO₂ and CH₄ would have been reachable at temperatures above ∼200 °C in hydrothermal systems. The oxidation state of the hydrothermal systems would have been close to the pyrrhotite-pyrite-magnetite (PPM) or fayalite-magnetite-quartz (FMQ) redox buffer (i.e., terrestrial-like) if the plume's CO₂ and CH₄ equilibrated in hydrothermal systems long ago. As for minerals, we suggest that iron metal would have been oxidized to magnetite by the escape of H₂ from the early satellite. Our calculations also indicate that, assuming CO₂ and CH₄ reached chemical equilibrium, magnetite would not have been oxidized to hematite in hydrothermal systems, perhaps due to insufficient H₂ escape. It is shown that, if Enceladus accreted as much NH₃ as comets contain, the presence of N₂ and deficiency of NH₃ in the plume can be understood in the context of chemical equilibrium in the C-N-O-H system. We conclude by proposing an evolutionary hypothesis in which the fairly oxidized nature of the plume can be explained by a brief episode of oxidation caused by short-lived radioactivity. These suggestions can be rigorously tested by acquiring gravity and isotopic data in the future.     

Orbital resonances in the inner neptunian system: I. The 2:1 Proteus-Larissa mean-motion resonance

We investigate the orbital resonant history of Proteus and Larissa, the two largest inner neptunian satellites discovered by Voyager 2. Due to tidal migration, these two satellites probably passed through their 2:1 mean-motion resonance a few hundred million years ago. We explore this resonance passage as a method to excite orbital eccentricities and inclinations, and find interesting constraints on the satellites' mean density () and their tidal dissipation parameters (Qs>10). Through numerical study of this mean-motion resonance passage, we identify a new type of three-body resonance between the satellite pair and Triton. These new resonances occur near the traditional two-body resonances between the small satellites and, surprisingly, are much stronger than their two-body counterparts due to Triton's large mass and orbital inclination. We determine the relevant resonant arguments and derive a mathematical framework for analyzing resonances in this special system.     

On the orbits and masses of the satellites of the Pluto-Charon system

Two small satellites of Pluto, S/2005 P1 (hereafter P1) and S/2005 P2 (hereafter P2), have recently been discovered outside the orbit of Charon, and their orbits are nearly circular and nearly coplanar with that of Charon. Because the mass ratio of Charon-Pluto is ∼0.1, the orbits of P2 and P1 are significantly non-Keplerian even if P2 and P1 have negligible masses. We present an analytic theory, with P2 and P1 treated as test particles, which shows that the motion can be represented by the superposition of the circular motion of a guiding center, the forced oscillations due to the non-axisymmetric components of the potential rotating at the mean motion of Pluto-Charon, the epicyclic motion, and the vertical motion. The analytic theory shows that the azimuthal periods of P2 and P1 are shorter than the Keplerian orbital periods, and this deviation from Kepler's third law is already detected in the unperturbed Keplerian fit of Buie and coworkers. In this analytic theory, the periapse and ascending node of each of the small satellites precess at nearly equal rates in opposite directions. From direct numerical orbit integrations, we show the increasing influence of the proximity of P2 and P1 to the 3:2 mean-motion commensurability on their orbital motion as their masses increase within the ranges allowed by the albedo uncertainties. If the geometric albedos of P2 and P1 are high and of order of that of Charon, the masses of P2 and P1 are sufficiently low that their orbits are well described by the analytic theory. The variation in the orbital radius of P2 due to the forced oscillations is comparable in magnitude to that due to the best-fit Keplerian eccentricity, and there is at present no evidence that P2 has any significant epicyclic eccentricity. However, the orbit of P1 has a significant epicyclic eccentricity, and the prograde precession of its longitude of periapse with a period of 5300 days should be easily detectable. If the albedos of P2 and P1 are as low as that of comets, the large inferred masses induce significant short-term variations in the epicyclic eccentricities and/or periapse longitudes on the 400-500-day timescales due to the proximity to the 3:2 commensurability. In fact, for the maximum inferred masses, P2 and P1 may be in the 3:2 mean-motion resonance, with the resonance variable involving the periapse longitude of P1 librating. Observations that sample the orbits of P2 and P1 well on the 400-500-day timescales should provide strong constraints on the masses of P2 and P1 in the near future.     

Total particulate mass in Enceladus plumes and mass of Saturn’s E ring inferred from Cassini ISS images

The eclipse mosaic (PIA08329) of the Saturn system, taken on September 15, 2006 when Cassini was in Saturn’s shadow, contains numerous color images of the Enceladus plume and the E ring at phase angles ranging from 173° to 179°. These forward-scattering observations sample the diffraction peak for particle radii in the 1–5 μm range. The phase angle dependence and total brightness are sensitive indicators of the total mass of solid material in the plume. We fit the data with a variety of particle shapes and size distributions, and find that the median radius of the equivalent-volume sphere is 3.1 μm, with an uncertainty of ±0.5 μm. The total mass of particles in the plume is (1.45 ± 0.5) × 10⁵ kg. We have not considered variations with altitude in the particle size and shape distribution, and we leave that for another paper. We find that the brightness of the E ring varies with position in the orbit, not only because of the viewing geometry, e.g., variations in phase angle, but also because of some unknown intrinsic variability. The total mass of solid material in the E ring is (12 ± 5.5) × 10⁸ kg. For the plume, the production rate of particles – the mass per unit time leaving the vents is 51 ± 18 kg s⁻¹. We estimate that 9% of these particles are escaping from Enceladus, implying lifetimes of ∼8 years for the E ring particles. Based on three comparisons with vapor amounts from ultraviolet spectroscopy, the ice/vapor ratio is in the range 0.35–0.70. This high ratio poses a problem for theories in which particles form by condensation from the gas phase, and could indicate that particles are formed as spray from a liquid reservoir.     

Saturn in hot water: Viscous evolution of the Enceladus torus

The detection of outgassing water vapor from Enceladus is one of the great breakthroughs of the Cassini mission. The fate of this water once ionized has been widely studied; here we investigate the effects of purely neutral-neutral interactions within the Enceladus torus. We find that, thanks in part to the polar nature of the water molecule, a cold (∼180 K) neutral torus would undergo rapid viscous heating and spread to the extent of the observed hydroxyl cloud, before plasma effects become important. We investigate the physics behind the spreading of the torus, paying particular attention to the competition between heating and rotational line cooling. A steady-state torus model is constructed, and it is demonstrated that the torus will be observable in the millimeter band with the upcoming Herschel satellite. The relative strength of rotational lines could be used to distinguish between physical models for the neutral cloud.     

How the Enceladus dust plume feeds Saturn’s E ring

Pre-Cassini models of Saturn’s E ring [Horányi, M., Burns, J., Hamilton, D., 1992. Icarus 97, 248-259; Juhász, A., Horányi, M., 2002. J. Geophys. Res. 107, 1-10] failed to reproduce its peculiar vertical structure inferred from Earth-bound observations [de Pater, I., Martin, S.C., Showalter, M.R., 2004. Icarus 172, 446-454]. After the discovery of an active ice-volcanism of Saturn’s icy moon Enceladus the relevance of the directed injection of particles for the vertical ring structure of the E ring was swiftly recognised [Juhász, A., Horányi, M., Morfill, G.E., 2007. Geophys. Res. Lett. 34, L09104; Kempf, S., Beckmann, U., Moragas-Klostermeyer, G., Postberg, F., Srama, R., Economou, T., Schmidt, J., Spahn, F., Grün, E., 2008. Icarus 193, 420-437]. However, simple models for the delivery of particles from the plume to the ring predict a too small vertical ring thickness and overestimate the amount of the injected dust.Here we report on numerical simulations of grains leaving the plume and populating the dust torus of Enceladus. We run a large number of dynamical simulations including gravity and Lorentz force to investigate the earliest phase of the ring particle life span. The evolution of the electrostatic charge carried by the initially uncharged grains is treated selfconsistently. Freshly ejected plume particles are moving in almost circular orbits because the Enceladus orbital speed exceeds the particles’ ejection speeds by far. Only a small fraction of grains that leave the Hill sphere of Enceladus survive the next encounter with the moon. Thus, the flux and size distribution of the surviving grains, replenishing the ring particle reservoir, differs significantly from the flux and size distribution of the particles freshly ejected from the plume. Our numerical simulations reproduce the vertical ring profile measured by the Cassini Cosmic Dust Analyzer (CDA) [Kempf, S., Beckmann, U., Moragas-Klostermeyer, G., Postberg, F., Srama, R., EconoDmou, T., Smchmidt, J., Spahn, F., Grün, E., 2008. Icarus 193, 420-437]. From our simulations we calculate the deposition rates of plume particles hitting Enceladus’ surface. We find that at a distance of 100 m from a jet a 10 m sized ice boulder should be covered by plume particles in 10⁵-10⁶ years.     

The fate of primordial lunar Trojans

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.     

Orbital evolution of small binary asteroids

About 15% of both near-Earth and main-belt asteroids with diameters below 10 km are now known to be binary. These small asteroid binaries are relatively uniform and typically contain a fast-spinning, flattened primary and a synchronously rotating, elongated secondary that is 20-40% as large (in diameter) as the primary. The principal formation mechanism for these binaries is now thought to be YORP (Yarkovsky-O’Keefe-Radzievskii-Paddack) effect induced spin-up of the primary followed by mass loss and accretion of the secondary from the released material. It has previously been suggested (?uk, M. [2007]. Astrophys. J. 659, L57-L60) that the present population of small binary asteroids is in a steady state between production through YORP and destruction through binary YORP (BYORP), which should increase or decrease secondary’s orbit, depending on the satellite’s shape. However, BYORP-driven evolution has not been directly modeled until now. Here we construct a simple numerical model of the binary’s orbital as well the secondary’s rotational dynamics which includes BYORP and selected terms representing main solar perturbations. We find that many secondaries should be vulnerable to chaotic rotation even for relatively low-eccentricity mutual orbits. We also find that the precession of the mutual orbit for typical small binary asteroids might be dominated by the perturbations from the prolate and librating secondary, rather than the oblate primary. When we evolve the mutual orbit by BYORP we find that the indirect effects on the binary’s eccentricity (through the coupling between the orbit and the secondary’s spin) dominate over direct ones caused by the BYORP acceleration. In particular, outward evolution causes eccentricity to increase and eventually triggers chaotic rotation of the secondary. We conclude that the most likely outcome will be reestablishing of the synchronous lock with a “flipped” secondary which would then evolve back in. For inward evolution we find an initial decrease of eccentricity and secondary’s librations, to be followed by later increase. We think that it is likely that various forms of dissipation we did not model may damp the secondary’s librations close to the primary, allowing for further inward evolution and a possible merger. We conclude that a merger or a tidal disruption of the secondary are the most likely outcomes of the BYORP evolution. Dissociation into heliocentric pairs by BYORP alone should be very difficult, and satellite loss might be restricted to the minority of systems containing more than one satellite at the time.