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Exploration of asteroid (101955) Bennu by the OSIRIS-REx mission has provided an in-depth look at this rubble-pile near-Earth asteroid. In particular, the measured gravity field and the detailed shape model of Bennu indicate significant heterogeneities in its interior structure, compatible with a lower density at its center. Here we combine gravity inversion methods with a statistical rubble-pile model to determine the density and size-frequency distribution (SFD) index of the rubble that constitutes Bennu. The best-fitting models indicate that the SFD of the interior is consistent with that observed on the surface, with a cumulative SFD index of approximately $-2.9$. The rubble bulk density is approximately $1.35$ g/cm$^3$, corresponding to a $12$% macro-porosity. We find the largest rubble particle to be approximately $145$ m, whereas the largest void is approximately $10$ m., 14 pages, 5 figures, accepted to Icarus

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In early 2019, the OSIRIS‐REx spacecraft discovered small particles being ejected from the surface of the near‐Earth asteroid Bennu. Although they were seen to be ejected at slow speeds, on the order of tens of cm/s, a number of particles were surprisingly seen to orbit for multiple revolutions and days, which requires a dynamical mechanism to quickly and substantially modify the orbit to prevent re‐impact upon their first periapse passage. This paper demonstrates that, based on simulations constrained by the conditions of the observed events, the combined effects of gravity, solar radiation pressure, and thermal radiation pressure from Bennu can produce many sustained orbits for ejected particles. Furthermore, the simulated populations exhibit two interesting phenomena that could play an important role in the geophysical evolution of bodies such as Bennu. First, small particles (

Ceres is the largest body in the main asteroid belt. It was recently explored by the Dawn mission to uncover strong similarities with other icy bodies. The morphological features observed on the surface of Ceres indicate a relatively wide range of water ice concentrations, leading us to investigate the magnitude and distribution of crustal density heterogeneities, and to consider whether they could have caused a reorientation of Ceres. Here, we present three independent and corroborating lines of evidence for the true polar wander of Ceres. Thanks to the global gravity inversion approach applied to the shape and gravity data of Ceres, we find crustal density heterogeneities up to approximately ±0.3 g cm−3, with a prominent positive density anomaly aligned with the equator, in the region of Ahuna Mons. The topography shows the remnants of an equatorial ridge compatible with the position of the palaeo-equator, and indicates that Ceres reoriented by approximately 36°, with the palaeo-pole following an indirect path to the current pole of Ceres. The tectonic patterns generated by the true polar wander are in close agreement with the location and orientation of the Samhain Catenae and Uhola Catenae crustal fractures. These results highlight the complex interior structure and richness of processes taking place in Ceres-scale icy bodies. The dwarf planet Ceres may have reoriented in the past due to a heterogeneously dense crust, a scenario consistent with gravity and topographic data and the distribution of crustal fractures.

INTRODUCTION Active asteroids are small bodies in the Solar System that show ongoing mass loss, such as the ejection of dust, which may be caused by large impacts, volatile release, or rotational acceleration. Studying them informs our understanding of the evolution and destruction of asteroids and the origin of volatile materials such as water on Earth. The OSIRIS-REx (Origins, Spectral Interpretation, Resource Identification, and Security–Regolith Explorer) spacecraft has rendezvoused with the near-Earth asteroid (101955) Bennu. The selection of Bennu as the OSIRIS-REx target was partially based on its spectral similarity to some active asteroids. Observations designed to detect mass loss at Bennu were conducted from Earth and during the spacecraft’s approach, but no signs of asteroid activity were found. However, when the spacecraft entered orbit in January 2019, we serendipitously observed particles in the vicinity of Bennu that had apparently been ejected from its surface. RATIONALE We analyzed the properties and behavior of particles ejected from Bennu to determine the possible mechanisms of ejection and provide understanding of the broader population of active asteroids. Images obtained by the spacecraft indicate multiple discrete ejection events with a range of energies and resultant particle trajectories. We characterized three large ejection events that respectively occurred on 6 January, 19 January, and 11 February 2019. Tracking of individual particles across multiple images by means of optical navigation techniques provided the initial conditions for orbit determination modeling. By combining these approaches, we estimated the locations and times of ejection events and determined initial velocity vectors of particles. We estimated the particle sizes and the minimum energies of the ejection events using a particle albedo and density consistent with observations of Bennu. RESULTS Particles with diameters from 3 m s–1. Estimated energies ranged from 270 mJ for the 6 January event to 8 mJ for the 11 February event. The three events arose from widely separated sites, which do not show any obvious geological distinction from the rest of Bennu’s surface. However, these events all occurred in the late afternoon, between about 15:00 and 18:00 local solar time. In addition to discrete ejection events, we detected a persistent background of particles in the Bennu environment. Some of these background particles have been observed to persist on temporary orbits that last several days—in one case, with a semimajor axis >1 km. The orbital characteristics of these gravitationally bound objects make it possible to determine the ratio of their cross-sectional area to their mass. Combined with their photometric phase functions, this information constrains the parameter space of the particles’ diameters, densities, and albedos. CONCLUSION Plausible mechanisms for the large ejection events include thermal fracturing, volatile release through dehydration of phyllosilicates, and meteoroid impacts. The late-afternoon timing of the events is consistent with any of these mechanisms. Bennu’s boulder geology indicates that thermal fracturing, perhaps enhanced by volatile release, could occur on the asteroid surface. Smaller events, especially those that occur on the night side of Bennu, could be attributable to reimpacting particles. Our observations classify Bennu as an active asteroid. Active asteroids are commonly identified by major mass loss events observable with telescopes, on scales much greater than we observed at Bennu. Our findings indicate that there is a continuum of mass loss event magnitudes among active asteroids.

Determining the size and orbital distribution of the population of near-Earth asteroids (NEAs) is the focus of intense research, with the most recent models converging to a population of approximately $1000$ NEAs larger than 1 km and up to approximately $10^9$ NEAs with absolute magnitude $H, 21 pages, 1 table, 10 figures, accepted for publication in Icarus

When comet C/2013 A1 (Siding Spring) passed nearby Mars in 2014, it offered an unprecedented opportunity to observe the interaction between the dust tail of the comet and the atmosphere of Mars. Here I provide an overview of a recent series of four articles reporting observations from three satellites fortuitously orbiting Mars at the appropriate time (MAVEN, MEX, and MRO). These observations reveal high-velocity ablation and ionization of metals from the comet, the diffusion and transport processes that operated in Mars' atmosphere, and the abundance of these metals in the comet.

Gravity inversion allows us to constrain the interior mass distribution of a planetary body using the observed shape, rotation, and gravity. Traditionally, techniques developed for gravity inversion can be divided into Monte Carlo methods, matrix inversion methods, and spectral methods. Here we employ both matrix inversion and Monte Carlo in order to explore the space of exact solutions, in a method which is particularly suited for arbitrary shape bodies. We expand the mass density function using orthogonal polynomials, and map the contribution of each term to the global gravitational field generated. This map is linear in the density terms, and can be pseudo-inverted in the under-determined regime using QR decomposition, to obtain a basis of the affine space of exact interior structure solutions. As the interior structure solutions are degenerate, assumptions have to be made in order to control their properties, and these assumptions can be transformed into scalar functions and used to explore the solutions space using Monte Carlo techniques. Sample applications show that the range of solutions tend to converge towards the nominal one as long as the generic assumptions made are correct, even in the presence of moderate noise. We present the underlying mathematical formalism and an analysis of how to impose specific features on the global solution, including uniform solutions, gradients, and layered models. Analytical formulas for the computation of the relevant quantities when the shape is represented using several common methods are included in the Appendix., Comment: 23 pages, 9 figures, 4 tables. Accepted for publication in Geophysical Journal International

Vesta to the Core Vesta is one of the largest bodies in the main asteroid belt. Unlike most other asteroids, which are fragments of once larger bodies, Vesta is thought to have survived as a protoplanet since its formation at the beginning of the solar system (see the Perspective by Binzel , published online 20 September). Based on data obtained with the Gamma Ray and Neutron Detector aboard the Dawn spacecraft, Prettyman et al. (p. 242 , published online 20 September) show that Vesta's reputed volatile-poor regolith contains substantial amounts of hydrogen delivered by carbonaceous chondrite impactors. Observations of pitted terrain on Vesta obtained by Dawn's Framing Camera and analyzed by Denevi et al. (p. 246 , published online 20 September), provide evidence for degassing of volatiles and hence the presence of hydrated materials. Finally, paleomagnetic studies by Fu et al. (p. 238 ) on a meteorite originating from Vesta suggest that magnetic fields existed on the surface of the asteroid 3.7 billion years ago, supporting the past existence of a magnetic core dynamo.

For absolute magnitudes greater than the current completeness limit of H-magnitude ∼15 the main asteroid belt's size distribution is imperfectly known. We have acquired good-quality orbital and absolute H-magnitude determinations for a sample of small main-belt asteroids in order to study the orbital and size distribution beyond H = 15 , down to sub-kilometer sizes ( H > 18 ). Based on six observing nights over a 11-night baseline we have detected, measured photometry for, and linked observations of 1087 asteroids which have one-week time baselines or more. The linkages allow the computation of full heliocentric orbits (as opposed to statistical distances determined by some past surveys). Judged by known asteroids in the field the typical uncertainty in the ( a / e / i ) orbital elements is less than 0.03 AU/0.03/0.5°. The distances to the objects are sufficiently well known that photometric uncertainties (of 0.3 magnitudes or better) dominate the error budget of their derived H-magnitudes. The detected asteroids range from H R = 12 – 22 and provide a set of objects down to sizes below 1 km in diameter. We find an on-sky surface density of 210 asteroids per square degree in the ecliptic with opposition magnitudes brighter than m R = 23 , with the cumulative number of asteroids increasing by a factor of 100.27/mag from m R = 18 down to the m R ≃ 23.5 limit of our survey. In terms of absolute H magnitudes, we find that beyond H = 15 the belt exhibits a constant power-law slope with the number increasing proportional to 10 0.30 H from H ≃ 15 to 18 , after which incompleteness begins in the survey. Examining only the subset of detections inside 2.5 AU, we find weak evidence for a mildly shallower slope for H = 15 – 19.5 . We provide the information necessary such that anyone wishing to model the main asteroid belt can compare a detailed model to our detected sample.

We derive an expression for the mutual gravitational force and torque of two bodies having arbitrary shapes and mass distributions, as an expansion in power series of their products of inertia and of the relative coordinates of their centres of mass. The absolute convergence of all the power series developed is rigorously demonstrated. The absence of transcendental functions makes this formalism suitable for fast numerical applications. The products of inertia used here are directly related to the spherical harmonics coefficients, and we provide a detailed analysis of this relationship., Comment: 13 pages, accepted by Celestial Mechanics and Dynamical Astronomy

A comprehensive characterization of the detection efficiency of nine of the major asteroid surveys that have been active over the past two decades is presented. The detection efficiency is estimated on a nightly basis by comparing the detected asteroids with the complete catalog of known asteroids propagated to the same observing epoch. Results include a nightly estimate of the detection efficiency curves as a function of apparent magnitude and apparent velocity of the asteroids, as well as a cumulative analysis to estimate the overall performance of each survey. The limiting magnitude distribution is estimated for each survey, and it is then modeled as a function of telescope aperture to obtain an estimate over a wide range of apertures., Accepted for publication in The Astronomical Journal, 7 pages, 7 figures

Earth-bound searches for natural satellites of 4 Vesta have been reported since 1987. With use of technological advances and observing capability has come a reduction in the detectable size of a possible satellite. The Dawn mission brought a small camera close to Vesta itself. In our search, which was carried out with a comprehensive data acquisition strategy and by experienced searchers, we find no satellites to a detection limit as small as 3-m radius. Various observation and analysis strategies are discussed in detail. It is now time to factor the null result of this search into the context of satellite formation among other main belt asteroids and to conduct dynamical modeling to explore the suspected forces contributing to the absence of satellites at Vesta today.

We investigate the dynamical stability of the 3/1 resonant planets b and c in the extrasolar planetary system around 55 Cancri by applying Laskar's frequency map analysis. We find that the region with low diffusion speed extends to high eccentricity for both planets and that the observed system is deeply embedded in this region. The dynamics while in resonance and the influence of planet e on the resonant couple are also analysed. Using a simple model for the capture of the planets in resonance during migration we show that evolutionary tracks from smaller to the presently observed eccentricities lie in the stable region.

A New Dawn Since 17 July 2011, NASA's spacecraft Dawn has been orbiting the asteroid Vesta—the second most massive and the third largest asteroid in the solar system (see the cover). Russell et al. (p. 684 ) use Dawn's observations to confirm that Vesta is a small differentiated planetary body with an inner core, and represents a surviving proto-planet from the earliest epoch of solar system formation; Vesta is also confirmed as the source of the howardite-eucrite-diogenite (HED) meteorites. Jaumann et al. (p. 687 ) report on the asteroid's overall geometry and topography, based on global surface mapping. Vesta's surface is dominated by numerous impact craters and large troughs around the equatorial region. Marchi et al. (p. 690 ) report on Vesta's complex cratering history and constrain the age of some of its major regions based on crater counts. Schenk et al. (p. 694 ) describe two giant impact basins located at the asteroid's south pole. Both basins are young and excavated enough amounts of material to form the Vestoids—a group of asteroids with a composition similar to that of Vesta—and HED meteorites. De Sanctis et al. (p. 697 ) present the mineralogical characterization of Vesta, based on data obtained by Dawn's visual and infrared spectrometer, revealing that this asteroid underwent a complex magmatic evolution that led to a differentiated crust and mantle. The global color variations detailed by Reddy et al. (p. 700 ) are unlike those of any other asteroid observed so far and are also indicative of a preserved, differentiated proto-planet.

The Vesta gravity field and related physical parameters have been precisely measured using 10-months of radiometric Doppler and range data and optical landmark tracking from the Dawn spacecraft. The gravity field, orientation parameters, landmark locations, and Vesta’s orbit are jointly estimated. The resulting spherical harmonic gravity field has a half-wavelength resolution of 42 km (degree 20). The gravitational mass uncertainty is nearly 1 part in 106. The inertial spin pole location is determined to better than 0.0001° and the uncertainty in the rotation period has been reduced by nearly a factor of 100. The combined precession and nutation of the pole of Vesta has been detected with angular rates about 70% of expected values, but not well enough to constrain the moment of inertia. The optical landmark position estimates reduce the uncertainty in the center-of-mass and center-of-figure offset to 10 m. The Vesta ephemeris uncertainty during the Dawn stay was reduced from 20 km to better than 10 m in the Earth–Vesta direction.

Comet C/2013 A1 (siding Spring) will experience a high velocity encounter with Mars on October 19, 2014 at a distance of 135,000 km +- 5000 km from the planet center. We present a comprehensive analysis of the trajectory of both the comet nucleus and the dust tail. The nucleus of C/2013 A1 cannot impact on Mars even in the case of unexpectedly large nongravitational perturbations. Furthermore, we compute the required ejection velocities for the dust grains of the tail to reach Mars as a function of particle radius and density and heliocentric distance of the ejection. A comparison between our results and the most current modeling of the ejection velocities suggests that impacts are possible only for millimeter to centimeter size particles released more than 13 au from the Sun. However, this level of cometary activity that far from the Sun is considered extremely unlikely. The arrival time of these particles spans a 20-minute time interval centered at October 19, 2014 at 20:09 TDB, i.e., around the time that Mars crosses the orbital plane of C/2013 A1. Ejection velocities larger than currently estimated by a factor >2 would allow impacts for smaller particles ejected as close as 3 au from the Sun. These particles would reach Mars from 43 to 130 min after the nominal close approach epoch of the purely gravitational trajectory of the nucleus.

Comet C/2013 A1 (Siding Spring) will have a close encounter with Mars on October 19, 2014. We model the dynamical evolution of dust grains from the time of their ejection from the comet nucleus to the Mars close encounter, and determine the flux at Mars. Constraints on the ejection velocity from Hubble Space Telescope observations indicate that the bulk of the grains will likely miss Mars, although it is possible that a few-percent of grains with higher velocities will reach Mars, peaking approximately 90--100 minutes after the close approach of the nucleus, and consisting mostly of millimeter-radius grains ejected from the comet nucleus at a heliocentric distance of approximately 9~AU or larger. At higher velocities, younger grains from sub-millimeter to several millimeter can reach Mars too, although an even smaller fraction of grains is expected have these velocities, with negligible effect on the peak timing. Using NEOWISE observations of the comet, we can estimate that the maximum fluence will be of the order of $10^{-7}$ grains/m$^2$. We include a detailed analysis of how the expected fluence depends on the grain density, ejection velocity, and size-frequency distribution, to account for current model uncertainties and in preparation of possible refined model values in the near future., Comment: 11 pages, 5 figures, accepted for publication in ApJL

The hydrostatic equilibrium of multi-layer bodies lacks a satisfactory theoretical treatment despite its wide range of applicability. Here we show that by using the exact analytical potential of homogeneous ellipsoids we can obtain recursive analytical solutions and an exact numerical method for the hydrostatic equilibrium shape problem of multi-layer planets and synchronous moons. The recursive solutions rely on the series expansion of the potential in terms of the polar and equatorial shape eccentricities, while the numerical method uses the exact potential expression. These solutions can be used to infer the interior structure of planets and synchronous moons from the observed shape, rotation, and gravity. When applied to dwarf planet Ceres, we show that it is most likely a differentiated body with an icy crust of equatorial thickness 30-90 km and a rocky core of density 2.4-3.1 g/cm$^3$. For synchronous moons, we show that the $J_2/C_{22} \simeq 10/3$ and the $(b-c)/(a-c) \simeq 1/4$ ratios have significant corrections of order $\Omega^2/(\pi G \rho)$, with important implications on how their gravitational coefficients are determined from flyby radio science data and on how we assess their hydrostatic equilibrium state., Comment: 12 pages, 6 figures, in press in ApJ

A New Dawn Since 17 July 2011, NASA's spacecraft Dawn has been orbiting the asteroid Vesta—the second most massive and the third largest asteroid in the solar system (see the cover). Russell et al. (p. 684 ) use Dawn's observations to confirm that Vesta is a small differentiated planetary body with an inner core, and represents a surviving proto-planet from the earliest epoch of solar system formation; Vesta is also confirmed as the source of the howardite-eucrite-diogenite (HED) meteorites. Jaumann et al. (p. 687 ) report on the asteroid's overall geometry and topography, based on global surface mapping. Vesta's surface is dominated by numerous impact craters and large troughs around the equatorial region. Marchi et al. (p. 690 ) report on Vesta's complex cratering history and constrain the age of some of its major regions based on crater counts. Schenk et al. (p. 694 ) describe two giant impact basins located at the asteroid's south pole. Both basins are young and excavated enough amounts of material to form the Vestoids—a group of asteroids with a composition similar to that of Vesta—and HED meteorites. De Sanctis et al. (p. 697 ) present the mineralogical characterization of Vesta, based on data obtained by Dawn's visual and infrared spectrometer, revealing that this asteroid underwent a complex magmatic evolution that led to a differentiated crust and mantle. The global color variations detailed by Reddy et al. (p. 700 ) are unlike those of any other asteroid observed so far and are also indicative of a preserved, differentiated proto-planet.

Dawn is the first NASA mission to operate in the vicinity of the two most massive asteroids in the main belt, Ceres and Vesta. This double-rendezvous mission is enabled by the use of low-thrust solar electric propulsion. Dawn will arrive at Vesta in 2011 and will operate in its vicinity for approximately one year. Vesta's mass and non-spherical shape, coupled with its rotational period, presents very interesting challenges to a spacecraft that depends principally upon low-thrust propulsion for trajectory-changing maneuvers. The details of Vesta's high-order gravitational terms will not be determined until after Dawn's arrival at Vesta, but it is clear that their effect on Dawn operations creates the most complex operational environment for a NASA mission to date. Gravitational perturbations give rise to oscillations in Dawn's orbital radius, and it is found that trapping of the spacecraft is possible near the 1:1 resonance between Dawn's orbital period and Vesta's rotational period, located approximately between 520 and 580 km orbital radius.This resonant trapping can be escaped by thrusting at the appropriate orbital phase. Having passed through the 1:1 resonance, gravitational perturbations ultimately limit the minimum radius for low-altitude operations to about 400 km,in order to safely prevent surface impact. The lowest practical orbit is desirable in order to maximize signal-to-noise and spatial resolution of the Gamma-Ray and Neutron Detector and to provide the highest spatial resolution observations by Dawn's Framing Camera and Visible InfraRed mapping spectrometer. Dawn dynamical behavior is modeled in the context of a wide range of Vesta gravity models. Many of these models are distinguishable during Dawn's High Altitude Mapping Orbit and the remainder are resolved during Dawn's Low Altitude Mapping Orbit, providing insight into Vesta's interior structure., Corrected normalization coefficients; updated table text and references

We numerically explore the long-term stability of planetary orbits locked in a 2:1 mean motion resonance for a wide range of planetary mass ratios and orbital parameters. Our major tool is Laskar's frequency map analysis. Regions of low diffusion rate are outlined in a phase space defined by the two planetary eccentricities and the libration amplitude of a critical resonance argument. Resonant systems that are dynamically stable on a long timescale must lie within these regions. The resonance locking between planets in high eccentric orbits may be destroyed by mutual close encounters. We discuss various dynamical protection mechanisms related to the resonant configuration, among which is the well-known apsidal corotation. In the case of moderate-to-low eccentricities, we find that apsidal circulators, little discussed till now, are very common among stable orbits. We also map the different types of resonant behaviour predicted by analytical theories in the phase space.

Using Laskar's frequency map analysis, we investigate the long-term stability of Venus Trojan orbits. By measuring the diffusion rate of proper frequencies, we outline in phase space the most stable region. It is located between 5° and 10° in proper inclination with libration amplitudes ranging from 50° to 110°. The proper eccentricity is lower than 0.13. The stable region is surrounded by secular resonances that destabilize orbits on short timescales. The dynamical half-life of orbits within the stable region is about 6 × 108 yr. The Yarkovsky effect further reduces the dynamical lifetime. Therefore, primordial Venus Trojans, if any, cannot have survived until the present. Transient Trojans, on the other hand, cannot be excluded.

In this paper we explore the dynamical stability of the Mars Trojan region applying mainly Laskar’s Frequency Map Analysis. This method yields the chaotic diffusion rate of orbits and allows to determine the most stable regions. It also gives the frequencies which are responsible for the instability of orbits. The most stable regions are found for inclinations between about 15 ◦ and 30 ◦ . For inclinations smaller than 15 ◦ , we confirm, by applying a synthetic secular theory, that the secular resonances ν3, ν4, ν13, ν14 rapidly excite asteroid orbits within a

Using the frequency map analysis (FMA) method we investigate the stability properties of Trojan-type orbits in the proximity of the L 4 and L 5 Lagrangian points of Jupiter. This study is part of the MATROS project. The orbits of about 2 x 10 4 virtual Trojans with random initial conditions have been computed numerically and for each body the diffusion rate in frequency space has been determined by spectral analysis. The diffusion portraits show where stable orbits are located in the space of proper elements for different values of inclination. For low inclined orbits we reproduce the stability region outlined by Levison, Shoemaker & Shoemaker and, due to our fast sampling capability, we find additional resonant features in the libration amplitude versus proper eccentricity space. At higher inclinations, the stability region gradually shrinks and it disappears for inclinations of about 40°. The maximal Lyapunov characteristic exponent is computed for a limited number of Trojan orbits in our sample and the predictions concerning the chaotic behaviour of each orbit are compared with those given by the FMA method. A good agreement is obtained and the value of the Lyapunov exponent may be used to tune the results of the FMA analysis. A synthetic secular theory for the proper frequencies of Jupiter Trojans is obtained by numerically fitting the outcome of the frequency map analysis.

We present in this paper an analysis of the long term stability of Trojan type orbits of both Uranus and Neptune. Employing the Frequency Map Analysis (hereinafter FMA) we measure the diffusion speed in the phase space for a large sample of Trojan orbits with short numerical integrations. High resolution diffusion maps are derived for different values of initial inclination. These maps outline where the most stable orbits can be found in the Trojan clouds of the two planets. The orbit of the newly discovered Neptune Trojan 2001 QR322 has been analysed in detail with the FMA method. In the phase space the body is located close to the border of a stable region for low inclination Neptune Trojans. Numerical integrations over 4.5 Gyr of clone orbits generated from the covariance matrix show that only 10% of the clones escape from the Trojan cloud. The proper frequencies of the Trojan motion computed with the FMA algorithm allow us to to derive a numerical secular theory. From this theory it is possible to locate in the phase space the main secular resonances that can perturb Trojan orbits of the two planets and lead to instability.

We model with numerical algorithms the dynamical processes that possibly lead to the trapping of Jupiter’s Trojans from a primordial population of planetesimals orbiting nearby a proto-Jupiter. The predictions of models based on mutual planetesimal collisions and on the mass growth of Jupiter are compared with observations. In particular, we concentrate on the distribution of the libration amplitude. The two mechanisms for trapping reproduce closely the libration amplitude distribution of the real Trojans only when the long-term dynamical diffusion described by Levison et al. (1997 , Nature 385, 42–44) is taken into account.

We use the frequency map analysis method to identify for Trojan orbits of Saturn the regions in the proper orbital element phase space characterized by higher stability. We find that Trojan orbits with proper eccentricity around 0.05, libration amplitude of about 80°, and inclination lower than 15° show a slow diffusion in the proper frequency of the longitude of perihelion , which indicates long-term stability. Numerical integration of some of these stable orbits indicates a half-life of about 2.5 Gyr. Orbits with inclination of about 20° are destabilized by a secular resonance with the forcing term 2g6 - g5. At higher inclinations Saturn Trojan orbits are unstable on a short timescale (a few × 105 yr). Applying the frequency map analysis to the numbered Jupiter Trojans, we find that the size of the stability region is much larger for Jupiter Trojans than for Saturn Trojans. Moreover, the diffusion rate is significantly lower, suggesting that the dynamical lifetimes of Jupiter Trojans are considerably longer. The frequency analysis method allows us to separate the proper and forced components of the eccentricity of Trojans. A semianalytical model for secular motion of Saturn Trojans is presented.

Although the nucleus of comet C/2013 A1 (Siding Spring) will safely pass Mars in October 2014, the dust in the coma and tail will more closely approach the planet. Using a dynamical model of comet dust, we estimate the impact fluence. Based on our nominal model no impacts are expected at Mars. Relaxing our nominal model's parameters, the fluence is no greater than ~10^-7 grains/m^2 for grain radii larger than 10 {\mu}m. Mars orbiting spacecraft are unlikely to be impacted by large dust grains, but Mars may receive as many as ~10^7 grains, or ~100 kg of total dust. We also estimate the flux of impacting gas molecules commonly observed in comet comae., Comment: Accepted for publication in Astrophysical Journal Letters. 7 pages, 3 figures, 2 tables

The LISA space mission, designed to monitor low frequency gravitational waves, is also sensitive to passages of asteroids nearby one of its three spacecrafts. We report the expected rate of detections of asteroid passages, using the known catalog of asteroids and a modeled population. The method adopted consists of determining for each known asteroid the critical encounter distance capable of producing a detectable event, and then computing the rate of encounters within this distance. Results are then scaled to the modeled population using its differential distribution in absolute magnitude, correcting for selection effects. We find that an average of 2.0 ± 0.1 events per year at a signal-to-noise ratio of 1 will be detected by LISA, including all the asteroids in the modeled population with absolute magnitude H < 22, roughly equivalent to all asteroids with a diameter larger than 100 m.

The asteroid (101955) Bennu has a heterogeneous internal mass distribution with an underdense center and equatorial bulge., The gravity field of a small body provides insight into its internal mass distribution. We used two approaches to measure the gravity field of the rubble-pile asteroid (101955) Bennu: (i) tracking and modeling the spacecraft in orbit about the asteroid and (ii) tracking and modeling pebble-sized particles naturally ejected from Bennu’s surface into sustained orbits. These approaches yield statistically consistent results up to degree and order 3, with the particle-based field being statistically significant up to degree and order 9. Comparisons with a constant-density shape model show that Bennu has a heterogeneous mass distribution. These deviations can be modeled with lower densities at Bennu’s equatorial bulge and center. The lower-density equator is consistent with recent migration and redistribution of material. The lower-density center is consistent with a past period of rapid rotation, either from a previous Yarkovsky-O’Keefe-Radzievskii-Paddack cycle or arising during Bennu’s accretion following the disruption of its parent body.

The cosmological origin of $\gamma$-ray bursts (GRBs) is now commonly accepted and, according to several models for the central engine, GRB sources should also emit at the same time gravitational waves bursts (GWBs). We have performed two correlation searches between the data of the resonant gravitational wave detector AURIGA and GRB arrival times collected in the BATSE 4B catalog. No correlation was found and an upper limit \bbox{$h_{\text{RMS}} \leq 1.5 \times 10^{-18}$} on the averaged amplitude of gravitational waves associated with $\gamma$-ray bursts has been set for the first time., Comment: 7 pages, 3 figures, submitted to Phys. Rev. D