Binary asteroid population: 1. Angular momentum content

We compiled a list of estimated parameters of binary systems among asteroids from near-Earth to trojan orbits. In this paper, we describe the construction of the list, and we present results of our study of angular momentum content in binary asteroids. The most abundant binary population is that of close binary systems among near-Earth, Mars-crossing, and main belt asteroids that have a primary diameter of about 10 km or smaller. They have a total angular momentum very close to, but not generally exceeding, the critical limit for a single body in a gravity regime. This suggests that they formed from parent bodies spinning at the critical rate (at the gravity spin limit for asteroids in the size range) by some sort of fission or mass shedding. The Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effect is a candidate to be the dominant source of spin-up to instability. Gravitational interactions during close approaches to the terrestrial planets cannot be a primary mechanism of formation of the binaries, but it may affect properties of the NEA part of the binary population.     

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.     

Feasibility study of a multiple flyby mission of main belt asteroids

Specific information on the surface morphology, composition, mean density, and internal structure of asteroids, which is necessary to advance our understanding of asteroids, can be obtained only by a detailed investigation of individual bodies: this will require space missions to individual targets. Since an essential characteristic of the asteroids is their variety, several objects must be visited. The Ariane launcher developed presently in Europe makes a multiple flyby mission possible. The first results of our feasibility study are particularly encouraging: during one revolution, five to six preselected main belt asteroids may be approached to within 1000 km with relative velocities which lie between 3 and 14 km/sec using a total impulse correction on the order of 1 to 2 km/sec. The weight of the spacecraft, excluding the engine and the propellant, would be at least 250 kg. This allows a scientific payload of 50 to 60 kg, in which priority will be given to an imaging system and radar altimeter.     

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.     

Equilibrium points and associated periodic orbits in the gravity of binary asteroid systems: (66391) 1999 KW4 as an example

The motion of a massless particle in the gravity of a binary asteroid system, referred as the restricted full three-body problem (RF3BP), is fundamental, not only for the evolution of the binary system, but also for the design of relevant space missions. In this paper, equilibrium points and associated periodic orbit families in the gravity of a binary system are investigated, with the binary (66391) 1999 KW4 as an example. The polyhedron shape model is used to describe irregular shapes and corresponding gravity fields of the primary and secondary of (66391) 1999 KW4, which is more accurate than the ellipsoid shape model in previous studies and provides a high-fidelity representation of the gravitational environment. Both of the synchronous and non-synchronous states of the binary system are considered. For the synchronous binary system, the equilibrium points and their stability are determined, and periodic orbit families emanating from each equilibrium point are generated by using the shooting (multiple shooting) method and the homotopy method, where the homotopy function connects the circular restricted three-body problem and RF3BP. In the non-synchronous binary system, trajectories of equivalent equilibrium points are calculated, and the associated periodic orbits are obtained by using the homotopy method, where the homotopy function connects the synchronous and non-synchronous systems. Although only the binary (66391) 1999 KW4 is considered, our methods will also be well applicable to other binary systems with polyhedron shape data. Our results on equilibrium points and associated periodic orbits provide general insights into the dynamical environment and orbital behaviors in proximity of small binary asteroids and enable the trajectory design and mission operations in future binary system explorations.     

Colors of dynamically associated asteroid pairs

Recent dynamical studies have identified pairs of asteroids that reside in nearly identical heliocentric orbits. Possible formation scenarios for these systems include dissociation of binary asteroids, collisional disruption of a single parent body, or spin-up and rotational fission of a rubble-pile. Aside from detailed dynamical analyses and measurement of rotational light curves, little work has been done to investigate the colors or spectra of these unusual objects. A photometric and spectroscopic survey was conducted to determine the reflectance properties of asteroid pairs. New observations were obtained for a total of 34 individual asteroids. Additional photometric measurements were retrieved from the Sloan Digital Sky Survey Moving Object Catalog. Colors or spectra for a total of 42 pair components are presented here. The main findings of this work are: (1) the components in the observed pair systems have the same colors within the uncertainties of this survey, and (2) the color distribution of asteroid pairs appears indistinguishable from that of all Main Belt asteroids. These findings support a scenario of pair formation from a common progenitor and suggest that pair formation is likely a compositionally independent process. In agreement with previous studies, this is most consistent with an origin via binary disruption and/or rotational fission.     

Orbital evolution of small binary asteroids

About 15% of both near-Earth and main-belt asteroids with diameters below 10 km are now known to be binary. These small asteroid binaries are relatively uniform and typically contain a fast-spinning, flattened primary and a synchronously rotating, elongated secondary that is 20-40% as large (in diameter) as the primary. The principal formation mechanism for these binaries is now thought to be YORP (Yarkovsky-O’Keefe-Radzievskii-Paddack) effect induced spin-up of the primary followed by mass loss and accretion of the secondary from the released material. It has previously been suggested (?uk, M. [2007]. Astrophys. J. 659, L57-L60) that the present population of small binary asteroids is in a steady state between production through YORP and destruction through binary YORP (BYORP), which should increase or decrease secondary’s orbit, depending on the satellite’s shape. However, BYORP-driven evolution has not been directly modeled until now. Here we construct a simple numerical model of the binary’s orbital as well the secondary’s rotational dynamics which includes BYORP and selected terms representing main solar perturbations. We find that many secondaries should be vulnerable to chaotic rotation even for relatively low-eccentricity mutual orbits. We also find that the precession of the mutual orbit for typical small binary asteroids might be dominated by the perturbations from the prolate and librating secondary, rather than the oblate primary. When we evolve the mutual orbit by BYORP we find that the indirect effects on the binary’s eccentricity (through the coupling between the orbit and the secondary’s spin) dominate over direct ones caused by the BYORP acceleration. In particular, outward evolution causes eccentricity to increase and eventually triggers chaotic rotation of the secondary. We conclude that the most likely outcome will be reestablishing of the synchronous lock with a “flipped” secondary which would then evolve back in. For inward evolution we find an initial decrease of eccentricity and secondary’s librations, to be followed by later increase. We think that it is likely that various forms of dissipation we did not model may damp the secondary’s librations close to the primary, allowing for further inward evolution and a possible merger. We conclude that a merger or a tidal disruption of the secondary are the most likely outcomes of the BYORP evolution. Dissociation into heliocentric pairs by BYORP alone should be very difficult, and satellite loss might be restricted to the minority of systems containing more than one satellite at the time.     

Observations of asteroids with ALMA

Thermal observations of large asteroids at millimeter wavelengths have revealed high amplitude rotational lightcurves. Such lightcurves are important constraints on thermophysical models of asteroids, and provide unique insight into the nature of their surface and subsurface composition. A better understanding of asteroid surfaces provides insight into the composition, physical structures, and processing history of these surviving remnants from the formation of our solar system. In addition, detailed observations of the larger asteroids, accompanied by thermophysical models with appropriate temporal and spatial resolution, promise to decrease uncertainties in their flux predictions. Of particular interest are the near-Earth objects, which can be observed at large phase angles, permitting better assessment of the thermal response of their unilluminated surfaces. The high sensitivity of ALMA will enable us to detect many small bodies in all the major groups, to obtain lightcurves for a large sample of main-belt and near-Earth objects, to resolve the surfaces of some large objects, and to separate the emission from primary and secondary objects in binary pairs. In addition to the science goals of asteroid studies, these bodies may also prove useful operationally because those with known shapes and well-characterized lightcurves could be employed for flux calibration by ALMA and other high frequency instruments.     

Surface studies of asteroids with the Faint Object Camera of the Space Telescope

Minor planets have been observed in the last few years for physical properties using photometry, polarimetry and IR-radiometry. Using the Faint Object Camera (FOC) of the Space Telescope (ST) it will be possible for the first time to observe a large number of asteroids with direct imaging systems.We propose to use the FOC with high resolution mode to examine minor planets with respect to (a) diameters and shapes, (b) surface and detail studies, (c) densities and (d) possible binary nature of selected asteroids.Paper presented at the European Workshop on Planetary Sciences, organised by the Laboratorio di Astrofisica Spaziale di Frascati, and held between April 23–27, 1979, at the Accademia Nazionale del Lincei in Rome, Italy.     

Yarkovsky detection opportunities: II. Binary systems

We consider the possibility of detecting the Yarkovsky orbital perturbation acting on binary systems among the near-Earth asteroids. This task is significantly more difficult than for solitary asteroids because the Yarkovsky force affects both the heliocentric orbit of the system's center of mass and the relative orbit of the two components. Nevertheless, we argue these are sufficiently well decoupled so that the major Yarkovsky perturbation is in the simpler heliocentric motion and is observable with the current means of radar astrometry. Over the long term, the Yarkovsky perturbation in the relative motion of the two components is also detectable for the best observed systems. However, here we consider a simplified version of the problem by ignoring mutual non-spherical gravitational perturbations between the two asteroids. With the orbital plane constant in space and the components' rotation poles fixed (and assumed perpendicular to the orbital plane), we do not examine the coupling between Yarkovsky and gravitational effects. While radar observations remain an essential element of Yarkovsky detections, lightcurve observations, with their ability to track occultation and eclipse phenomena, are also very important in the case of binaries. The nearest possible future detection of the Yarkovsky effect for a binary system occurs for (66063) 1998 RO₁ in September 2006. Farther out, even more statistically significant detections are possible for several other systems including 2000 DP₁₀₇, (66391) 1999 KW₄ and 1996 FG₃.     

E–ELT: Expected Applications to Asteroid Observations in the Thermal Infrared

Applications of the 42m European Extremely Large Telescope (E–ELT) for the physical characterization of asteroids is presented. In particular, this work focuses on the determination of sizes and other physical properties of asteroids from measurements of their heat emission in the thermal infrared (>5 μm). Here we show that E–ELT will be best suited for the physical characterization of some selected asteroids of particular interest, as for instance: (i) targets of sample return missions to near-Earth Asteroids (NEAs); (ii) km and sub-km binary asteroids for which size information will allow their bulk density to be derived; (iii) sizes and values of the thermal inertia of potentially hazardous asteroids (PHAs). These two parameters both affect the Yarkovsky effect, which plays a role in the orbital evolution of km sized asteroids and represents a large source of uncertainty in the Earth impact probability prediction of some PHAs. Thermal inertia is also a sensitive indicator for the presence or absence of thermal insulating regolith on the surface of atmosphere-less bodies. Knowledge of this parameter is thus important for the design and the development of lander- and sample return-missions to asteroids. The E–ELT will also be able to spatially resolve asteroids and detect binaries in a range of sizes that are at present not accessible to present day adaptive optics.     

Asteroidal binary systems: Detection and formation

Recent occultation data and an analysis of some photometric lightcurves have shown the possible existence of asteroidal binary systems.A simple geometrical model taking into account mutual shadowing effects shows some peculiar features of the lightcurve which can be recovered in several previously observed objects; therefore the hypothesis of a relatively high frequency of binary asteroids should be seriously considered.On the other hand, while the rotational period distribution of large asteroids (D>200 km) is sharply peaked at about 5–8 hours, the surprisingly higher dispersion towards longer periods for intermediate size objects (50<D<150 km) could be connected with a larger probability of binary nature within this class.From a theoretical point of view, the collisional fragmentation of asteroids could originate gravitationally bound fragments, with a tidal transfer of rotational into orbital angular momentum, causing a rapid synchronization of the system. This kind of processes could more easily occur for intermediate objects since: (a) for large ones, very massive colliding bodies are needed for fragmentation, that means a very rare event; (b) for smaller asteroids, solid state interactions are stronger than the gravitational ones, so that a breakage probably causes a complete disruption of the gravitational binding. Further collisional events could disintegrate some systems, so that the present frequency of binary asteroids could be lower than that of the objects whose rotational period was increased by such processes.Paper presented at the European Workshop on Planetary Sciences, organised by the Laboratorio di Astrofisica Spaziale di Frascati, and held between April 23–27, 1979, at the Accademia Nazionale del Lincei in Rome, Italy.     

Doublet craters on Venus

Of the impact craters on Earth larger than 20 km in diameter, 10-15% (3 out of 28) are doublets, having been formed by the simultaneous impact of two well-separated projectiles. The most likely scenario for their formation is the impact of well-separated binary asteroids. If a population of binary asteroids is capable of striking the Earth, it should also be able to hit the other terrestrial planets as well. Venus is a promising planet to search for doublet craters because its surface is young, erosion is nearly nonexistent, and its crater population is significantly larger than the Earth's. After a detailed investigation of single craters separated by less than 150 km and “multiple” craters having diameters greater than 10 km, we found that the proportion of doublet craters on Venus is at most 2.2%, significantly smaller than Earth's, although several nearly incontrovertible doublets were recognized. We believe this apparent deficit relative to the Earth's doublet population is a consequence of atmospheric screening of small projectiles on Venus rather than a real difference in the population of impacting bodies. We also examined “splotches,” circular radar reflectance features in the Magellan data. Projectiles that are too small to form craters probably formed these features. After a careful study of these patterns, we believe that the proportion of doublet splotches on Venus (14%) is comparable to the proportion of doublet craters found on Earth (10-15%). Thus, given the uncertainties of interpretation and the statistics of small numbers, it appears that the doublet crater population on Venus is consistent with that of the Earth.     

A steady-state model of NEA binaries formed by tidal disruption of gravitational aggregates

We present results of a simulation of a steady-state binary near-Earth asteroid (NEA) population. This study combines previous work on tidal disruption of gravitational aggregates [Walsh, K.J., Richardson, D.C., 2006. Icarus 180, 201-216] with a Monte Carlo simulation of NEA planetary encounters. Evolutionary effects include tidal evolution and binary disruption from close planetary encounters. The results show that with the best known progenitor (small Main Belt asteroids) shape and spin distributions, and current estimates of NEA lifetime and encounter probabilities, that tidal disruption should account for approximately 1-2% of NEAs being binaries. Given the best observed estimate of a ∼15% binary NEA fraction, we conclude that there are other formation mechanisms that contribute significantly to this population. We also present the expected distribution of binary orbital and physical properties for the steady-state binary NEAs formed by tidal disruption. We discuss the effects on binary fraction and properties due to changes in the least constrained parameters, and other possible effects on our model that could account for differences between the presented results and the observed binary population. Finally, we model possible effects of a significant population of binaries migrating to the near-Earth population from the Main Belt.     

Space weathering of small Koronis family members

The space weathering process and its implications for the relationships between S- and Q-type asteroids and ordinary chondrite meteorites is an often debated topic in asteroid science. Q-type asteroids have been shown to display the best spectral match to ordinary chondrites (McFadden, L.A., Gaffey, M.J., McCord, T.B. [1985]. Science 229, 160–163). While the Q-types and ordinary chondrites share some spectral features with S-type asteroids, the S-types have significantly redder spectral slopes than the Q-types in visible and near-infrared wavelengths. This reddening of spectral slope is attributed to the effects of space weathering on the observed surface composition. The analysis by Binzel et al. (Binzel, R.P., Rivkin, A.S., Stuart, J.S., Harris, A.W., Bus, S.J., Burbine, T.H. [2004]. Icarus 170, 259–294) provided a missing link between the Q- and S-type bodies in near-Earth space by showing a reddening of spectral slope in objects from 0.1 to 5 km that corresponded to a transition from Q-type to S-type asteroid spectra, implying that size, and therefore surface age, is related to the relationship between S- and Q-types. The existence of Q-type asteroids in the main-belt was not confirmed until Mothé-Diniz and Nesvorny (Mothé-Diniz, T., Nesvorny, D. [2008]. Astron. Astrophys. 486, L9–L12) found them in young S-type clusters. The young age of these families suggest that the unweathered surface could date to the formation of the family. This leads to the question of whether older S-type main-belt families can contain Q-type objects and display evidence of a transition from Q- to S-type. To answer this question we have carried out a photometric survey of the Koronis family using the Kitt Peak 2.1 m telescope. This provides a unique opportunity to compare the effects of the space weathering process on potentially ordinary chondrite-like bodies within a population of identical initial conditions. We find a trend in spectral slope for objects 1–5 km that shows the transition from Q- to S-type in the main-belt. This data set will prove crucial to our understanding of the space weathering process and its relevant timescales.     

Trojans’ Odyssey: Unveiling the early history of the Solar System

In our present understanding of the Solar System, small bodies (asteroids, Jupiter Trojans, comets and TNOs) are the most direct remnants of the original building blocks that formed the planets. Jupiter Trojan and Hilda asteroids are small primitive bodies located beyond the ‘snow line’, around respectively the L₄ and L₅ Lagrange points of Jupiter at ～5.2?AU (Trojans) and in the 2:3 mean-motion resonance with Jupiter near 3.9?AU (Hildas). They are at the crux of several outstanding and still conflicting issues regarding the formation and evolution of the Solar System. They hold the potential to unlock the answers to fundamental questions about planetary migration, the late heavy bombardment, the formation of the Jovian system, the origin and evolution of trans-neptunian objects, and the delivery of water and organics to the inner planets. The proposed Trojans’ Odyssey mission is envisioned as a reconnaissance, multiple flyby mission aimed at visiting several objects, typically five Trojans and one Hilda. It will attempt exploring both large and small objects and sampling those with any known differences in photometric properties. The orbital strategy consists in a direct trajectory to one of the Trojan swarms. By carefully choosing the aphelion of the orbit (typically 5.3?AU), the trajectory will offer a long arc in the swarm thus maximizing the number of flybys. Initial gravity assists from Venus and Earth will help reducing the cruise time as well as the ΔV needed for injection thus offering enough capacity to navigate among Trojans. This solution further opens the unique possibility to flyby a Hilda asteroid when leaving the Trojan swarm. During the cruise phase, a Main Belt Asteroid could be targeted if requiring a modest ΔV. The specific science objectives of the mission will be best achieved with a payload that will perform high-resolution panchromatic and multispectral imaging, thermal-infrared imaging/ radiometry, near- and mid-infrared spectroscopy, and radio science/mass determination. The total mass of the payload amounts to 50?kg (including margins). The spacecraft is in the class of Mars-Express or a down-scaled version of Jupiter Ganymede Orbiter. It will have a dry mass of 1200?kg, a total mass at launch of 3070?kg and a ΔV capability of 700?m/s (after having reached the first Trojan) and can be launched by a Soyuz rocket. The mission operations concept (ground segment) and science operations are typical of a planetary mission as successfully implemented by ESA during, for instance, the recent flybys of Main Belt asteroids Steins and Lutetia.     

Origin and continuation of 3/2, 5/2, 3/1, 4/1 and 5/1 resonant periodic orbits in the circular and elliptic restricted three-body problem

We consider a planetary system consisting of two primaries, namely a star and a giant planet, and a massless secondary, say a terrestrial planet or an asteroid, which moves under their gravitational attraction. We study the dynamics of this system in the framework of the circular and elliptic restricted three-body problem, when the motion of the giant planet describes circular and elliptic orbits, respectively. Originating from the circular family, families of symmetric periodic orbits in the 3/2, 5/2, 3/1, 4/1 and 5/1 mean-motion resonances are continued in the circular and the elliptic problems. New bifurcation points from the circular to the elliptic problem are found for each of the above resonances, and thus, new families continued from these points are herein presented. Stable segments of periodic orbits were found at high eccentricity values of the already known families considered as whole unstable previously. Moreover, new isolated (not continued from bifurcation points) families are computed in the elliptic restricted problem. The majority of the new families mainly consists of stable periodic orbits at high eccentricities. The families of the 5/1 resonance are investigated for the first time in the restricted three-body problems. We highlight the effect of stable periodic orbits on the formation of stable regions in their vicinity and unveil the boundaries of such domains in phase space by computing maps of dynamical stability. The long-term stable evolution of the terrestrial planets or asteroids is dependent on the existence of regular domains in their dynamical neighbourhood in phase space, which could host them for long-time spans. This study, besides other celestial architectures that can be efficiently modelled by the circular and elliptic restricted problems, is particularly appropriate for the discovery of terrestrial companions among the single-giant planet systems discovered so far.     

Trajectory exploration within asynchronous binary asteroid systems using refined Lagrangian coherent structures

Ground observations have found that asynchronous systems constitute most of the population of the near-Earth binary asteroids. This paper concerns the trajectory of a particle in the asynchronous system which is systematically described using periodic ellipsoidal and spherical body models. Due to the non-autonomous characteristics of the asynchronous system, Lagrangian coherent structures (LCS) are employed to identify the various dynamical behaviors. To enhance the accuracy of LCS, a robust LCS finding algorithm is developed incorporating hierarchical grid refinement, one-dimensional search and variational theory verification. In this way, the intricate dynamical transport boundaries are detected efficiently. These boundaries indicate that a total of 15 types of trajectories exist near asynchronous binary asteroids. According to their Kepler energy variations, these trajectories can be grouped into four basic categories, i.e., transitory, escape, impact and flyby trajectories. Furthermore, the influence of the ellipsoid’s spin period on the dynamical behavior is discussed in the context of the change of dynamical regions. We found that the transitory and impact motions occur easily in the synchronous-like binary systems, in which the rotation period of the ellipsoid is nearly equal to that of the mutual orbit. Meanwhile, the results confirm a positive correlation between the spinning rate of the ellipsoid and the probability of the escape and flyby trajectories. The LCS also reveal a marked increase in trajectory diversity after a larger initial energy is selected.     

Populating the Galaxy with pulsars – I. Stellar and binary evolution

The computation of theoretical pulsar populations has been a major component of pulsar studies since the 1970s. However, the majority of pulsar population synthesis has only regarded isolated pulsar evolution. Those that have examined pulsar evolution within binary systems tend to either treat binary evolution poorly or evolve the pulsar population in an ad hoc manner. Thus, no complete and direct comparison with observations of the pulsar population within the Galactic disc has been possible to date. Described here is the first component of what will be a complete synthetic pulsar population survey code. This component is used to evolve both isolated and binary pulsars. Synthetic observational surveys can then be performed on this population for a variety of radio telescopes. The final tool used for completing this work will be a code comprised of three components: stellar/binary evolution, Galactic kinematics and survey selection effects. Results provided here support the need for further (apparent) pulsar magnetic field decay during accretion, while they conversely suggest the need for a re-evaluation of the assumed typical millisecond pulsar formation process. Results also focus on reproducing the observed     diagram for Galactic pulsars and how this precludes short time-scales for standard pulsar exponential magnetic field decay. Finally, comparisons of bulk pulsar population characteristics are made to observations displaying the predictive power of this code, while we also show that under standard binary evolutionary assumption binary pulsars may accrete much mass.