Radar observations of asteroid 1998 ML14

Abstract— Goldstone and Arecibo delay‐Doppler radar imaging of asteroid 1998 ML 14 shortly after its discovery reveals a 1 km diameter spheroid with prominent topography on one side and subdued topography on the other. The object's radar and optical properties are typical for S‐class near‐Earth asteroids. The gravitational slopes of a shape model derived from the images and assumed to have a uniform density are shallow, exceeding 30° over only 4% of the surface. If 1998 ML14's density distribution is uniform, then its orbital environment is similar to a planetary body with a spheroidal gravitational field and is relatively stable. Integration of a radar‐refined orbit reveals that the 1998 apparition was the asteroid's closest approach to Earth since at least 1100 and until 2283, when it approaches to within 2.4 lunar distances. Outside of that time interval, orbit uncertainties based on the present set of observations preclude reliable prediction.     

Using Chebyshev polynomial interpolation to improve the computational efficiency of gravity models near an irregularly-shaped asteroid

In asteroid rendezvous missions, the dynamical environment near an asteroid's surface should be made clear prior to launch of the mission. However, most asteroids have irregular shapes,which lower the efficiency of calculating their gravitational field by adopting the traditional polyhedral method. In this work, we propose a method to partition the space near an asteroid adaptively along three spherical coordinates and use Chebyshev polynomial interpolation to represent the gravitational acceleration in each cell. Moreover, we compare four different interpolation schemes to obtain the best precision with identical initial parameters. An error-adaptive octree division is combined to improve the interpolation precision near the surface. As an example, we take the typical irregularly-shaped nearEarth asteroid 4179 Toutatis to demonstrate the advantage of this method; as a result, we show that the efficiency can be increased by hundreds to thousands of times with our method. Our results indicate that this method can be applicable to other irregularly-shaped asteroids and can greatly improve the evaluation efficiency.     

Stability of Surface Motion on a Rotating Ellipsoid

The dynamical environment on the surface of a rotating, massive ellipsoid is studied, with applications to surface motion on an asteroid. The analysis is performed using a combination of classical dynamics and geometrical analysis. Due to the small sizes of most asteroids, their shapes tend to differ from the classical spheroids found for the planets. The tri-axial ellipsoid model provides a non-trivial approximation of the gravitational potential of an asteroid and is amenable to analytical computation. Using this model, we study some properties of motion on the surface of an asteroid. We find all the equilibrium points on the surface of a rotating ellipsoid and we show that the stability of these points is intimately tied to the conditions for a Jacobi or MacLaurin ellipsoid of equilibria. Using geometrical analysis we can define global constraints on motion as a function of shape, rotation rate, and density, we find that some asteroids should have accumulation of material at their ends, while others should have accumulation of surface material at their poles. This study has implications for motion of a rover on an asteroid, and for the distribution of natural material on asteroids, and for a spacecraft hovering over an asteroid.     

Determination of asteroid masses from their close encounters with Mars

An obstacle to the asteroid mass determination lies in the difficulty in isolating the gravitational perturbation exerted by a single asteroid on the planets, being strongly correlated and mixed up with those of many other asteroids. This hindrance may be avoided by the method of analysis presented here: an asteroid mass is estimated in correspondence with its close encounters with Mars where the acceleration it induces on the planet can be sufficiently disentangled from those generated by the remaining asteroid masses to calculate. We test this technique in the analysis of range observations to Mars Global Surveyor and Mars Express performed from 1999 to 2007. For this purpose, we adopt the dynamical model of the planetary ephemeris INPOP06 (Fienga et al., 2008), which includes the gravitational influences of the 300 most perturbing asteroids of the Martian orbit. We obtain the solutions of 10 asteroid masses that have the largest effects on this orbit over the period examined: they are generally in good agreement with determinations recently published.     

The role of regolith redistribution in influencing the evolution of the shapes of asteroids

Abstract— ‐Major surface fissures and relatively large‐scale, angular surface irregularities are expected to have been present on many asteroids at early stages in their histories as a byproduct of at least two processes (impact disruption and reassembly into rubble piles for all classes of asteroid and, for carbonaceous chondrite parent bodies, aqueous alteration) which led to the low bulk densities currently being observed for asteroids. However, in all cases where high‐enough resolution images exist, such abrupt, deep irregularities are not observed. We model the spatial redistribution of impact‐generated regolith on an asteroid with an idealized irregular shape to show how the complex gravitational field of such a body will lead to the systematic infilling of deep valleys in the surface. Our analysis emphasizes the high efficiency with which regolith redistribution can act to disguise the internal structures of asteroids with sizes in the 20–100 km range.     

Critical crater diameter and asteroid impact seismology

Abstract— If impact stress reverberation is the primary gradational process on an asteroid at global scales, then the largest undegraded crater records an asteroid's seismological response. The critical crater diameter D_crit is defined as the smallest crater whose formation disrupts all previous craters globally up to its size; it is solved for by combining relationships for crater growth and for stress attenuation. The computation for D_crit gives a simple explanation for the curious observation that small asteroids have only modest undegraded craters, in comparison to their size, whereas large asteroids have giant undegraded craters. D_crit can even exceed the asteroid diameter, in which case all craters are “local” and the asteroid becomes crowded with giant craters. D_crit is the most recent crater to have formed on a blank slate; when it is equated to the measured diameter of the largest undegraded crater on known asteroids, peak particle velocities are found to attenuate with the 1.2–1.3 power of distance—less attenuative than strong shocks, and more characteristic of powerful seismic disturbances. This is to be expected, since global degradation can result from seismic (cm s^?1) particle velocities on small asteroids. Attenuation, as modeled, appears to be higher on asteroids known to be porous, although these are also bodies for which different crater scaling rules might apply.     

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.     

Mutual gravitational potential,force, and torque of a homogeneous polyhedron and an extended body: an application to binary asteroids

Binary systems are quite common within the populations of near-Earth asteroids, main-belt asteroids, and Kuiper belt asteroids. The dynamics of binary systems, which can be modeled as the full two-body problem, is a fundamental problem for their evolution and the design of relevant space missions. This paper proposes a new shape-based model for the mutual gravitational potential of binary asteroids, differing from prior approaches such as inertia integrals, spherical harmonics, or symmetric trace-free tensors. One asteroid is modeled as a homogeneous polyhedron, while the other is modeled as an extended rigid body with arbitrary mass distribution. Since the potential of the polyhedron is precisely described in a closed form, the mutual gravitational potential can be formulated as a volume integral over the extended body. By using Taylor expansion, the mutual potential is then derived in terms of inertia integrals of the extended body, derivatives of the polyhedron’s potential, and the relative location and orientation between the two bodies. The gravitational forces and torques acting on the two bodies described in the body-fixed frame of the polyhedron are derived in the form of a second-order expansion. The gravitational model is then used to simulate the evolution of the binary asteroid (66391) 1999 KW4, and compared with previous results in the literature.     

Accretion of jet streams and formation of asteroids

Our basic view on the formation of asteroids, stated in [1], is that the initial physical and chemical conditions in the asteroid region led to a slow growth of planetesimals in the region and a transfer of accretable matter to the Jupitor region, resulting in the planetesimals stopping at the “half-finished” stage, eventually forming only asteroids and not major planets. In this paper, using the conditions of the nebular disk obtained in that paper and the formula for gravitational instability and regarding the rings resulting from gravitational instability as “jet streams”, we apply the theory of accretion of jet streams to calculate the growth of the planetesimals and discuss the question of the transfer of accretable material, providing further confirmation of our basic view.     

Rosetta target asteroid 2867 Steins: An unusual E‐type asteroid

Abstract— ESA's Rosetta spacecraft will fly by main‐belt asteroid 2867 Steins on September 5, 2008. We obtained new visible wavelength spectra of 2867 Steins on December 19, 2006 (UT), using the Palomar 5 m telescope and the facility Double Spectrograph. Two sets of spectra, taken ～3 h apart, one half of the rotation period for 2867 Steins, show it to be an E‐type asteroid. The asteroid displays a 0.50 μm feature that is considered diagnostic of the E(II) sub‐class, but is deeper than any previously observed E‐type. This feature is most likely due to the presence of oldhamite (CaS) on the asteroid's surface. Also, the observed Steins spectra are far redder than any other known E‐types. There is potential evidence for heterogeneity on hemispheric scales, one side of the asteroid appearing to be significantly redder than the other. No known recovered meteorite sample matches the unusual spectra of 2867 Steins, but the closest analog would be similar to an enstatite achondrite (aubrite).     

Impact origin of the Vesta family

Abstract— The compelling petrographic link (Consolmagno and Drake, 1977; Gaffey, 1983) between basaltic achondrite meteorites and the ～530 km diameter asteroid 4 Vesta has been tempered by a perceived difficulty in launching rocks from this asteroid's surface at speeds sufficient to bring them to Earth (Wasson and Wetherill, 1979) without obliterating Vesta's signature crust. I address this impasse in response to recent imaging (Zellner et al, 1996; Dumas and Hainaut, 1996) of a ～450 km impact basin across Vesta's southern hemisphere (Thomas et al., 1997) and model the basin-forming collision using a detailed two-dimensional hydrocode with brittle fracture including self-gravitational compression (cf., Asphaug and Melosh, 1993). A ～42 km diameter asteroid striking Vesta's basaltic crust (atop a denser mantle and iron core) at 5.4 km/s launches multikilometer fragments up to ～600 m/s without inverting distal stratigraphy, according to the code. This modeling, together with collisional, dynamical, rheological and exposure-age timescales (Marzari et al., 1996; Welten et al., 1996), and observations of V-type asteroids (Binzel and Xu, 1993) suggests a recent (<～1 Ga) impact origin for the Vesta family and a possible Vesta origin for Earth-approaching V-type asteroids (Cruik-shank et al., 1991).     

Problems of origin of asteroids and comets

Abstract— Various hypotheses of the origin of asteroids and comets are briefly discussed. Interaction of planetesimals in the asteroid zone (AZ) with the gas, their perturbations by proto-Jupiter, and sweeping them out by more massive Jupiter zone bodies when they penetrated the AZ are considered. If the gas was turbulent, it could prevent a settling of dust particles to the equatorial plane of the disk and formation of dust condensations due to gravitational instability. Then particles grew by sticking upon collision. Gas moved radially due to turbulent viscosity and its dissipation. Small particles moved more-or-less together with the gas. As a result of gas drag, larger particles and bodies moved relative to the gas in the direction of increasing gas pressure. Gas would remove much of the solid material from the AZ if most bodies larger than a few km disintegrated by collisions into fragments smaller than a few tens of meters. Most of these fragments would then move into the Martian zone, and the small mass of Mars would have no explanation. Resonant perturbations of asteroids by Jupiter are discussed. In the model of a small mass disk they could scan through the asteroid belt due to changes in Jupiter's distance from the Sun that occurred when this planet accreted the gas and ejected the bodies from the solar system. Such a scanning considerably accelerated the removal of asteroids from the AZ. Massive Jupiter zone bodies with large orbital eccentricities that crossed the AZ were probably efficient at sweeping out bodies. Larger bodies increased the random velocities of the remaining asteroids at close encounters to the present values ～ 5 km/s. Restrictions on the runaway growth of giant planets, on the relative velocities of bodies and the disk surface density that follow from the consideration of the origin of the asteroid belt and the cometary cloud are considered.     

Detection by MEGNO of the gravitational resonances between a rotating ellipsoid and a point mass satellite

Nowadays the scientific community considers that more than a third of the asteroids are double. The study of the stability of these systems is quite complex, because of their irregular shapes and tumbling rotations, and requires a full body–full body approach. A particular case is analysed here, when the secondary body is sufficiently small and distant from the primary to be considered as a point mass satellite. Gravitational resonances (between the revolution of the satellite and the rotation of the asteroid) of a small body in fast or slow rotation around a rigid ellipsoid are studied. The same model can be used for the motion of a probe around an irregular asteroid. The gravitational potential induced by the primary body is modelled by the MacMillan potential. The stability of the satellite is measured thanks to the MEGNO indicator (Mean Exponential Growth Factor of Nearby Orbits). We present stability maps in the plane (\fracbd, \fraccd){\left(\frac{b}{d}, \frac{c}{d}\right)} where d, b, and c are the three semi-axes of the ellipsoid shaping the asteroid. Special stable conic-like curves are detected on these maps and explained by an analytical model, based on a simplification of the MacMillan potential for some specific resonances (1 : 1 and 2 : 1). The efficiency of the MEGNO to detect stability is confirmed.     

Periodic Orbits Around a Massive Straight Segment

In this paper, we consider the motion of a particle under the gravitational field of a massive straight segment. This model is used as an approximation to the gravitational field of irregular shaped bodies, such as asteroids, comet nuclei and planets's moons. For this potential, we find several families of periodic orbits and bifurcations. This revised version was published online in July 2006 with corrections to the Cover Date.     

Secular spin dynamics of inner main-belt asteroids

Understanding the evolution of asteroid spin states is challenging work, in part because asteroids have a variety of orbits, shapes, spin states, and collisional histories but also because they are strongly influenced by gravitational and non-gravitational (YORP) torques. Using efficient numerical models designed to investigate asteroid orbit and spin dynamics, we study here how several individual asteroids have had their spin states modified over time in response to these torques (i.e., 951 Gaspra, 60 Echo, 32 Pomona, 230 Athamantis, 105 Artemis). These test cases which sample semimajor axis and inclination space in the inner main belt, were chosen as probes into the large parameter space described above. The ultimate goal is to use these data to statistically characterize how all asteroids in the main belt population have reached their present-day spin states. We found that the spin dynamics of prograde-rotating asteroids in the inner main belt is generally less regular than that of the retrograde-rotating ones because of numerous overlapping secular spin-orbit resonances. These resonances strongly affect the spin histories of all bodies, while those of small asteroids (?40 km) are additionally influenced by YORP torques. In most cases, gravitational and non-gravitational torques cause asteroid spin axis orientations to vary widely over short (?1 My) timescales. Our results show that (951) Gaspra has a highly chaotic rotation state induced by an overlap of the s and s₆ spin-orbit resonances. This hinders our ability to investigate its past evolution and infer whether thermal torques have acted on Gaspra's spin axis since its origin.     

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.     

The shape of asteroids: Theoretical considerations

Theoretical consideration and observations by other authors indicate that small asteroids are capable of maintaining irregular shapes, notably the shape of a cigar and even of a dumb-bell. This paper presents a model which describes the changes in the shape of an asteroid due to collisions of smaller objects (meteoroids) with the asteroid. The following assumptions must be approximately valid: (1) collisions are not uncommon; (2) collisions between a (relatively) large asteroid and small objects (meteroids) are more common than collisions between asteroids; (3) the cumulative probability of the collision of a meteoroid on a point on the surface of an asteroid is proportional to the zenith angle of the horizon as seen by that point; (4) obliquities of all but the major asteroids are random, so that there is not a preferred side on which collisions occur; (5) a considerable percentage of collision ejecta achieves escape velocity; and (6) the rate of erosion of each point on the surface of an asteroid is proportional to the cumulative probability of collision.Generalized conclusions that are obtained from the computer running of the model indicate that both cigars and dumb-bells are possible outcomes. Sharp corners are smoothed away, the radius of curvature of rounded surfaces increases to the point of going from convexity to concavity, and flat surfaces develop into gentle concavities.Collisions of an asteroid with an object of sufficient size such that the impact causes the breakage of the asteroid or the formation of a large crater, are not discussed in this paper. Previous work, however, suggests that the crater will undergo geomorphological changes of different geometry than a similar crater on the Moon.     

Determining asteroid spin states using radar speckles

Knowing the shapes and spin states of near-Earth asteroids is essential to understanding their dynamical evolution because of the Yarkovsky and YORP effects. Delay-Doppler radar imaging is the most powerful ground-based technique for imaging near-Earth asteroids and can obtain spatial resolution of <10 m, but frequently produces ambiguous pole direction solutions. A radar echo from an asteroid consists of a pattern of speckles caused by the interference of reflections from different parts of the surface. It is possible to determine an asteroid’s pole direction by tracking the motion of the radar speckle pattern. Speckle tracking can potentially measure the poles of at least several radar targets each year, rapidly increasing the available sample of NEA pole directions. We observed the near-Earth asteroid 2008 EV5 with the Arecibo planetary radar and the Very Long Baseline Array in December 2008. By tracking the speckles moving from the Pie Town to Los Alamos VLBA stations, we have shown that EV5 rotates retrograde. This is the first speckle detection of a near-Earth asteroid.     

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...