The internal structures and densities of asteroids

Abstract— Four asteroidal bodies (the Martian satellites Phobos and Deimos and the main-belt asteroids 243 Ida and 253 Mathilde) have now been the subjects of sufficiently close encounters by spacecraft that the masses and sizes and, hence, the densities of these bodies can be estimated to ～10%. All of these asteroids are significantly less dense than most members of the classes of meteorites identified as being compositionally most nearly similar to them on the basis of spectral characteristics. We show that two processes can act, independently or in concert, during the evolutionary histories of asteroids to produce a low bulk density. One of these processes is the result of one or more impact events and can affect any asteroid type, whereas the other can occur only for certain types of small asteroids that have undergone aqueous alteration.     

A particle-linkage model for non-axisymmetric elongated asteroids

This paper investigates a simplified model for describing the gravitational fields of nonaxisymmetric elongated asteroids. The connection between the simplified model and the target asteroid is built by considering the positions of equilibrium points. To improve the performance of position matching for the equilibrium points associated with these non-axisymmetric asteroids, a nonaxisymmetric triple-particle-linkage model is proposed based on two existing axisymmetric particlelinkage models. The unknown parameters of the simplified model are determined by minimizing the matching error using the nonlinear optimization method. The proposed simplified model is applied for three realistic elongated asteroids, 243 Ida, 433 Eros and(8567) 1996 HW1. The simulation results verify that the current particle-linkage model has better matching accuracy than the two existing particle-linkage models. The comparison, between the simplified model and the polyhedral model, on the topological cases of the equilibrium points and the distribution of gravitational potential further validate the rationality and accuracy of the simplified model.     

A theory of the Trojan asteroids

The paper constructs a long-periodic solution for the case of 11 resonance in the restricted problem of three bodies. The solution is smoothed by the exclusion of the internal resonant terms arising from the near-commensurability between the long and the short periods of the asteroid.Although the Brown (1911) conjecture regarding the termination of the family of the tadpoles at the Lagrangian pointL ₃ is not supported by our analysis, the conjecture seems to hold in the limit asm0.     

Dynamical model of motion for asteroids based on the DE405 theory

A numerical model of motion for asteroids was developed on the basis of the DE405 theory. The positions of main-belt asteroids are calculated accurate to 0.03 mas when the integration is taken over a 50-year interval. For the model to be computationally stable, the local truncation error of integration should be equal to 10^?14 and the double precision of the Standard for Binary Floating-Point Arithmetic IEEE 754-1985 should be used.     

A semi-analytic method for pole determination of asteroids

A semi-analytic method, obtained collecting amplitude-aspect and magnitude-aspect relations, is given in order to deduce the pole coordinates of asteroids. The accuracy of this method (5–10°), which needs some restrictive hypotheses, seems to be sufficient for statistical purposes. Possible ambiguities on the results could be resolved by comparison with other methods (like photometric astrometry), which start from different observational data and follow different procedures.     

A three-parameter magnitude phase function for asteroids

We develop a three-parameter H, G₁, G₂ magnitude phase function for asteroids starting from the current two-parameter H, G phase function. We describe stochastic optimization of the basis functions of the magnitude phase function based on a carefully chosen set of asteroid photometric observations covering the principal types of phase dependencies. We then illustrate the magnitude phase function with a chosen set of observations. It is shown that the H, G₁, G₂ phase function systematically improves fits to the existing data and considerably so, warranting the utilization of three parameters instead of two. With the help of the linear three-parameter phase function, we derive a nonlinear two-parameter H, G₁₂ phase function, and demonstrate its applicability in predicting phase dependencies based on small numbers of observations.     

Rushing to equilibrium: a simple model for the collisional evolution of asteroids

A simple mathematical model for the evolution of a system of collisionally interacting bodies—such as the asteroid population—consists of two coupled, nonlinear, first-order differential equations for the abundances of “small” and “big” bodies. The model easily allows us to recover Dohnanyi's value for the exponent of the equilibrium mass distribution. Moreover, the model shows that any initial value for the ratio of “big” to “small” bodies rapidly relaxes to the equilibrium ratio, corresponding to the exponent, and that integrating the evolution equations backward in time—an attractive possibility to investigate the mass distribution of primordial planetesimals—leads to strong numerical instability.     

Meteoritic and other constraints on the internal structure and impact history of small asteroids

Studies of the internal structure of asteroids, which are crucial for understanding their impact history and for hazard mitigation, appear to be in conflict for the S-type asteroids, Eros, Gaspra, and Ida. Spacecraft images and geophysical data show that they are fractured, coherent bodies, whereas models of catastrophic asteroidal impacts, family and satellite formation, and studies of asteroid spin rates, and other diverse properties of asteroids and planetary craters suggest that such asteroids are gravitationally bound aggregates of rubble. These conflicting views may be reconciled if 10-50 km S-type asteroids formed as rubble piles, but were later consolidated into coherent bodies. Many meteorites are breccias that testify to a long history of impact fragmentation and consolidation by alteration, metamorphism, igneous and impact processes. Ordinary chondrites, which are the best analogs for S asteroids, are commonly breccias. Some may have formed in cratering events, but many appear to have formed during disruption and reaccretion of their parent asteroids. Some breccias were lithified during metamorphism, and a few were lithified by injected impact melt, but most are regolith and fragmental breccias that were lithified by mild or moderate shock, like their lunar analogs. Shock experiments show that porous chondritic powders can be consolidated during mild shock by small amounts of silicate melt that glues grains together, and by friction and pressure welding of silicate and metallic Fe,Ni grains. We suggest that the same processes that converted impact debris into meteorite breccias also consolidated asteroidal rubble. Internal voids would be partly filled with regolith by impact-induced seismic shaking. Consolidation of this material beneath large craters would lithify asteroidal rubble to form a more coherent body. Fractures on Ida that were created by antipodal impacts and are concentrated in and near large craters, and small positive gravity anomalies associated with the Psyche and Himeros craters on Eros, are consistent with this concept. Spin data suggest that smaller asteroids 0.6-6 km in size are unconsolidated rubble piles. C-type asteroids, which are more porous than S-types, and their analogs, the volatile-rich carbonaceous chondrites, were probably not lithified by shock.     

A survey of main-belt asteroids. II. Positions and improved orbital elements for 62 unnumbered asteroids

More than 7 000 positions of moving objects were detected on 33 films obtained with the Schmidt telescope at the European Southern Observatory in Chile during August and September 1995. The majority of these asteroids are previously unobserved. This paper presents the results for 62 unnumbered asteroids with provisional designations found in the fields. References to the derived positions for these asteroids are given and improved orbital elements have been calculated using all available positions.     

Application of the Brown-Shook model to the Kirkwood gaps and resonant asteroids

The mathematical model developed by Brown and Shook is used to explain the absence of asteroids in the Kirkwood gaps as well as the existence of some resonant asteroids with orbital periods commensurable to that of Jupiter. In addition, this model can possibly explain the biased number distributions at the commensurable positions of both resonant gaps and clusters. However, this resonant model is probably not applicable to the Saturnian ring system due to the possible cosmogonic plasma process during its formation.     

A survey of main-belt asteroids I. Positions and improved orbital elements for 75 numbered asteroids.

More than 7000 positions of moving objects have been detected on 33 films obtained with the Schmidt telescope at the European Southern Observatory in Chile during August and September 1995. The majority of these asteroids are previously unobserved. This paper presents the astrometric methods as well as the magnitude determinations. The derived positions for the numbered asteroids are presented and for these improved orbital elements have been calculated using all available positions.     

Optimal searches for asteroids

Optimal searches for a fixed object are discussed and the rigorous analytical results of discrete search theory are presented. They show that the totally optimal, the uniformly optimal, the locally optimal, and the fastest searches are identical under not too restrictive assumptions. The Mathematical formalism is illustrated by an Earth-approaching asteroid search and optimal searches for such objects are explicitly constructed. The approximation that Earth-approaching asteroids are fixed is equivalent to having a very high $\text{(}\text{1}\text{?}\text{00}\text{square degrees/hr)}$ search rate. Generalizations to other types of astronomical search are briefly mentioned.     

Angular momentum drain: A mechanism for despinning asteroids

It is proposed that a new mechanism—angular momentum drain—helps account for the relatively slow rotation rates of intermediate-sized asteroids. Impact ejecta on a spinning body preferentially escape in the direction of rotation. This material systematically drains away spin angular momentum, leading to the counterintuitive result that collisions can reduce the spin of midsized objects. For an asteroid of mass M spinning at frequency ω, a mass loss δM correspond to an average decrease in rotation rate $\text{δω ≈}\text{ωδM}\text{M}$. A. W. Harris' (1979), Icarus40, 145–153) theory for the collisional evolution of asteroidal spins is significantly altered by inlusion of this effect. While the modified theory is still somewhat artificial, comparison of its predictions with the data of S. F. Dermott, A. W. Harris, and C. D. Murray (1984, Icarus57, 14–34) suggests that angular momentum drain is essential for understanding the statistics of asteroidal rotations.     

Rotational excitation and damping as probes of interior structures of asteroids and comets

Abstract— Rotational excitation and damping are discussed in the context of inferring structural properties of asteroids and comets. Opportunities for carrying out deterministic experiments are outlined and basic concepts involving space missions are discussed. Spacecraft carrying an impactor or explosives together with an orbiter are suggested as effective probes of the interiors of asteroid and comets. The feasibility of such missions, especially to near‐Earth objects (NEOs), is highlighted as NEOs provide an appropriate cost‐effective path to explore interiors of asteroids and comets.     

Optimized Nekhoroshev stability estimates for the Trojan asteroids with a symplectic mapping model of co-orbital motion

We present new important results about the intermediate-type Seyfert galaxy Mrk 315, recently observed through optical imaging and integral-field spectroscopy. Broad-band images were used to study the morphology of the host galaxy, narrow-band Hα images to trace the star-forming regions, and middle-band [O  iii ] images to evidence the distribution of the highly ionized gas. Some extended emission regions were isolated and their physical properties studied by means of flux-calibrated spectra. High-resolution spectroscopy was used to separate different kinematic components in the velocity fields of gas and stars. Some peculiar features characterize this apparently undisturbed and moderately isolated active galaxy. Such features, already investigated by other authors, are re-analysed and discussed in the light of these new observations. The most relevant results we obtained are: the multitiers structure of the disc; the presence of a quasi-ring of regions with star formation much higher than previous claims; a secondary nucleus confirmed by a stellar component kinematically decoupled by the main galaxy; a new hypothesis about the controversial nature of the long filament, initially described as hook shaped, and more likely made of two independent filaments caused by interaction events between the main galaxy and two dwarf companions.     

A test of the plausibility of eclipsing binary asteroids

We present an analytic method for producing the lightcurve of a system of spherical bodies in circular orbit about their common center of mass and then use it to model a lightcurve of 171 Ophelia. We find that a model in which the components have a diameter ratio of 1:2.96, have equal albedos, and circle one another in a synchronous orbit (period = 13.146 hr) inclined by 15° to our line of sight provides a reasonable fit to the observed lightcurve. An expression is given for the density in terms of the model parameters. If this lightcurve of Ophelia is produced by mutual eclipses of spherical components the mean density of the system can not exceed 1.7 g cm^?3. In view of these results we conclude that it is possible for Ophelia to be a binary.     

Grooves on asteroids: A prediction

The characteristics of the grooves on Phobos indicate that these features were formed by a large impact—an observation which implies that grooves may occur on other small bodies. Published data on fragmentation experiments suggest that the energy of the impact which produced the grooves on Phobos was in a critical range, strong enough to produce fracturing at large distances from the crater, but too weak to fragment the object. Other small bodies, such as asteroids, which have experienced an impact flux sufficient to include one such critical cratering event should show grooves, unless they have been fragmented subsequently by a more severe impact. We estimate that between $\text{1}\text{12}\text{th}\text{and}\text{1}\text{4}\text{th}$ of asteroids smaller than 100 km in diameter may have surface features resembling grooves associated with large impact craters. Several morphologically distinct types of grooves can be expected, depending on the thickness and composition of the regolith of the parent body. The full development of Phobos-like grooves seems to require a thick, and possibly volatile-rich, regolith—conditions which might obtain on certain C-asteroids.     

A concept for providing warning of earth impacts by small asteroids

The atmospheric detonation of a 17 m-asteroid above Chelyabinsk, Russia on 2013 February 15 shows that even small asteroids can cause extensive damage. Earth-based telescopes have found smaller harmless objects, such as 2008 TC3, a 4 m-asteroid that was discovered 20h before it exploded over northeastern Sudan (Jenniskens, 2009). 2008 TC3 remains the only asteroid discovered before it hit Earth because it approached Earth from the night side, where it was observed by large telescopes searching for near-Earth objects (NEO’s). The larger object that exploded over Chelyabinsk approached Earth from the day side, from too close to the Sun to be detected from Earth. A sizeable telescope in an orbit about the Sun-Earth L1 (SE-L1) libration point could find objects like the “Chelyabinsk” asteroid approaching approximately from the line of sight to the Sun about a day before Earth closest approach. Such a system would have the astrometric accuracy needed to determine the time and impact zone for a NEO on a collision course. This would give at least several hours, and usually 2–4 days, to take protective measures, rather than the approximately two-minute interval between the flash and shock wave arrival that occurred in Chelyabinsk. A perhaps even more important reason for providing warning of these events, even smaller harmless ones that explode high in the atmosphere with the force of an atomic bomb, is to prevent mistaking such an event for a nuclear attack that could trigger a devastating nuclear war. A concept using a space telescope similar to that needed for an SE-L1 monitoring satellite, is already conceived by the B612 Foundation, whose planned Sentinel Space Telescope could find nearly all 140 m and larger NEO’s, including those in orbits mostly inside the Earth’s orbit that are hard to find with Earth-based telescopes, from a Venus-like orbit (Lu, 2013). Few modifications would be needed to the Sentinel Space Telescope to operate in a SE-L1 orbit, 0.01 AU from Earth towards the Sun, to find most asteroids larger than about 5 meters that approach the Earth from the solar direction. The spacecraft would scan 165 square degrees of the sky around the Earth every hour, finding asteroids when they are brightest (small phase angle) as they approach Earth. We will undertake Monte Carlo studies to see what fraction of asteroids 5 m and larger approaching from the Sun might be found by such a mission, and how much warning time might typically be expected. Also, we will check the overall coverage for all Earth-approaching NEO’s, including ground-based observations and observations by the recently-launched NEOSSat, which may best fill any gaps in coverage between that provided by an SE-L1 telescope and ground-based surveys. Many of the objects as large as 50 m, like the one that created Meteor Crater in Arizona, will not be found by current NEO surveys, while they would usually be seen by this possible mission even if they approached from the direction of the Sun. We should give better warning for future “Bolts out of the blue.”