Mutual Orbit Research Articles

FORMATION OF THE WIDE ASYNCHRONOUS BINARY ASTEROID POPULATION

We propose and analyze a new mechanism for the formation of the wide asynchronous binary population. These binary asteroids have wide semi-major axes relative to most near-Earth and Main Belt asteroid systems. Confirmed members have rapidly rotating primaries and satellites that are not tidally locked. Previously suggested formation mechanisms from impact ejecta, planetary flybys and directly from rotational fission events cannot satisfy all of the observations. The newly hypothesized mechanism works as follows: (i) these systems are formed from rotational fission, (ii) their satellites are tidally locked, (iii) their orbits are expanded by the BYORP effect, (iv) their satellites de-synchronize due to the adiabatic invariance between the libration of the secondary and the mutual orbit, and (v) the secondary avoids resynchronization due to the the YORP effect. This seemingly complex chain of events is a natural pathway for binaries with satellites that have particular shapes, which define the BYORP effect torque that acts on the system. After detailing the theory, we analyze each of the wide asynchronous binary members and candidates to assess their most likely formation mechanism. Finally, we suggest possible future observations to check and constrain our hypothesis.

Gravity from the uncertainty principle

It is shown here that Newton’s gravity law can be derived from the uncertainty principle. The idea is that as the distance between two bodies in mutual orbit decreases, their uncertainty of position decreases, so their momentum and hence the force on them must increase to satisfy the uncertainty principle. When this result is summed over all the possible interactions between the Planck masses in the two bodies, Newton’s gravity law is obtained. This model predicts that masses less than the Planck mass will be unaffected by gravity and so it may be tested by looking for an abrupt decrease in the density of space dust, for masses above the Planck mass.

Greatly enhanced eccentricity oscillations in quadruple systems composed of two binaries: implications for stars, planets and transients

We study the orbital evolution of hierarchical quadruple systems composed of two binaries on a long mutual orbit, where each binary acts as a Kozai–Lidov (KL) perturber on the other. We find that the coupling between the two binaries qualitatively changes the behaviour of their KL cycles. The binaries can experience coherent eccentricity oscillations as well as excursions to very high eccentricity that occur over a much larger fraction of the parameter space than in triple systems. For a ratio of outer to inner semimajor axes of 10–20, about 30–50 per cent of equal-mass quadruples reach eccentricity 1 − e < 10−3 in one of the binaries. This is about 4–12 times more than for triples with equivalent parameters. Orbital ‘flips’ and collisions without previous tidal interaction are similarly enhanced in quadruples relative to triples. We argue that the frequency of evolutionary paths influenced by KL cycles is comparable in the triple and quadruple populations even though field quadruples are a factor of ∼5 less frequent than triples. Additionally, quadruples might be a non-negligible source of triples and provide fundamentally new evolutionary outcomes involving close binaries, mergers, collisions and associated transients, which occur without any fine tuning of parameters. Finally, we study the perturbations to a planetary orbit due to a distant binary and we find that the fraction of orbital flips is a factor of 3–4 higher than for the corresponding triple system given our fiducial parameters with implications for hot Jupiters and star–planet collisions.

Analysis of potential locations of asteroidal moonlets★

In this study, the potential locations of asteroidal small satellites (also called moonlets) with quasi-circular mutual orbit are analysed. For the motion of the moonlets, only the solar gravity perturbation and the primary's second degree-and-order gravity field are considered. By eliminating short periodic terms, the dynamical behaviour of the Hamiltonian for the moonlets is investigated. The observational data of some high-size-ratio binary asteroids show that the orbits of the moonlets lie close to the classical Laplace equilibrium points, which reach global minimum values of the Hamiltonian. It is found that tides or Yarkovsky effects alone cannot account for the reason why the orbits of asteroidal moonlets are not exactly at the classical Laplace equilibrium points. The analysis in this study is expected to provide useful information for the potential locations of asteroidal moonlets, and contribute to principles to relate predictions to observations.

Reading Goethe at Midlife: Ancient Wisdom, German Classicism, and Jung by Paul Bishop (review)

Reviewed by: Reading Goethe at Midlife: Ancient Wisdom, German Classicism, and Jung by Paul Bishop Jane K. Brown Paul Bishop, Reading Goethe at Midlife: Ancient Wisdom, German Classicism, and Jung. New Orleans: Spring Journal Books, 2011. 257 pp. As the title suggests, this book offers a historical context for the modern psychological concept of “midlife crisis” from three perspectives: an overview of the idea of stages of life, C. G. Jung’s essay “Die Lebenswende” (1931), and Goethe’s “Urworte orphisch.” On the basis of extensive knowledge of all three topics it makes a strong and interesting argument for the poem as a psychological analysis of life stages, without it being necessary to take the term “midlife” too literally. There is no claim that “Urworte orphisch,” written in 1818, is a midlife product or that Goethe’s life and thinking about development did not involve repeated crises and turns. Bishop rather pursues a single literary example of the implications of his important two-volume work on Jung’s roots in German classicism (Analytical Psychology and German Classical Aesthetics: Goethe, Schiller, and Jung [Routledge, 2007]) to demonstrate Goethe’s anticipation of later professional wisdom on the emotional crises that accompany the transition between life stages. Based on a series of lectures delivered for the Zurich Lecture Series in Analytical Psychology in 2010, the book addresses primarily Jungian psychoanalysts. Nevertheless, it should interest Goethe scholars for its extended commentary on “Urworte orphisch” and for its provocative achronological structure that treats Goethe and Jung as a pair of stars in mutual orbit around each other. The book falls into two symmetrical parts, with the first two chapters focused on analytical psychology, the second two on Goethe. Chapter 1 surveys in largely, though not entirely, chronological order, the notion of stages of life from antiquity to Hermann Hesse, then surveys the concept “midlife crisis,” a term that emerged as a psychological category only in 1965. Bishop claims neither completeness for his surveys nor any particular shape, except for occasional assert ions, with documentation, that Goethe anticipated one or another observation. The second chapter analyzes “Die Lebenswende,” where the analogy of human life to the daily course of the sun grounds the notion of midlife change and embeds the structure of human life in the order of the cosmos. Frequent parallels to Goethe adumbrate more clearly the central theme, and the last two pages on symbol draw Goethe and Jung together clearly. The last two chapters turn explicitly to Goethe, first to his “orphism” and then to “Urworte orphisch.” Chapter 3 begins with an overview of Goethe’s “profound and far-reaching” influence on Jung, which Bishop understands as conceptual, “stylistic,” and “subterranean” (119). He lists five points: (1) the limitation of reason, (2) imagery of light and darkness, (3) focus on the maternal, (4) polarity, and (5) the notion of a midlife crisis (expressed in conversation with Eckermann on March 11, 1828). (I don’t actually see anything stylistic here, but the assertion could certainly be supported by considering the debt Jung’s analogical reasoning owed to Goethe’s morphological thinking.) The remainder of the chapter weaves together classical philosophy, fragments of ancient mystery cults, modern anthropology of religion (for example, Mircea Eliade), and German romantic interest in mystery cults (Creuzer et al.) to define “Goethe’s orphism” with its strong focus on the turn to hope. The last chapter comments in detail on “Urworte orphisch” in terms of its mythological underpinnings and its psychological significance. Bishop operates within the canon of Jung’s followers and Jung’s own canon—Nietzsche, nineteenth-century philosophy, mythology, anthropology. Similarly the Goethe invoked here is largely Jung’s Goethe, who speaks in aphorisms, essays, [End Page 272] gnomic poetry, correspondence, and to Eckermann. There are a few references to Werther, and several to Faust, of course, but to the few parts of Faust that interested Jung: Mephistopheles as a principle of evil, Gretchen as the object of tragedy, the Mothers, bits of the classical Walpurgisnight, and bits of act five. Strikingly absent is Die Wahlverwandtschaften—today, surely, Goethe’s psychological novel par excellence, but perhaps more Freudian than Jungian. The approach also seems characteristically Jungian with its...

Resonant orbits in the vicinity of asteroid 216 Kleopatra

This investigation examines the resonant orbits in the vicinity of asteroid 216 Kleopatra using a precise gravitational model, with emphasis on their crucial role in determining the global orbital behaviors. Three-dimensional Monte Carlo simulations of test particle trajectories are launched to find the condition and probability distribution of resonance. It is revealed the resonant orbits are rich and concentrated in the near-field regime, which provides a short-term mechanism to clear the vicinal ejecta away from the asteroid. The unstable boundary predicted in our calculations is consistent with the observed mutual orbits of satellites S/2008 (216) 1 and S/2008 (216) 2. The probability distribution of resonance is considered as an indicator of the stability of vicinal orbits, and the results are identical to the previous analysis by Scheeres et al. (Icarus 121:67, 1996) for the stability of retrograde orbits around asteroid 4769 Castalia.

MarcoPolo-R: Near Earth Asteroid Sample Return Mission candidate as ESA-M3 class mission

AbstractMarcoPolo-R is a sample return mission to a primitive Near-Earth Asteroid (NEA) selected in February 2011 for the Assessment Study Phase at ESA in the framework of ESAfs Cosmic Vision 2 program. MarcoPolo-R is a European-led mission with a proposed NASA contribution. MarcoPolo-R takes advantage of three industrial studies completed as part of the previous Marco Polo mission (see ESA/SRE (2009)3). The aim of the new Assessment Study is to reduce the cost of the mission while maintaining its high science level, on the basis of advanced studies and technologies, as well as optimization of the mission. MarcoPolo-R will rendezvous with a unique kind of target, a primitive binary NEA, scientifically characterize it at multiple scales, and return a unique pristine sample to Earth unaltered by the atmospheric entry process or terrestrial weathering. The baseline target of MarcoPolo-R is the primitive binary NEA (175706) 1996 FG3, which offers a very efficient operational and technical mission profile. A binary target also provides enhanced science return: the choice of this target will allow new investigations to be performed more easily compared to a single object, and also enables investigations of the fascinating geology and geophysics of asteroids that are impossible to obtain from a single object. Precise measurements of the mutual orbit and rotation state of both components can be used to probe higher-level harmonics of the gravitational potential, and therefore the internal structure. A unique opportunity is offered to study the dynamical evolution driven by the YORP/Yarkovsky thermal effects. Possible migration of regolith on the primary from poles to equator allows the increasing maturity of asteroidal regolith with time to be expressed as a latitude-dependent trend, with the most-weathered material at the equator matching what is seen in the secondary. MarcoPolo-R will allow us to study the most primitive materials available to investigate early solar system formation processes. Moreover, MarcoPolo-R will provide a sample from a known target with known geological context. Direct investigation of both the regolith and fresh interior fragments is also impossible by any means other than sample return. The main goal of the MarcoPolo-R mission is to return unaltered NEA material for detailed analysis in ground-based laboratories. The limited sampling provided by meteorites does not offer the most primitive material available in near-Earth space. More primitive material, having experienced less alteration on the asteroid, will be more friable and would not survive atmospheric entry in any discernible amount. Only in the laboratory can instruments with the necessary precision and sensitivity be applied to individual components of the complex mixture of materials that forms an asteroid regolith, to determine their precise chemical and isotopic composition. Such measurements are vital for revealing the evidence of stellar, interstellar medium, pre-solar nebula and parent body processes that are retained in primitive asteroidal material, unaltered by atmospheric entry or terrestrial contamination. It is no surprise therefore that sample return missions are considered a priority by a number of the leading space agencies.

Discovery of a double eclipsing binary with periods near a 3:2 ratio

The evolution of multiple stellar systems can be driven by Kozai cycles and tidal friction (KCTF), which shrink the orbit of the inner binary. There is an interesting possibility that two close binaries on a common long-period orbit experience mutually-induced KCTF. We present the discovery of a possible new quadruple system composed of two unresolved eclipsing binaries (EBs), CzeV343 (V~13.5 mag). We obtained photometric observations of CzeV343 that completely cover the two orbital periods and we successfully model the light curves as the sum of two detached EBs. We provide confidence intervals for the model parameters and minima timings by bootstrap resampling of our data. One of the EBs shows a distinctly eccentric orbit with a total eccentricity of about 0.18. The two orbital periods, 1.20937 and 0.80693 days, are within 0.1% of a 3:2 ratio. We speculate that this might be the result of KCTF-driven evolution of a quadruple system and we discuss this hypothesis in the context of other quadruple systems composed of two EBs. We make our double EB fitting code publicly available to provide a tool for long-term monitoring of the mutual orbit in such systems.

KCTF evolution of trans-neptunian binaries: Connecting formation to observation

Recent observational surveys of trans-neptunian binary (TNB) systems have dramatically increased the number of known mutual orbits. Our Kozai Cycle Tidal Friction (KCTF) simulations of synthetic trans-neptunian binaries show that tidal dissipation in these systems can completely reshape their original orbits. Specifically, solar torques should have dramatically accelerated the semimajor axis decay and circularization timescales of primordial (or recently excited) TNBs. As a result, our initially random distribution of TNBs in our simulations evolved to have a large population of tight circular orbits. This tight circular population appears for a range of TNO physical properties, though a strong gravitational quadrupole can prevent some from fully circularizing. We introduce a stability parameter to predict the effectiveness of KCTF on a TNB orbit, and show that a number of known TNBs must have a large gravitational quadrupole to be stable.

Determination of binary asteroid orbits with a genetic-based algorithm

Aims: Over the past decade, discoveries of multiple and binary asteroid systems have played a significant role in our general understanding of small solar system bodies. Direct observations of satellites of asteroids are rare and difficult since they require the use of already over-subscribed facilities such as adaptive optics (AO) on large 8-10 m class telescopes and the Hubble Space Telescope (HST). The scarcity of data and the long temporal baseline of observations (up to 10 years) significantly complicate the determination of the mutual orbits of these systems. Methods: We implemented a new approach for determining the mutual orbits of directly-imaged multiple asteroids using a genetic-based algorithm. This approach was applied to several known binary asteroid systems (22 Kalliope, 3749 Balam, and 50 000 Quaoar) observed with AO systems and HST. This statistical method is fast enough to permit the search for an orbital solution across a large parameter space and without a priori information about the mutual orbit. Results: From 10 years of observation, we derived an orbital solution for Linus, companion of (22) Kalliope, with an accuracy close to the astrometric limit provided by the AO observations, assuming a purely Keplerian orbit. A search for non-Keplerian orbit confirmed that a J2 ~ 0 is the best-fitting solution. We show that the precession of the nodes could be detected without ambiguity, implying that Kalliope's primary may have an inhomogeneous internal structure. HST astrometric observations of Weywot, companion of the trans-Neptunian object (50 000) Quaoar, were used to derive its mass and its bulk density, which appears to be higher than the density of other TNOs. Finally, we derived a bundle of orbital solutions for (3749) Balam, with equally good fits, from the limited set of astrometric positions. They provide a realistic density between 1.3 and 3.7 g/cm3 for this S-type asteroid.

POSSIBLE DISINTEGRATING SHORT-PERIOD SUPER-MERCURY ORBITING KIC 12557548

We report here on the discovery of stellar occultations, observed with Kepler, that recur periodically at 15.685 hour intervals, but which vary in depth from a maximum of 1.3% to a minimum that can be less than 0.2%. The star that is apparently being occulted is KIC 12557548, a K dwarf with T_eff = 4400 K and V = 16. Because the eclipse depths are highly variable, they cannot be due solely to transits of a single planet with a fixed size. We discuss but dismiss a scenario involving a binary giant planet whose mutual orbit plane precesses, bringing one of the planets into and out of a grazing transit. We also briefly consider an eclipsing binary, that either orbits KIC 12557548 in a hierarchical triple configuration or is nearby on the sky, but we find such a scenario inadequate to reproduce the observations. We come down in favor of an explanation that involves macroscopic particles escaping the atmosphere of a slowly disintegrating planet not much larger than Mercury. The particles could take the form of micron-sized pyroxene or aluminum oxide dust grains. The planetary surface is hot enough to sublimate and create a high-Z atmosphere; this atmosphere may be loaded with dust via cloud condensation or explosive volcanism. Atmospheric gas escapes the planet via a Parker-type thermal wind, dragging dust grains with it. We infer a mass loss rate from the observations of order 1 M_E/Gyr, with a dust-to-gas ratio possibly of order unity. For our fiducial 0.1 M_E planet, the evaporation timescale may be ~0.2 Gyr. Smaller mass planets are disfavored because they evaporate still more quickly, as are larger mass planets because they have surface gravities too strong to sustain outflows with the requisite mass-loss rates. The occultation profile evinces an ingress-egress asymmetry that could reflect a comet-like dust tail trailing the planet; we present simulations of such a tail.

Mutual events in the Cold Classical transneptunian binary system Sila and Nunam

Hubble Space Telescope observations between 2001 and 2010 resolved the binary components of the Cold Classical transneptunian object (79360) Sila–Nunam (provisionally designated 1997 CS29). From these observations we have determined the circular, retrograde mutual orbit of Nunam relative to Sila with a period of 12.50995±0.00036days and a semimajor axis of 2777±19km. A multi-year season of mutual events, in which the two near-equal brightness bodies alternate in passing in front of one another as seen from Earth, is in progress right now, and on 2011 February 1UT, one such event was observed from two different telescopes. The mutual event season offers a rich opportunity to learn much more about this barely-resolvable binary system, potentially including component sizes, colors, shapes, and albedo patterns. The low eccentricity of the orbit and a photometric lightcurve that appears to coincide with the orbital period are consistent with a system that is tidally locked and synchronized, like the Pluto–Charon system. The orbital period and semimajor axis imply a system mass of (10.84±0.22)×1018kg, which can be combined with a size estimate based on Spitzer and Herschel thermal infrared observations to infer an average bulk density of 0.72-0.23+0.37gcm-3, comparable to the very low bulk densities estimated for small transneptunian binaries of other dynamical classes.

Physical and dynamical characterisation of the unbound asteroid pair 7343-154634

Context. Models have shown that asteroids can undergo fission if their rate of rotation is steadily increased. The forces acting to pull the asteroid apart exceed the material strength and gravitational force holding the asteroid together and material can escape from the surface of the asteroid. Initially forming a binary asteroid system, the components are capable of decoupling at low relative velocity from their mutual orbit if their mass ratio is less than 0.2. A number of asteroids with very similar orbital elements have been shown to have had very recent (<1 Myr) encounters at distances smaller than the Hill sphere radius of the larger of the asteroids. The mass ratio of the asteroids in each pair is estimated to be less than 0.2, suggesting that these unbound pairs are the result of rotational fission. Aims. We determine whether the asteroids in one such unbound pair, (7343) Ockeghem and (154 634) 2003 XX28, share a common composition, indicative of asteroids formed from a common parent and further constrain a likely formation age for this pair. Methods. We have obtained spectroscopic observations of each asteroid covering the wavelength range 0.45 to 1.0 microns. Using thermal observations we have measured the size and albedo of (7343) Ockeghem. Combined with optical lightcurve data of both asteroids, we have constrained the size and density of the asteroids and estimated the strength of the Yarkovsky force experienced by both. This improved physical information has been used in new dynamical simulations of the asteroids’ orbits to better constrain a formation time of this pair. Results. We find that the asteroids have very similar spectra consistent with an S-type taxonomy. The geometric albedo of (7343) Ockeghem, 0.20 ± 0.06 is consistent with this classification. The mass ratio range of the asteroids assuming an equal density, 0.007 to 0.065, is consistent with models of unbound asteroid pair formation. A new dynamical analysis has indicated that an absolute lower limit for the age of this pair is 400 kyr with a more likely age around 560 kyr, lower than a previous estimate of 800 kyr.

COLLISIONAL EVOLUTION OF ULTRA-WIDE TRANS-NEPTUNIAN BINARIES

The widely-separated, near-equal mass binaries hosted by the cold Classical Kuiper Belt are delicately bound and subject to disruption by many perturbing processes. We use analytical arguments and numerical simulations to determine their collisional lifetimes given various impactor size distributions, and include the effects of mass-loss and multiple impacts over the lifetime of each system. These collisional lifetimes constrain the population of small (R > ~1 km) objects currently residing in the Kuiper Belt, and confirm that the size distribution slope at small size cannot be excessively steep - likely q < ~3.5. We track mutual semi-major axis, inclination, and eccentricity evolution through our simulations, and show that it is unlikely that the wide binary population represents an evolved tail of the primordially-tight binary population. We find that if the wide binaries are a collisionally-eroded population, their primordial mutual orbit planes must have preferred to lie in the plane of the solar system. Finally, we find that current limits on the size distribution at small radii remain high enough that the prospect of detecting dust-producing collisions in real-time in the Kuiper Belt with future optical surveys is feasible.

NEAR-EARTH BINARIES AND TRIPLES: ORIGIN AND EVOLUTION OF SPIN-ORBITAL PROPERTIES

In the near-Earth asteroid population, binary and triple systems have been discovered with mutual orbits that have significant eccentricities as well as large semi-major axes. All known systems with eccentric orbits and all widely-separated primary-satellite pairs have rapidly rotating satellites. Here we study processes that can elucidate the origin of these spin-orbital properties. Binary formation models based on rotational fissioning can reproduce asynchronous satellites on orbits with high eccentricities and a wide range of separations, but do not match observed properties. We explore whether any evolutionary mechanisms can link the spin and orbital parameters expected from post-fission dynamics to those observed today. We investigate four processes: tidal torques, radiative perturbations (BYORP), close planetary encounters, and Kozai oscillations. We find that a combination of post-fission dynamics and tidal evolution can explain nearly all the spin-orbit properties in a sample of nine well-characterized near-Earth binaries and triples. The other mechanisms may act but are not required to explain the observed data. Lastly, we describe evolutionary pathways between observed spin-orbital states including synchronous and circular, asynchronous and circular, and asynchronous and eccentric configurations.

BINARY ASTEROID ENCOUNTERS WITH TERRESTRIAL PLANETS: TIMESCALES AND EFFECTS

Many asteroids that make close encounters with terrestrial planets are in a binary configuration. Here we calculate the relevant encounter timescales and investigate the effects of encounters on a binary's mutual orbit. We use a combination of analytical and numerical approaches with a wide range of initial conditions. Our test cases include generic binaries with close, moderate, and wide separations, as well as seven well-characterized near-Earth binaries. We find that close approaches (<10 Earth radii) occur for almost all binaries on 1-10 million year timescales. At such distances, our results suggest substantial modifications to a binary's semi-major axis, eccentricity, and inclination, which we quantify. Encounters within 30 Earth radii typically occur on sub-million year timescales and significantly affect the wider binaries. Important processes in the lives of near-Earth binaries, such as tidal and radiative evolution, can be altered or stopped by planetary encounters.

Binary asteroid population. 2. Anisotropic distribution of orbit poles of small, inner main-belt binaries

Our photometric observations of 18 main-belt binary systems in more than one apparition revealed a strikingly high number of 15 having positively re-observed mutual events in the return apparitions. Our simulations of the survey showed that it cannot be due to an observational selection effect and that the data strongly suggest that poles of mutual orbits between components of binary asteroids in the primary size range 3–8km are not distributed randomly: The null hypothesis of an isotropic distribution of the orbit poles is rejected at a confidence level greater than 99.99%. Binary orbit poles concentrate at high ecliptic latitudes, within 30° of the poles of the ecliptic. We propose that the binary orbit poles oriented preferentially up/down-right are due to either of the two processes: (i) the YORP tilt of spin axes of their parent bodies toward the asymptotic states near obliquities 0° and 180° (pre-formation mechanism) or (ii) the YORP tilt of spin axes of the primary components of already formed binary systems toward the asymptotic states near obliquities 0° and 180° (post-formation mechanism). The alternative process of elimination of binaries with poles closer to the ecliptic by dynamical instability, such as the Kozai effect due to gravitational perturbations from the Sun, does not explain the observed orbit pole concentration. This is because for close binary asteroid systems, the gravitational effects of primary’s irregular shape dominate the solar-tide effect.

CHARACTERIZATION OF SEVEN ULTRA-WIDE TRANS-NEPTUNIAN BINARIES

The low-inclination component of the Classical Kuiper Belt is host to a population of extremely widely-separated binaries. These systems are similar to other Trans-Neptunian binaries (TNBs) in that the primary and secondary components of each system are of roughly equal size. We have performed an astrometric monitoring campaign of a sample of seven wide-separation, long-period TNBs and present the first-ever well-characterized mutual orbits for each system. The sample contains the most eccentric (2006 CH69, e=0.9) and the most widely-separated, weakly bound (2001 QW322, a/Rh~0.22) binary minor planets known, and also contains the system with lowest-measured mass of any TNB (2000 CF105, M~1.85E17 kg). Four systems orbit in a prograde sense, and three in a retrograde sense. They have a different mutual inclination distribution compared to all other TNBs, preferring low mutual-inclination orbits. These systems have geometric r-band albedos in the range of 0.09-0.3, consistent with radiometric albedo estimates for larger solitary low-inclination Classical Kuiper Belt objects, and we limit the plausible distribution of albedos in this region of the Kuiper Belt. We find that gravitational collapse binary formation models produce a similar orbital distribution to that currently observed, which along with a confluence of other factors supports formation of the cold Classical Kuiper Belt in situ through relatively rapid gravitational collapse rather than slow hierarchical accretion. We show that these binary systems are sensitive to disruption via collisions, and their existence suggests that the size distribution of TNOs at small sizes remains relatively shallow.

LONG-TERM STABLE EQUILIBRIA FOR SYNCHRONOUS BINARY ASTEROIDS

Synchronous binary asteroids may exist in a long-term stable equilibrium, where the opposing torques from mutual body tides and the binary YORP (BYORP) effect cancel. Interior of this equilibrium, mutual body tides are stronger than the BYORP effect and the mutual orbit semi-major axis expands to the equilibrium; outside of the equilibrium, the BYORP effect dominates the evolution and the system semi-major axis will contract to the equilibrium. If the observed population of small (0.1 - 10 km diameter) synchronous binaries are in static configurations that are no longer evolving, then this would be confirmed by a null result in the observational tests for the BYORP effect. The confirmed existence of this equilibrium combined with a shape model of the secondary of the system enables the direct study of asteroid geophysics through the tidal theory. The observed synchronous asteroid population cannot exist in this equilibrium if described by the canonical "monolithic" geophysical model. The "rubble pile" geophysical model proposed by \citet{Goldreich2009} is sufficient, however it predicts a tidal Love number directly proportional to the radius of the asteroid, while the best fit to the data predicts a tidal Love number inversely proportional to the radius. This deviation from the canonical and \citet{Goldreich2009} models motivates future study of asteroid geophysics. Ongoing BYORP detection campaigns will determine whether these systems are in an equilibrium, and future determination of secondary shapes will allow direct determination of asteroid geophysical parameters.

Five new and three improved mutual orbits of transneptunian binaries

We present three improved and five new mutual orbits of transneptunian binary systems (58534) Logos-Zoe, (66652) Borasisi-Pabu, (88611) Teharonhiawako-Sawiskera, (123509) 2000 WK 183, (149780) Altjira, 2001 QY 297, 2003 QW 111, and 2003 QY 90 based on Hubble Space Telescope and Keck II laser guide star adaptive optics observations. Combining the five new orbit solutions with 17 previously known orbits yields a sample of 22 mutual orbits for which the period P, semimajor axis a, and eccentricity e have been determined. These orbits have mutual periods ranging from 5 to over 800 days, semimajor axes ranging from 1600 to 37,000 km, eccentricities ranging from 0 to 0.8, and system masses ranging from 2 × 10 17 to 2 × 10 22 kg. Based on the relative brightnesses of primaries and secondaries, most of these systems consist of near equal-sized pairs, although a few of the most massive systems are more lopsided. The observed distribution of orbital properties suggests that the most loosely-bound transneptunian binary systems are only found on dynamically cold heliocentric orbits. Of the 22 known binary mutual orbits, orientation ambiguities are now resolved for 9, of which 7 are prograde and 2 are retrograde, consistent with a random distribution of orbital orientations, but not with models predicting a strong preference for retrograde orbits. To the extent that other perturbations are not dominant, the binary systems undergo Kozai oscillations of their eccentricities and inclinations with periods of the order of tens of thousands to millions of years, some with strikingly high amplitudes.