Energy and Stress Distributions in Ellipsoids

A closed form solution for a uniform, isotropic, homogenous, rotating, and self-gravitating solid ellipsoid is analyzed as a function of its material properties and angular momentum. This solution recovers the classical results for an incompressible material, namely that Maclaurin and Jacobi ellipsoids minimize the total strain energy of an ellipsoid. As the solid becomes compressible we find that Maclaurin-type spheroids are energetically preferred over all relevant values of angular momentum, although the gradient toward these spheroids is weak, at best. Compressibility allows the weak minima to encompass most observed asteroid shapes.Using this solution, a simple failure criterion of maximum principal stress is examined. Under this failure criterion, an ellipsoid rotating at a sufficiently rapid rate can have positive stress on the periphery and in the polar regions. Contours for this failure theory are compared with estimated asteroid rotation rates and ellipsoidal shape estimates. For compressible materials there is surprisingly good correspondence for such a simple theory and criterion, with the failure curve delimiting a demarcation that few observed asteroids cross.This research has implications for the shapes and distortions of rubble pile asteroids. In particular, the theory gives insight into the internal stress field and the effects of energy dissipation in an asteroid after it has been boosted into a nonminimum energy configuration due to an impact event or a close flyby with a planet. Internally there are double-lobed compressive stress regions reminiscent of the external shape of Kleopatra.     

Estimation of statistical geometrical properties of the surface of asteroids from simulations

In order to evaluate the scientific feedback of a spaceborne radar in the frame of future space missions towards the asteroids, we present a method able to calculate mono-dimensional or two-dimensional simulations of the surface of any asteroid, or of the Moon.A first set of results related to statistical geometrical properties of the surface, i.e. height and slope distributions, etc..., is given. Discussion shows that these results are in good agreement with observational data obtained from Earth for the Moon and for a few asteroids. In particular, we find r.m.s. slopes much greater on big asteroids than on the Moon.     

Orbits and manifolds near the equilibrium points around a rotating asteroid

We study the orbits and manifolds near the equilibrium points of a rotating asteroid. The linearised equations of motion relative to the equilibrium points in the gravitational field of a rotating asteroid, the characteristic equation and the stable conditions of the equilibrium points are derived and discussed. First, a new metric is presented to link the orbit and the geodesic of the smooth manifold. Then, using the eigenvalues of the characteristic equation, the equilibrium points are classified into 8 cases. A theorem is presented and proved to describe the structure of the submanifold as well as the stable and unstable behaviours of a massless test particle near the equilibrium points. The linearly stable, the non-resonant unstable, and the resonant equilibrium points are discussed. There are three families of periodic orbits and four families of quasi-periodic orbits near the linearly stable equilibrium point. For the non-resonant unstable equilibrium points, there are four relevant cases; for the periodic orbit and the quasi-periodic orbit, the structures of the submanifold and the subspace near the equilibrium points are studied for each case. For the resonant equilibrium points, the dimension of the resonant manifold is greater than 4, and we find at least one family of periodic orbits near the resonant equilibrium points. As an application of the theory developed here, we study relevant orbits for the asteroids 216 Kleopatra, 1620 Geographos, 4769 Castalia and 6489 Golevka.     

Dust motions in quasi-statically charged binary asteroid systems

In this paper, we discuss dust motion and investigate possible mass transfer of charged particles in a binary asteroid system, in which the asteroids are electrically charged due to solar radiation. The surface potential of the asteroids is assumed to be a piecewise function, with positive potential on the sunlit half and negative potential on the shadow half. We derive the nonautonomous equations of motion for charged particles and an analytic representation for their lofting conditions. Particle trajectories and temporary relative equilibria are examined in relation to their moving forbidden regions, a concept we define and discuss. Finally, we use a Monte Carlo simulation for a case study on mass transfer and loss rates between the asteroids.     

Rotational fission of contact binary asteroids

The energetics and dynamics of contact binary asteroids as they approach and pass the rotational fission limit is studied. We presume that the asteroids are subject to an external torque, such as from the YORP effect, that increases their angular momentum. Furthermore, we assume the asteroids can be described by a fairly minimal model comprised of a sphere and ellipsoid resting on each other. The minimum energy configurations for contact binary asteroids at different levels of angular momentum are computed and discussed. We find distinct transitions between different configurations as the angular momentum of the system is increased. These indicate that rapidly rotating contact binary asteroids may seek out clearly different relative configurations than slowly rotating systems. We find a single end state of the systems prior to rotational fission, and distinct dynamical outcomes as a function of mass distribution and shape when the rotational fission limit is exceeded. Our theoretical results agree qualitatively with observed properties of near-Earth asteroids, and can be used to help explain the spin-rate barrier, contact binaries, and the observed morphology of most NEO binaries.     

Orbital dynamics and equilibrium points around an asteroid with gravitational orbit–attitude coupling perturbation

The strongly perturbed dynamical environment near asteroids has been a great challenge for the mission design. Besides the non-spherical gravity, solar radiation pressure, and solar tide, the orbital motion actually suffers from another perturbation caused by the gravitational orbit–attitude coupling of the spacecraft. This gravitational orbit–attitude coupling perturbation (GOACP) has its origin in the fact that the gravity acting on a non-spherical extended body, the real case of the spacecraft, is actually different from that acting on a point mass, the approximation of the spacecraft in the orbital dynamics. We intend to take into account GOACP besides the non-spherical gravity to improve the previous close-proximity orbital dynamics. GOACP depends on the spacecraft attitude, which is assumed to be controlled ideally with respect to the asteroid in this study. Then, we focus on the orbital motion perturbed by the non-spherical gravity and GOACP with the given attitude. This new orbital model can be called the attitude-restricted orbital dynamics, where restricted means that the orbital motion is studied as a restricted problem at a given attitude. In the present paper, equilibrium points of the attitude-restricted orbital dynamics in the second degree and order gravity field of a uniformly rotating asteroid are investigated. Two kinds of equilibria are obtained: on and off the asteroid equatorial principal axis. These equilibria are different from and more diverse than those in the classical orbital dynamics without GOACP. In the case of a large spacecraft, the off-axis equilibrium points can exist at an arbitrary longitude in the equatorial plane. These results are useful for close-proximity operations, such as the asteroid body-fixed hovering.     

The angular momenta of solar system bodies: Implications for asteroid strengths

The angular momentum H is plotted versus mass M for the planets and for all asteroids with known rotation rates and shapes, primarily taken from D. C. McAdoo and J. A. Burns [Icarus18, 285–293 (1973)]. An asteroid's angular momentum is derived from its rotation rate as determined by the period of its lightcurve, its shape as indicated by the lightcurve amplitude, and where possible its size as given by polarimetry or radiometry. The asteroid is assumed to be rotating about its axis of maximum moment of inertia. As previously found by F. F. Fish [Icarus7, 251–256 (1967]) and W. K. Hartmann and S. M. Larson [Icarus7, 257–260 (1967)], H is approximately proportional to $\text{M}{}^{\mathrm{<mtext>5</mtext><mtext>3</mtext>}}$, which shows that the asteroids and most planets spin with nearly the same rate. The very smallest asteroids on the plot deviate from the above reaction, usually containing excess angular momentum. This suggests that collisions have transferred substantial angular momentum to the smallest asteroids, perhaps causing their internal stress states to be substantially modified by centrifugal effects.The forces produced by gravitation are then compared to centrifugal effects for a rotating, triaxial ellipsoid of density 3 g cm^?3. For all asteroids with known properties the gravitational attraction is shown to be larger than the centrifugal acceleration of a particle on the surface: thus the observed asteroid regoliths are gravitationally bound. Poisson's equation for the gravitational potential is investigated and it is shown by mathematical and physical arguments that any arbitrarily shaped ellipsoid with the attractive surface force boundary condition found above will have only attractive internal forces. Thus the internal stress states in asteroids are always compressive so that asteroids could be internally fractured without losing their integrity.     

The resonant structure of Jupiter's Trojan asteroids – I. Long-term stability and diffusion

We study the global dynamics of the jovian Trojan asteroids by means of the frequency map analysis. We find and classify the main resonant structures that serve as skeleton of the phase space near the Lagrangian points. These resonances organize and control the long-term dynamics of the Trojans. Besides the secondary and secular resonances, that have already been found in other asteroid sets in mean motion resonance (e.g. main belt, Kuiper belt), we identify a new type of resonance that involves secular frequencies and the frequency of the great inequality, but not the libration frequency. Moreover, this new family of resonances plays an important role in the slow transport mechanism that drives Trojans from the inner stable region to eventual ejections. Finally, we relate this global view of the dynamics with the observed Trojans, identify the asteroids that are close to these resonances and study their long-term behaviour.     

Flora小行星族自转特性研究

小行星族作为灾变碰撞的残留物,其基础物理性质提供了其母体以及后续演化信息.其中轨道以及自转特性分别反映了Yarkovsky效应以及Yarkovsky-O’Keefe-Radzievskii-Paddack效应(YORP效应)对于小行星族演化的影响.基于小行星光变数据库(Asteroid Lightcurve Database),通过对Flora小行星族自转速率分布进行研究,发现随着直径减小,族成员自转速率倾向于主要集中在3–5 d^-1的范围内.同时,可以注意到Flora小行星族整体表现出更倾向于顺行自转状态的现象,但对于轨道半长轴小于2.2au的成员来说,其顺行自转与逆行自转状态成员数目比接近于近地小行星中顺逆行自转状态源1:3的比例;此外,对于轨道半长轴大于2.2 au且具有顺行自转状态的部分族成员,在轨道半长轴-绝对星等分布中表现出聚集现象,并在聚集区域中有9颗成员展现出类似Slivan状态特征.     

Impact evolution of asteroid shapes: 1. random mass redistribution

We explore whether the cumulative effect of small-scale meteoroid bombardment can drive asteroids into nonaxisymmetric shapes comparable to those of known objects (elongated prolate forms, twin-lobed binaries, etc). We simulate impact cratering as an excavation followed by the launch, orbit, and reimpact of ejecta. Orbits are determined by the gravity and rotation of the evolving asteroid, whose shape and spin change as cratering occurs repeatedly. For simplicity we consider an end-member evolution where impactors are all much smaller than the asteroid and where all ejecta remain bound. Given those assumptions, we find that cumulative small impacts on rotating asteroids lead to oblate shapes, irrespective of the chosen value for angle of repose or for initial angular momentum. The more rapidly a body is spinning, the more flattened the outcome, but oblateness prevails. Most actual asteroids, by contrast, appear spherical to prolate. We also evaluate the timescale for reshaping by small impacts and compare it to the timescale for catastrophic disruption. For all but the steepest size distributions of impactors, reshaping from small impacts takes more than an order of magnitude longer than catastrophic disruption. We conclude that small-scale cratering is probably not dominant in shaping asteroids, unless our assumptions are naive. We believe we have ruled out the end-member scenario; future modeling shall include angular momentum evolution from impacts, mass loss in the strength regime, and craters with diameters up to the disruption threshold. The ultimate goal is to find out how asteroids get their shapes and spins and whether tidal encounters in fact play a dominant role.     

The global effects of impact-induced seismic activity on fractured asteroid surface morphology

Impact-induced seismic vibrations have long been suspected of being an important surface modification process on small satellites and asteroids. In this study, we use a series of linked seismic and geomorphic models to investigate the process in detail. We begin by developing a basic theory for the propagation of seismic energy in a highly fractured asteroid, and we use this theory to model the global vibrations experienced on the surface of an asteroid following an impact. These synthetic seismograms are then applied to a model of regolith resting on a slope, and the resulting downslope motion is computed for a full range of impactor sizes. Next, this computed downslope regolith flow is used in a morphological model of impact crater degradation and erasure, showing how topographic erosion accumulates as a function of time and the number of impacts. Finally, these results are applied in a stochastic cratering model for the surface of an Eros-like body (same volume and surface area as the asteroid), with craters formed by impacts and then erased by the effects of superposing craters, ejecta coverage, and seismic shakedown. This simulation shows good agreement with the observed 433 Eros cratering record at a Main Belt exposure age of 400±200 Myr, including the observed paucity of small craters. The lowered equilibrium numbers (loss rate = production rate) for craters less than ∼100 m in diameter is a direct result of seismic erasure, which requires less than a meter of mobilized regolith to reproduce the NEAR observations. This study also points to an upper limit on asteroid size for experiencing global, surface-modifying, seismic effects from individual impacts of about 70-100 km (depending upon asteroid seismic properties). Larger asteroids will experience only localized (regional) seismic effects from individual impacts.     

The strength of regolith and rubble pile asteroids

We explore the hypothesis that, due to small van der Waals forces between constituent grains, small rubble pile asteroids have a small but nonzero cohesive strength. The nature of this model predicts that the cohesive strength should be constant independent of asteroid size, which creates a scale dependence with relative strength increasing as size decreases. This model counters classical theory that rubble pile asteroids should behave as scale‐independent cohesionless collections of rocks. We explore a simple model for asteroid strength that is based on these weak forces, validate it through granular mechanics simulations and comparisons with properties of lunar regolith, and then explore its implications and ability to explain and predict observed properties of small asteroids in the NEA and Main Belt populations, and in particular of asteroid 2008 TC₃. One conclusion is that the population of rapidly rotating asteroids could consist of both distributions of smaller grains (i.e., rubble piles) and of monolithic boulders.     

Atlas of the mean motion resonances in the Solar System

The aim of this work is to present a systematic survey of the strength of the mean motion resonances (MMRs) in the Solar System. We know by applying simple formulas where the resonances with the planets are located but there is no indication of the strength that these resonances have. We propose a numerical method for the calculation of this strength and we present an atlas of the MMRs constructed with this method. We found there exist several resonances unexpectedly strong and we look and find in the small bodies population several bodies captured in these resonances. In particular in the inner Solar System we find one asteroid in the resonance 6:5 with Venus, five asteroids in resonance 1:2 with Venus, three asteroids in resonance 1:2 with Earth and six asteroids in resonance 2:5 with Earth. We find some new possible co-orbitals of Earth, Mars, Saturn, Uranus and Neptune. We also present a discussion about the behavior of the resonant disturbing function and where the stable equilibrium points can be found at low and high inclination resonant orbits.     

Determination of Large Asteroid Masses by the Dynamical Method

Masses of 19 asteroids have been determined from the analysis of their gravitational effect on the motion of perturbed bodies. The following asteroids were selected as perturbed bodies: (1) those which had single close encounters with the perturbing asteroid; (2) those whose mean motion was in a 1 : 1 commensurability with that of the perturber and which had close or moderate recurrent encounters with the perturber. The perturber mass was determined from observations of several tens of perturbed asteroids that were selected from these two groups. The selection criterion was the error of the mass determined from observations of only one asteroid. Positional observations of the asteroids on the interval 1900–2002 were used. The masses were determined with errors by an order-half an order of magnitude smaller than the masses found. The results are compared with those of other authors.     

Capillary action in a crack on the surface of asteroids with an application to 433 Eros

Some asteroids contain water ice, and a space mission landing on an asteroid may take liquid to the surface of the asteroid. Gas pressure is very weak on the surface of asteroids. Here we consider the capillary action in a crack on the surface of irregular asteroids. The crack is modeled as a capillary which has a fixed radius. An asteroid's irregular gravitational potential influences the height of the liquid in the capillary. The height of the liquid in the capillary on the surface of such asteroids is derived from the asteroid's irregular gravitational potential. Capillary mechanisms are expected to produce an inhomogeneaous distribution of emergent liquid on the surface. This result is applied to asteroid 433 Eros, which has an irregular, elongated, and concave shape. Two cases are considered: (1) we calculate the height of the liquid in the capillary when the direction of the capillary is perpendicular to the local surface of the asteroid; (2) we calculate the height of the liquid in the capillary when the direction of the capillary is parallel to the vector from the center of mass to the surface position. The projected height in the capillary on the local surface of the asteroid seems to depend on the assumed direction of the capillary.     

Potential generated by a massive inhomogeneous straight segment

The discoveries of binary asteroids have opened an important new field of research concerning the calculation of potential generated by irregular bodies.Some of them have an elongated shape.A simple model to describe the motion of a test particle in that kind of potential requires consideration of a finite homogeneous straight segment.We construct this model by adding an inhomogeneous distribution of mass. To be consistent with the geometrical shape of the asteroid,we explore a parabolic profile of the dens...     

Evidence for the insignificance of ordinary chondritic material in the asteroid belt

Abstract— We review the meteoritical and astronomical literature to answer the question: What is the evidence for the importance of ordinary chondritic material to the composition of the asteroid belt? From the meteoritical literature, we find that currently (1) our meteorite collections sample at least 135 different asteroids; (2) out of 25+ chondritic meteorite parent bodies, 3 are (by definition) ordinary chondritic; (3) out of 14 chondritic grouplets and unique chondrites, 11 are affiliated with a carbonaceous group/clan of chondrites; (4) out of 24 differentiated groups of meteorites, only the HE iron meteorites clearly formed from ordinary chondritic precursor material; (5) out of 12 differentiated grouplets and unique differentiated meteorites, 8 seem to have had carbonaceous chondritic precursors; (6) a high frequency of carbonaceous clasts in ordinary chondritic breccias suggests that ordinary chondrites have been embedded in a swarm of carbonaceous material. The rare occurrence (only one example) of ordinary chondritic clasts in carbonaceous chondritic breccias indicates that ordinary chondritic material has not been widespread in the asteroid belt; (7) cosmic spherules, micrometeorites, and stratospheric interplanetary dust particles—believed to represent a less biased sampling of asteroidal material—show that only a very small fraction (less than ～1%) of asteroidal dust has an ordinary chondritic composition. From the astronomical literature, we find that currently (8) spectroscopic surveys of the main asteroid belt are finding more and more nonordinary chondritic primitive material in the inner main belt; (9) the increase in spectroscopic data has increased the inferred mineralogical diversity of main belt asteroids; and (10) no ordinary chondritic asteroids have been directly observed in the main belt. These lines of evidence strongly suggest a scenario in which ordinary chondritic asteroids were never abundant in the main belt. The S-type asteroids may currently be primarily differentiated, but the precursor material is more likely to have been carbonaceous chondritic, not ordinary chondritic. Historically, carbonaceous material could have dominated the entire main belt. This could explain the presence in the inner main belt of asteroids linked to the primitive carbonaceous chondrites, and the absence of asteroids linked to the ordinary chondrites. The implications of this scenario for the asteroid heating mechanism(s) are briefly discussed.     

Physical characteristics of Hayabusa target Asteroid 25143 Itokawa

In March 2001, the Hayabusa spacecraft target, Asteroid 25143 Itokawa, made its final close approach to Earth prior to the spacecraft's launch. We carried out an extensive observing campaign from January to September 2001 to better characterize this near-Earth asteroid. Global physical properties of the surface of Itokawa were characterized by analyzing its photometric properties and behavior. Results included here capitalize on analysis of broadband photometric observations taken with a number of telescopes, instruments, and observers. We employed a Hapke model to estimate the surface roughness, single particle scattering albedo, single particle scattering characteristics, phase integral, and geometric and bond albedo. We find that this asteroid has a higher geometric albedo than average main belt S-class asteroids; this is consistent with results from other observers. The broadband colors of Itokawa further support evidence that this is an atypical S-class asteroid. Broadband colors show spectral characteristics more typically found on large-diameter main-belt asteroids believed to be space-weathered, suggesting the surface of this small diameter, near-Earth asteroid could likewise be space-weathered.     

High‐calcium pyroxene as an indicator of igneous differentiation in asteroids and meteorites

Abstract— Our analyses of high quality spectra of several S‐type asteroids (17 Thetis, 847 Agnia, 808 Merxia, and members of the Agnia and Merxia families) reveal that they include both low‐ and high‐calcium pyroxene with minor amounts of olivine (<20%). In addition, we find that these asteroids have ratios of high‐calcium pyroxene to total pyroxene of >～0.4. High‐calcium pyroxene is a spectrally detectable and petrologically important indicator of igneous history and may prove critical in future studies aimed at understanding the history of asteroidal bodies. The silicate mineralogy inferred for Thetis and the Merxia and Agnia family members requires that these asteroids experienced igneous differentiation, producing broadly basaltic surface lithologies. Together with 4 Vesta (and its smaller “Vestoid” family members) and the main‐belt asteroid 1489 Magnya, these new asteroids provide strong evidence for igneous differentiation of at least five asteroid parent bodies. Based on this analysis of a small subset of the near‐infrared asteroid spectra taken to date with SpeX at the NASA IRTF, we expect that the number of known differentiated asteroids will increase, consistent with the large number of parent bodies inferred from studies of iron meteorites.