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.     

Observations of asteroid occultations by the trailed-image method

The method of trailed CCD images for observations of asteroid occultations is described. This method was used to observe 9 asteroid occupations at the Lisnyky observational station in 2006 with the telescope AZT-8 (D= 0.7m and F= 2.8m) equipped by the CCD ST-8 XME. In the case of occultation of the star TYC 0587-00209-1U by the asteroid 76 Freia in November 4, 2006, the distance between the asteroid center and the star, as well as the time of asteroid occultation were determined. The size of asteroid 76 Freia is determined assuming that its shape is spherically symmetric. In other cases, the minimal distances between the asteroid center and the star are determined. The method makes it possible to observe asteroid occultations with high time resolution.     

Extended Schubart Averaging

The purpose of this paper is the presentation of an integrator for the average motion of an asteroid in mean motion commensurability with Jupiter. The program is valid for any (p+q)/p mean motion commensurability (except whenq=0) and uses a double precision version of DE (Shampine and Gordon 1975) as propagator. The averaged equations of motion of the asteroid are evaluated in a non-singular way for any value of the eccentricities and the inclinations and the orbit of Jupiter is described by the most important terms in Longstop 1B (Nobiliet al. 1989). This integrator can be considered as an extension of the well known Schubart Averaging (Schubart 1978) in which Jupiter is moving on a fixed ellipse.     

Dynamical parameters of spacecraft motion near small celestial body

The paper considers how a spacecraft can be put into orbit around a small asteroid to function as its artificial moon. We study the general behavior of perturbations that affect the current coordinates of an orbiting spacecraft and estimate the perturbations caused by the main perturbing factors, i.e., (1) the irregular shape of an asteroid and (2) celestial bodies of the Solar System. With specific orbital parameters, a long-term targeted operation of a spacecraft can be actualized in a mission to the asteroid Apophis where the spacecraft will carry a radio beacon transponder.     

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).     

The OSIRIS‐REx target asteroid (101955) Bennu: Constraints on its physical,geological, and dynamical nature from astronomical observations

We review the results of an extensive campaign to determine the physical, geological, and dynamical properties of asteroid (101955) Bennu. This investigation provides information on the orbit, shape, mass, rotation state, radar response, photometric, spectroscopic, thermal, regolith, and environmental properties of Bennu. We combine these data with cosmochemical and dynamical models to develop a hypothetical timeline for Bennu's formation and evolution. We infer that Bennu is an ancient object that has witnessed over 4.5 Gyr of solar system history. Its chemistry and mineralogy were established within the first 10 Myr of the solar system. It likely originated as a discrete asteroid in the inner Main Belt approximately 0.7–2 Gyr ago as a fragment from the catastrophic disruption of a large (approximately 100‐km), carbonaceous asteroid. It was delivered to near‐Earth space via a combination of Yarkovsky‐induced drift and interaction with giant‐planet resonances. During its journey, YORP processes and planetary close encounters modified Bennu's spin state, potentially reshaping and resurfacing the asteroid. We also review work on Bennu's future dynamical evolution and constrain its ultimate fate. It is one of the most Potentially Hazardous Asteroids with an approximately 1‐in‐2700 chance of impacting the Earth in the late 22nd century. It will most likely end its dynamical life by falling into the Sun. The highest probability for a planetary impact is with Venus, followed by the Earth. There is a chance that Bennu will be ejected from the inner solar system after a close encounter with Jupiter. OSIRIS‐REx will return samples from the surface of this intriguing asteroid in September 2023.     

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.     

Orbit Determination of the Asteroid (469219) Kamoòalewa and Its Error Analysis

As an Earth co-orbital asteroid, (469219) Kamoòalewa is a near earth object (NEO) with high value of research, and one of the targets explored by the first Chinese asteroid exploration mission. Given its orbit characteristics, we build a refined dynamical model for this asteroid, in which the effects induced by nonspherical gravitational fields of the Sun, the Earth, and the Moon are combined. On the basis of the dynamical model of the asteroid (469219) Kamoòalewa, its orbit is determined with optical data from 2004 to 2018 available on the Minor Planet Center (MPC) database. The root mean square error of post-fit residuals is about 0.2 arc second (comparable with that of the Jet Propulsion Laboratory (JPL)/Horizons), and the post-fit residuals of optical observations in 2004 are decreased. At the end, we implement error analysis on the asteroid (469219) Kamoòalewa's orbit in detail, and also predict its orbit error at the time interval between 2020 and 2025.     

On the bulk density of the M-type asteroid 16 Psyche

Recent estimates of the bulk density of the largest M-type asteroid 16 Psyche (1.4 and 1.8 g/cm³) seem to be too low for asteroids of this type. The interpretation of such low densities for the asteroid 16 Psyche with its increased metal content led to estimates of its macroporosity of 70%. In the present paper, it has been shown that the extremely low density estimates are caused primarily by the usage of a very high value of the IRAS diameter of the asteroid (D = 264 km, which corresponds to an IRAS albedo of 0.10). The application of the more accurate polarimetric albedo (0.170) and diameter (213 km) of Psyche results in a bulk density of the asteroid of 3.3 ± 0.7 g/cm³. For a moderate asteroid macroporosity of 30–40%, this density even agrees with the 50% metal content and, therefore, removes both the contradiction with the radar data and the problems of the very low density and unlikely high porosity of the asteroid 16 Psyche.     

A Research on the Imaging Strategy and Imaging Simulation of Toutatis in the Chang’e-2 Flyby Mission

For the Chang’e-2 extended mission of asteroid exploration, the illumination conditions for imaging the asteroid Toutatis are calculated in this paper according to the orbital parameters of both the Chang’e-2 detector and the asteroid, as well as the incident angles of sunlight. On this basis, it is suggested to take photographs after flyby, and the orientation of the camera's optical axis in the coordinate system deflned by Earth's mean equator and equinox at J2000.0 is proposed to be (118.02°, 22.03°). Based on the shape model of Toutatis determined by the foreign radar data, the orientation of the asteroid in the inertial space is calculated at the rendezvous time. Using the Oren-Nayar diffuse-reflection model and the relative positions among the sun, the asteroid, and the detector, together with the cameras orientation, the imaging simulations are performed on the starry sky background respectively at the distances of 300 km, 500 km, and 1000 km from the asteroid after flyby. The results of simulations are verified further by the optical images of Toutatis obtained in the mission.     

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.     

Space weathering and the interpretation of asteroid reflectance spectra

Lunar-style space weathering is well understood, but cannot be extended to asteroids in general. The two best studied Asteroids (433 Eros and 243 Ida) exhibit quite different space weathering styles, and neither exhibits lunar-style space weathering. It must be concluded that at this time the diversity and mechanisms of asteroid space weathering are poorly understood. This introduces a significant unconstrained variable into the problem of analyzing asteroid spectral data. The sensitivity of asteroid surface material characterizations to space weathering effects - whatever their nature - is strongly dependent upon the choice of remote sensing methodology. The effects of space weathering on some methodologies such as curve matching are potentially devastating and at the present time essentially unmitigated. On other methodologies such as parametric analysis (e.g., analyses based on band centers and band area ratios) the effects are minimal. By choosing the appropriate methodology(ies) applied to high quality spectral data, robust characterizations of asteroid surface mineralogy can be obtained almost irrespective of space weathering. This permits sophisticated assessments of the geologic history of the asteroid parent bodies and of their relationships to the meteorites. Investigations of the diversity of space weathering processes on asteroid surfaces should be a fruitful area for future efforts.     

Dynamics of rotationally fissioned asteroids: Source of observed small asteroid systems

We present a model of near-Earth asteroid (NEA) rotational fission and ensuing dynamics that describes the creation of synchronous binaries and all other observed NEA systems including: doubly synchronous binaries, high-e binaries, ternary systems, and contact binaries. Our model only presupposes the Yarkovsky-O’Keefe-Radzievskii-Paddack (YORP) effect, “rubble pile” asteroid geophysics, and gravitational interactions. The YORP effect torques a “rubble pile” asteroid until the asteroid reaches its fission spin limit and the components enter orbit about each other (Scheeres, D.J. [2007]. Icarus 189, 370-385). Non-spherical gravitational potentials couple the spin states to the orbit state and chaotically drive the system towards the observed asteroid classes along two evolutionary tracks primarily distinguished by mass ratio. Related to this is a new binary process termed secondary fission - the secondary asteroid of the binary system is rotationally accelerated via gravitational torques until it fissions, thus creating a chaotic ternary system. The initially chaotic binary can be stabilized to create a synchronous binary by components of the fissioned secondary asteroid impacting the primary asteroid, solar gravitational perturbations, and mutual body tides. These results emphasize the importance of the initial component size distribution and configuration within the parent asteroid. NEAs may go through multiple binary cycles and many YORP-induced rotational fissions during their approximately 10 Myr lifetime in the inner Solar System. Rotational fission and the ensuing dynamics are responsible for all NEA systems including the most commonly observed synchronous binaries.     

小行星(469219) Kamo`oalewa轨道的确定与误差分析

作为一颗与地球共轨道的小行星,(469219)Kamo'oalewa是一个具有很高研究价值的近地小天体,也是中国首次小行星探测计划的目标天体之一.针对其轨道特性,建立了兼顾太阳、地球和月球非球形引力作用的小行星动力学模型.并在该模型的基础上,利用国际小行星中心(Minor Planet Center,MPC)提供的2004|2018年间的光学观测数据对该小行星的轨道进行确定.拟合后观测残差的均方根误差约为0:2″(与美国喷气推进实验室的Horizons在线历表系统相当),其中2004年期间数据的观测残差有所改进.最后,对小行星(469219)Kamo'oalewa的轨道误差进行了详细分析,并预报了2020-2025年期间该小行星的轨道误差.     

Karin cluster formation by asteroid impact

Insights into collisional physics may be obtained by studying the asteroid belt, where large-scale collisions produced groups of asteroid fragments with similar orbits and spectra known as the asteroid families. Here we describe our initial study of the Karin cluster, a small asteroid family that formed 5.8±0.2 Myr ago in the outer main belt. The Karin cluster is an ideal ‘natural laboratory’ for testing the codes used to simulate large-scale collisions because the observed fragments produced by the 5.8-Ma collision suffered apparently only limited dynamical and collisional erosion. To date, we have performed more than 100 hydrocode simulations of impacts with non-rotating monolithic parent bodies. We found good fits to the size-frequency distribution of the observed fragments in the Karin cluster and to the ejection speeds inferred from their orbits. These results suggest that the Karin cluster was formed by a disruption of an ≈33-km-diameter asteroid, which represents a much larger parent body mass than previously estimated. The mass ratio between the parent body and the largest surviving fragment, (832) Karin, is ≈0.15-0.2, corresponding to a highly catastrophic event. Most of the parent body material was ejected as fragments ranging in size from yet-to-be-discovered sub-km members of the Karin cluster to dust grains. The impactor was ≈5.8 km across. We found that the ejections speeds of smaller fragments produced by the collision were larger than those of the larger fragments. The mean ejection speeds of >3-km-diameter fragments were . The model and observed ejection velocity fields have different morphologies perhaps pointing to a problem with our modeling and/or assumptions. We estimate that ∼5% of the large asteroid fragments created by the collision should have satellites detectable by direct imaging (separations larger than 0.1 arcsec). We also predict a large number of ejecta binary systems with tight orbits. These binaries, located in the outer main belt, could potentially be detected by lightcurve observations. Hydrocode modeling provides important constraints on the interior structure of asteroids. Our current work suggests that the parent asteroid of the Karin cluster may have been an unfractured (or perhaps only lightly fractured) monolithic object. Simulations of impacts into fractured/rubble pile targets were so far unable to produce the observed large gap between the first and second largest fragment in the Karin cluster, and the steep slope at small sizes (≈6.3 differential index). On the other hand, the parent asteroid of the Karin cluster was produced by an earlier disruptive collision that created the much larger, Koronis family some 2-3 Gyr ago. Standard interpretation of hydrocode modeling then suggests that the parent asteroid of the Karin cluster should have been formed as a rubble pile from Koronis family debris. We discuss several solutions to this apparent paradox.     

On the prevention of a possible collision of asteroid Apophis with the Earth

Currently, there is some positive probability of a collision of the asteroid Apophis with the Earth in 2036. In this study, the problem of preventing the collision by correcting the asteroid’s orbit is examined. The characteristics of the impulsive correction are investigated, as well as the ways of its implementation by kinetic and nuclear impacts. Impulsive and weak effects are compared. Weak effects leading to slow changes in the asteroid’s orbit are considered to be more usable because of the potentially higher accuracy of this correction. The characteristics of the gravitational effect of the asteroid by a special spacecraft (SC) kept by its control jet engines at a certain point near the asteroid and gravitationally perturbing the motion of Apophis are analyzed. The change in the perigee radius of the Apophis orbit in 2036 and the SC mass consumption are examined as functions of the effect duration, the SC mass, its distance to the asteroid, the start time of the correction, and the velocity of the SC engine exhaust jet.     

First lightcurve observations and rotation of minor planet 127 Johanna

Photoelectric observations of the minor planet 127 Johanna were made in the UBV (RI)_c photometric system during its apparition in 1991 at the Piszkéstetõ mountain-station of Konkoly Observatory from August to December, when it showed a brightness variation with an amplitude of about 0.2 magnitude. The derived H, G values in the two-parameter magnitude system in V are 8.459 ± 0.013 and 0.114 ± 0.020, respectively. The determined V linear phase coefficient is of 0.036 ± 0.001 (mag/deg). The value of G and the observed values of color indices (U-B), (B-V) confirm that this asteroid belongs to the C taxonomic class as it was previously classified. The estimated effective diameter is between 96 and 118 km if the assumed V geometric albedo is of 0.06 and 0.04, respectively. The available data suggest a pure principal axis rotation mode. The mean synodic rotational period of the asteroid 127 Johanna is 6.94 ± 0.29 h. The uncertainty is due to the changing of aspect geometry. This value of the synodic rotation period means that this asteroid has an intermediate rotation period. The sense of rotation is prograde as indicated by the temporal evolution of the time derivative of the ecliptic longitude of the phase angle bisector as well as with the increasing synodic period of rotation during the same interval (October/November and December in 1991). The composite lightcurves created for short arc time data reveal structures with breakings and linear portions in V; this fact and the Fourier coefficients indicate a probably irregularly shaped body. There are slight indications that the B-V is redder close to the brightness minimum and the V-R_c is redder at the brightness maximum, and the periodic behavior cannot be proved in V-I_c. The less full rotational phase coverage of the observational data is insufficient to construct a shape model. The accurate pole orientation obviously cannot be determined using one opposition lightcurve data only. Further observations are required to get a more accurate knowledge of the physical parameters of this asteroid. For this purpose, a good opportunity to perform observations arose in December 1996, when this asteroid was in opposition at the northernmost declination.     

Mass distribution in the asteroid belt

The dependence of the cumulative number of numbered asteroids (up to 3720) on their absolute magnitude is investigated. The differential mass index k is derived from these relations for fainter asteroids. A steeper slope (2.2 < k < 2.4) is found in the four most populous asteroid familes (Flora, Koronis, Eos and Themis) and a flatter slope (1.3 < k < 1.6) for non-family asteroids. This indicates that there are two different asteroid populations in the asteorid belt. Total masses of the asteroid families may be greater than it is commonly accepted.     

Collisional evolution of the asteroid belt

A new synthesis of asteroid collisional evolution is motivated by the question of whether most asteroids larger than ∼1 km size are strengthless gravitational aggregates (rubble piles). NEAR found Eros not to be a rubble pile, but a shattered collisional fragment, with a through-going fracture system, and an average of about 20 m regolith cover. Of four asteroids visited by spacecraft, none appears likely to be a rubble pile, except perhaps Mathilde. Nevertheless, current understanding of asteroid collisions and size-dependent strength, and the observed distribution of rotation rates versus size, have led to a theoretical consensus that many or most asteroids larger than 1 km should be rubble piles. Is Eros, the best-observed asteroid, highly unusual because it is not a rubble pile? Is Mathilde, if it is a rubble pile, like most asteroids? What would be expected for the small asteroid Itokawa, the MUSES-C sample return target? An asteroid size distribution is synthesized from the Minor Planet Center listing and results of the Sloan Digital Sky Survey, an Infrared Space Observatory survey, the Small Main-belt Asteroid Spectroscopic Survey and the Infrared Astronomical Satellite survey. A new picture emerges of asteroid collisional evolution, in which the well-known Dohnanyi result, that the size distribution tends toward a self-similar form with a 2.5-index power law, is overturned because of scale-dependent collision physics. Survival of a basaltic crust on Vesta can be accommodated, together with formation of many exposed metal cores. The lifetimes against destruction are estimated as 3 Gyr at the size of Eros, 10 Gyr at ten times that size, and 40 Gyr at the size of Vesta. Eros as a shattered collisional fragment is not highly unusual. The new picture reveals the new possibility of a transition size in the collisional state, where asteroids below 5 km size would be primarily collisional breakup fragments whereas much larger asteroids are mostly eroded or shattered survivors of collisions. In this case, well-defined families would be found in asteroids larger than about 5 km size, but for smaller asteroids, families may no longer be readily separated from a background population. Moreover, the measured boulder size distribution on Eros is re-interpreted as a sample of impactor size distributions in the asteroid belt. The regolith on Eros may result largely from the last giant impact, and the same may be true of Itokawa, in which case about a meter of regolith would be expected there. Even a small asteroid like Itokawa may be a shattered object with regolith cover.     

On asteroid distribution

The existing explanations for the asteroid distribution in the main belt (between the orbits of Mars and Jupiter) are based on numerical integration of resonance orbits in models with more than two degrees of freedom. We suggest an approach based on the investigation of the families of periodic solutions of the planar circular restricted three-body problem, i.e., a model with two degrees of freedom. This work shows that (a) the distribution of asteroids near the (p + 1)/p resonances and position of the outer boundary of the main asteroid belt can be explained within the planar circular restricted three-body problem and (b) this problem does not explain the asteroid distribution near other resonances.