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The bearing capacity - the ability of a surface to support applied loads - is an important parameter for understanding and predicting the response of a surface. Previous work has inferred the bearing capacity and trafficability of specific regions of the Moon using orbital imagery and measurements of the boulder tracks visible on its surface. Here, we estimate the bearing capacity of the surface of an asteroid for the first time using DART/DRACO images of suspected boulder tracks on the surface of asteroid (65803) Didymos. Given the extremely low surface gravity environment, special attention is paid to the underlying assumptions of the geotechnical approach. The detailed analysis of the boulder tracks indicates that the boulders move from high to low gravitational potential, and provides constraints on whether the boulders may have ended their surface motion by entering a ballistic phase. From the 9 tracks identified with sufficient resolution to estimate their dimensions, we find an average boulder track width and length of 8.9 ± 1.5 m and 51.6 ± 13.3 m, respectively. From the track widths, the mean bearing capacity of Didymos is estimated to be 70 N/m2, implying that every 1 m2 of Didymos' surface at the track location can support only ~70 N of force before experiencing general shear failure. This value is at least 3 orders of magnitude less than the bearing capacity of dry sand on Earth, or lunar regolith. Bearing capacity, the ability of a surface to support applied loads, is a critical property in planetary exploration to understand a surface's response to landing or roving. Here, the bearing capacity of the asteroid Didymos is estimated using DART images of suspected boulder tracks on its surface. [ABSTRACT FROM AUTHOR]

A new bound on the amended potential in an n-body system is derived and applied to the partitioning of energy and angular momentum in a disrupting gravitational aggregate. This result provides analytic insight into how energy and angular momentum can be lost or partitioned between different collections of bodies as they escape from each other. To better understand the possible outcomes in such a situation, some specific numerical tests are also performed for systems of N = 3 , 4 , 5 , 6 . The results confirm that disrupting systems always lose energy, with a characteristic stochastic distribution of the lost energy. We also find that the system loses most of its angular momentum, although individual escaping components can retain significant nonzero angular momentum vectors that can be uniformly distributed in space as the number of bodies in the system increases. [ABSTRACT FROM AUTHOR]

The OSIRIS-REx mission collected a sample from the surface of the asteroid (101955) Bennu in 2020 October. Here, we study the impact of the OSIRIS-REx Touch-and-Go Sampling Acquisition Mechanism (TAGSAM) interacting with the surface of an asteroid in the framework of granular physics. Traditional approaches to estimating the penetration depth of a projectile into a granular medium include force laws and scaling relationships formulated from laboratory experiments in terrestrial-gravity conditions. However, it is unclear that these formulations extend to the OSIRIS-REx scenario of a 1300-kg spacecraft interacting with regolith in a microgravity environment. We studied the TAGSAM interaction with Bennu through numerical simulations using two collisional codes, pkdgrav and gdc-i. We validated their accuracy by reproducing the results of laboratory impact experiments in terrestrial gravity. We then performed TAGSAM penetration simulations varying the following geotechnical properties of the regolith: packing fraction (P), bulk density, inter-particle cohesion (σ c), and angle of friction (ϕ). We find that the outcome of a spacecraft-regolith impact has a non-linear dependence on packing fraction. Closely packed regolith (P ≳ 0.6) can effectively resist the penetration of TAGSAM if ϕ ≳ 28° and/or σ c ≳ 50 Pa. For loosely packed regolith (P ≲ 0.5), the penetration depth is governed by a drag force that scales with impact velocity to the 4/3 power, consistent with energy conservation. We discuss the importance of low-speed impact studies for predicting and interpreting spacecraft–surface interactions. We show that these low-energy events also provide a framework for interpreting the burial depths of large boulders in asteroidal regolith. [ABSTRACT FROM AUTHOR]

The exploration of near‐Earth asteroids has revealed dynamic surfaces characterized by mobile, unconsolidated material that responds to local geophysical gradients, resulting in distinct morphologies and boulder distributions. The OSIRIS‐REx (Origins, Spectral Interpretation, Resource Identification, and Security‐Regolith Explorer) mission confirmed that asteroid (101955) Bennu is a rubble pile with an unconsolidated surface dominated by boulders. In this work, we documented morphologies indicative of mass movement on Bennu and assessed the relationship to slope and other geologic features on the surface. We found globally distributed morphologic evidence of mass movement on Bennu up to ~70° latitude and on spatial scales ranging from individual boulders (meter scale) to a single debris flow ~100 m long and several meters thick. The apparent direction of mass movement is consistent with the local downslope direction and dominantly moves from the midlatitudes toward the equator. Mass movement appears to have altered the surface expression of large (≥30m diameter) boulders, excavating them in the midlatitudes and burying them in the equatorial region. Up to a 10 ± 1 m depth of material may have been transported away from the midlatitudes, which would have deposited a layer ~5 ± 1 m thick in the equatorial region assuming a stagnated flow model. This mass movement could explain the observed paucity of small (<50‐m diameter) craters and may have contributed material to Bennu's equatorial ridge. Models of changes in slope suggest that the midlatitude mass movement occurred in the past several hundred thousand years in regions that became steeper by several degrees. Plain Language Summary: Mass movement is the flow of loose material such as rock fragments across the surface of a planetary body (for instance, a landslide). We searched images of the surface of asteroid (101955) Bennu for evidence of mass movement. We found that rocks of various sizes have moved downslope, and evidence of this movement is apparent at most locations on the asteroid. By measuring the distribution of, and surface elevation around, the largest boulders on the surface of Bennu, we also found that the downslope movement of material appears to have excavated large boulders from the subsurface in the midlatitudes and buried large boulders near the equator. Our observation that material on Bennu has moved in what is currently the local downslope direction is not necessarily expected, because the downslope direction can change based on how quickly the asteroid is rotating, which varies over time. Thus, we can infer that this movement happened in the geologically recent past—probably within the past several hundred thousand years. These results can help us understand how geologic features like craters are erased, how the equatorial ridge formed, and how Bennu (and potentially other asteroids) change shape over time. Key Points: Signatures of mass movement on Bennu are globally distributed at multiple spatial scalesMass movement may have removed a ~10‐m‐thick layer of material from the midlatitudes and deposited a ~5‐m‐thick layer near the equatorMass movement that left visible evidence on Bennu occurred within the past several hundred thousand years [ABSTRACT FROM AUTHOR]

We analyze the trajectories of 313 particles seen in the near‐Bennu environment between December 2018 and September 2019. Of these, 65% follow suborbital trajectories, 20% undergo more than one orbital revolution around the asteroid, and 15% directly escape on hyperbolic trajectories. The median lifetime of these particles is ∼6 hr. The trajectories are sensitive to Bennu's gravitational field, which allows us to reliably estimate the spherical harmonic coefficients through degree 8 and to resolve nonuniform mass distribution through degree 3. The particles are perturbed by solar radiation pressure, enabling effective area‐to‐mass ratios to be estimated. By assuming that particles are oblate ellipsoids of revolution, and incorporating photometric measurements, we find a median axis ratio of 0.27 and diameters for equivalent‐volume spheres ranging from 0.22–6.1 cm, with median 0.74 cm. Our size distribution agrees well with that predicted for fragmentation due to diurnal thermal cycling. Detailed models of known accelerations do not produce a match to the observed trajectories, so we also estimate empirical accelerations. These accelerations appear to be related to mismodeling of radiation pressure, but we cannot rule out contributions from mass loss. Most ejections take place at local solar times in the afternoon and evening (12:00–24:00), although they occur at any time of day. We independently identify ten ejection events, some of which have previously been reported. We document a case where a particle ricocheted off the surface, revealing a coefficient of restitution 0.57±0.01 and demonstrating that some apparent ejections are not related to surface processes. Plain Language Summary: The Origins, Spectral Interpretation, Resource Identification, Security, Regolith Explorer (OSIRIS‐REx) mission discovered that near‐Earth asteroid (101955) Bennu is periodically ejecting small particles from its surface, placing it in the uncommon class of "active asteroids." We linked together individual detections of ejected particles and used numerical models of the forces acting on them to ascertain their trajectories and fates. We found that most particles have suborbital trajectories, meaning they fall back to Bennu's surface shortly after being ejected, but some orbit Bennu for days at a time, and some escape directly into space. From the particle trajectories, we are able to estimate their sizes (comparable to pebbles, from a few millimeters to a few centimeters in diameter) and shapes (probably flake like). Their trajectories also make it possible to estimate Bennu's gravity field more precisely than spacecraft measurements and help shed light on the possible causes of the ejections. Key Points: Most of the 313 particles we study have suborbital trajectories, but some orbit Bennu and others directly escapeThe particles appear to have flake‐like shapes and have effective diameters 0.22–6.1 cm with median 0.74 cmEjections tend to take place in the local afternoon and evening but can occur anytime [ABSTRACT FROM AUTHOR]

This paper explores the implications of the observed Bennu particle ejection events for that asteroid's spin rate and orbit evolution, which could complicate interpretation of the Yarkovsky‐O'Keefe‐Radzievskii‐Paddack (YORP) and Yarkovsky effects on this body's spin rate and orbital evolution. Based on current estimates of particle ejection rates, we find that the overall contribution to Bennu's spin and orbital drift is small or negligible as compared to the Yarkovsky and YORP effects. However, if there is a large unseen component of smaller mass ejections or a strong directionality in the ejection events, it could constitute a significant contribution that could mask the overall YORP effect. This means that the YORP effect may be stronger than currently assumed. The analysis is generalized so that the particle ejection effect can be assessed for other bodies that may be subject to similar mass loss events. Further, our model can be modified to address different potential mechanisms of particle ejection, which are a topic of ongoing study. Plain Language Summary: The near‐Earth asteroid Bennu has been observed to be ejecting particles of rock from its surface. The possible effect of these particle ejections on the asteroid's spin rate and orbit is studied using numerical modeling. We show that the effect is likely minimal, although for certain ejection geometries, their effect on the spin rate could be more important. The loss of mass caused by the particle ejections would likely limit the asteroid's rotational acceleration, suggesting that the acceleration effect on this body may be larger than assumed. We consider how different mechanisms of ejection could be modeled using our approach. Key Points: The net contribution of particle ejection from Bennu's surface on its spin rate and orbit evolution is minimal under some assumptionsIf there are systematics in ejection geometry, there may be meaningful contributions to rotational accelerationOur model can be tuned to address different potential mechanisms of particle ejection [ABSTRACT FROM AUTHOR]

This paper considers the energy required for collections of finite-density bodies to undergo escape under internal gravitational interactions alone. As the level of the system energy is increased, there are different combinations of components that can escape, until the total energy becomes positive, when the entire system can undergo mutual disruption. The results are also defined for bodies modeled as a continuum. These results provide rigorous constraints for the disruption of rubble-pile asteroids when only considering gravitational interaction effects, with the energy provided by rotation of an initial collection of the system. These issues are considered for discrete particles in the N-body problem and for size distributions of discrete particles in the continuum limit. [ABSTRACT FROM AUTHOR]

Asteroids and other Small Solar System Bodies (SSSBs) are of high general and scientific interest in many aspects. The origin, formation, and evolution of our Solar System (and other planetary systems) can be better understood by analysing the constitution and physical properties of small bodies in the Solar System. Currently, two space missions (Hayabusa2, OSIRIS-REx) have recently arrived at their respective targets and will bring a sample of the asteroids back to Earth. Other small body missions have also been selected by, or proposed to, space agencies. The threat posed to our planet by near-Earth objects (NEOs) is also considered at the international level, and this has prompted dedicated research on possible mitigation techniques. The DART mission, for example, will test the kinetic impact technique. Even ideas for industrial exploitation have risen during the last years. Lastly, the origin of water and life on Earth appears to be connected to asteroids. Hence, future space mission projects will undoubtedly target some asteroids or other SSSBs. In all these cases and research topics, specific knowledge of the structure and mechanical behaviour of the surface as well as the bulk of those celestial bodies is crucial. In contrast to large telluric planets and dwarf planets, a large proportion of such small bodies is believed to consist of gravitational aggregates ('rubble piles') with no—or low—internal cohesion, with varying macro-porosity and surface properties (from smooth regolith covered terrain, to very rough collection of boulders), and varying topography (craters, depressions, ridges). Bodies with such structure can sustain some plastic deformation without being disrupted in contrast to the classical visco-elastic models that are generally valid for planets, dwarf planets, and large satellites. These SSSBs are hence better described through granular mechanics theories, which have been a subject of intense theoretical, experimental, and numerical research over the last four decades. This being the case, it has been necessary to use the theoretical, numerical and experimental tools developed within soil mechanics, granular dynamics, celestial mechanics, chemistry, condensed matter physics, planetary and computer sciences, to name the main ones, in order to understand the data collected and analysed by observational astronomy (visible, thermal, and radio), and different space missions. In this paper, we present a review of the multi-disciplinary research carried out by these different scientific communities in an effort to study SSSBs. [ABSTRACT FROM AUTHOR]

We observed the near‐Earth asteroid (101955) Bennu from the ground in 1999 and 2005, and with the Hubble Space Telescope (HST) in 2012, to constrain its rotation rate. The data reveal an acceleration of 2.64 ± 1.05 × 10−6 deg/day2, which could be due to a change in the moment of inertia of Bennu or to spin up from the Yarkovsky‐O'Keefe‐Radzievskii‐Paddack effect or other source of angular momentum. The best solution is within 1 σ of the period determined by Nolan et al. (2013, https://doi.org/10.1016/j.icarus.2013.05.028). The Origins, Spectral Interpretation, Resource Identification, and Security–Regolith Explorer (OSIRIS‐REx) mission will determine the rotation state independently in 2019. Those measurements should show whether the change in rotation rate is a steady increase (due, e.g., to the Yarkovsky‐O'Keefe‐Radzievskii‐Paddack effect) or some other phenomenon. The precise shape and surface properties measured by the OSIRIS‐REx science team will allow for a better understanding of variations in rotation rate of small asteroids. Plain Language Summary: We observed near‐Earth asteroid (101955) Bennu—the target of the Origins, Spectral Interpretation, Resource Identification, and Security–Regolith Explorer (OSIRIS‐REx) spacecraft mission—using ground‐based telescopes and the Hubble Space Telescope. Our measurements show that its rotation has been speeding up since 1999. This change could be due to a change in the shape of Bennu or to the Yarkovsky‐O'Keefe‐Radzievskii‐Paddack effect: As the sunlight received by an asteroid is reflected or radiated back to space, the change in direction of the light coming in and going out pushes on the asteroid and can cause it to spin faster or slower, depending on its shape and orientation. The specific properties of the surface, such as the position of boulders, can have a large influence on the outcome. In the next few years, the OSIRIS‐REx team will study Bennu and independently measure its rotation, helping us to better understand the structure and dynamical evolution of small asteroids. Key Points: Asteroid (101955) Bennu has been rotating faster over time since 1999An acceleration in its rotation rate is needed to fit all the photometric measurements of asteroid BennuThe measured acceleration of Bennu is consistent with theoretical calculations of the total effects of the YORP effect [ABSTRACT FROM AUTHOR]

We study the roto-orbital dynamics of a uniform sphere and a body with axial symmetry by means of a radial intermediary, which defines an integrable system. Numerical comparisons of the MacCullagh’s truncation of the gravity gradient potential and intermediary models are performed, concluding that the intermediary provides a valuable approximation with small differences when compared with the MacCullagh’s one. Our analysis includes the analytical integration and a study of the special solutions and relative equilibria. [ABSTRACT FROM AUTHOR]

The OSIRIS-REx mission will conduct a Radio Science investigation of the asteroid Bennu with a primary goal of estimating the mass and gravity field of the asteroid. The spacecraft will conduct proximity operations around Bennu for over 1 year, during which time radiometric tracking data, optical landmark tracking images, and altimetry data will be obtained that can be used to make these estimates. Most significantly, the main Radio Science experiment will be a 9-day arc of quiescent operations in a 1-km nominally circular terminator orbit. The pristine data from this arc will allow the Radio Science team to determine the significant components of the gravity field up to the fourth spherical harmonic degree. The Radio Science team will also be responsible for estimating the surface accelerations, surface slopes, constraints on the internal density distribution of Bennu, the rotational state of Bennu to confirm YORP estimates, and the ephemeris of Bennu that incorporates a detailed model of the Yarkovsky effect. [ABSTRACT FROM AUTHOR]

We perform a large number of gravitational granular mechanics simulations to investigate the role of energy dissipation in the sphere-restricted planar three-body problem where, for a given angular momentum, multiple end-state configurations are available to the system. For the case of three equal spheres, previous studies have mapped all relative equilibria of the problem as a function of angular momentum. We find trends in the production of end states as a function of angular momentum and dissipation parameters, as well as outline the dynamical–mechanical interactions that generate these results. For strongly dissipative systems a relationship between the minimum energy function of the system and the end-state dynamics is uncovered. In particular, the likelihood of achieving one end state over another is largely governed by the geometrical projection of the minimum energy function. In contrast, for systems with low-energy dissipation the end state becomes a function of the relative depth of the different energy wells available to the system. This study highlights the importance of having well-defined dissipative properties of a gravitational granular system, such as those used to study the dynamics of rubble pile asteroids and planetary rings. [ABSTRACT FROM AUTHOR]

The rotational fission of asteroids has been studied previously with simplified models restricted to planar motion. However, the observed physical configuration of contact binaries leads one to conclude that most of them are not in a planar configuration and hence would not be restricted to planar motion once they undergo rotational fission. This motivated a study of the evolution of initially non-planar binaries created by fission. Using a two-ellipsoid model, we performed simulations taking only gravitational interactions between components into account. We simulate 91 different initial inclinations of the equator of the secondary body for 19 different mass ratios. After disruption, the binary system dynamics are chaotic, as predicted from theory. Starting the system in a non-planar configuration leads to a larger energy and enhanced coupling between the rotation state of the smaller fissioned body and the evolving orbital system, and enables re-impact to occur. This leads to differences with previous planar studies, with collisions and secondary spin fission occurring for all mass ratios with inclinations θ0 ≥ 40°, and mimics a Lidov-Kozai mechanism. Out of 1729 studied cases, we found that ~14 per cent result in secondary fission, ~25 per cent result in collisions and ~6 per cent have lifetimes longer than 200 yr. In Jacobson & Scheeres stable binaries only formed in cases with mass ratios q < 0.20. Our results indicate that it should be possible to obtain a stable binary with the same mechanisms for cases with mass ratios larger than this limit, but that the system should start in a non-planar configuration. [ABSTRACT FROM AUTHOR]

We propose an analytic model for the normal Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) and diurnal Yarkovsky effects experienced by a convex asteroid. Both the YORP torque and the Yarkovsky force are expressed as integrals of a universal function over the surface of an asteroid. Although in general this function can only be calculated numerically from the solution of the heat conductivity equation, approximate solutions can be obtained in quadratures for important limiting cases. We consider three such simplified models: Rubincam's approximation (zero heat conductivity), low thermal inertia limit (including the next order correction and thus valid for small heat conductivity), and high thermal inertia limit (valid for large heat conductivity). All three simplified models are compared with the exact solution. [ABSTRACT FROM AUTHOR]

Stable motions around the triangular libration points (TLP) in the Earth-Moon system perturbed by Sun are described. Two special quasi-periodic orbits around each TLP (called dynamical substitutes in this paper) are given. They were previously described in the planar Sun-Earth-Moon system by Kamel and are numerically obtained in the spatial Sun-Earth- Moon system. Linearized motions around the dynamical substitute are described in a semianalytical way. The size of the stable region around the substitute is described via a numerical approach, along with the resonance mechanisms that determine the boundary of the stable region. Possible temporary capture from the near Earth objects population is discussed. An observation algorithm to search permanent or temporarily captured objects in this region is given. Some potential applications of the TLPs of the Earth-Moon system in space missions are discussed. [ABSTRACT FROM AUTHOR]

Rigorous results on Hill Stability for the classical N-body problem are in general unknown for N ≥ 3, due to the complex interactions that may occur between bodies and the many different outcomes which may occur. However, the addition of finite density for the bodies along with a rigidity assumption on their mass distribution allows for Hill stability to be easily established. In this note we generalize results on Hill stability developed for the Full 3-body problem and show that it can be applied to the Full N-body problem. Further, we find that Hill Stability concepts can be applied to identify types of configurations which can escape and types which cannot as a function of the system energy. [ABSTRACT FROM PUBLISHER]

We explore the hypothesis that, due to small van der Waals forces between constituent grains, small rubble pile asteroids have a small but nonzero cohesive strength. The nature of this model predicts that the cohesive strength should be constant independent of asteroid size, which creates a scale dependence with relative strength increasing as size decreases. This model counters classical theory that rubble pile asteroids should behave as scale-independent cohesionless collections of rocks. We explore a simple model for asteroid strength that is based on these weak forces, validate it through granular mechanics simulations and comparisons with properties of lunar regolith, and then explore its implications and ability to explain and predict observed properties of small asteroids in the NEA and Main Belt populations, and in particular of asteroid 2008 TC3. One conclusion is that the population of rapidly rotating asteroids could consist of both distributions of smaller grains (i.e., rubble piles) and of monolithic boulders. [ABSTRACT FROM AUTHOR]

A direct comparison of the dynamical environments and mass measurements of asteroids (101955) Bennu and (162173) Ryugu are made, leveraging recently published data for both bodies as well as the latest results. The comparisons are of interest both for the design of close proximity operations and for the geophysical analysis of these bodies. The motivation for this discussion is to provide better insight into the diversity of small, primitive small bodies. Even though these two asteroids share many similarities, they are also individual worlds to be explored, with their own unique attributes. [ABSTRACT FROM AUTHOR]

The current best estimates of Bennu's gravity field will be presented, based on the independent solutions from four different teams involved on the OSIRISREx mission. The discovery of ejected particles about Bennu that may remain in orbit for several days or more provide a unique opportunity to probe the gravity field to higher degree and order than possible by using conventional spacecraft tracking. However, the non-gravitational forces acting on these particles must also be characterized, and their impact on solution accuracy must be assessed. This talk will present the latest results from the mission, incorporating spacecraft tracking from the lowest orbit in which the satellite will be during the mission. [ABSTRACT FROM AUTHOR]

Pairs of asteroids sharing similar heliocentric orbits, but not bound together, were found recently. Backward integrations of their orbits indicated that they separated gently with low relative velocities, but did not provide additional insight into their formation mechanism. A previously hypothesized rotational fission process may explain their formation—critical predictions are that the mass ratios are less than about 0.2 and, as the mass ratio approaches this upper limit, the spin period of the larger body becomes long. Here we report photometric observations of a sample of asteroid pairs, revealing that the primaries of pairs with mass ratios much less than 0.2 rotate rapidly, near their critical fission frequency. As the mass ratio approaches 0.2, the primary period grows long. This occurs as the total energy of the system approaches zero, requiring the asteroid pair to extract an increasing fraction of energy from the primary's spin in order to escape. We do not find asteroid pairs with mass ratios larger than 0.2. Rotationally fissioned systems beyond this limit have insufficient energy to disrupt. We conclude that asteroid pairs are formed by the rotational fission of a parent asteroid into a proto-binary system, which subsequently disrupts under its own internal system dynamics soon after formation. [ABSTRACT FROM AUTHOR]

In this paper we present and review a number of fundamental constraints that exist on the propagation of orbit uncertainty and phase volume flows in astrodynamics. These constraints arise due to the Hamiltonian nature of spacecraft dynamics. First we review the role of integral invariants and their connection to orbit uncertainty, and show how they can be used to formally solve the diffusion-less Fokker-Plank equation for a spacecraft probability density function. Then, we apply Gromov's Non-Squeezing Theorem, a recent advance in symplectic topology, to find a previously unrecognized fundamental constraint that exists on general, nonlinear mappings of orbit distributions. Specifically, for a given orbit distribution, it can be shown that the projection of future orbit uncertainties in each coordinate-momentum pair describing the system must be greater than or equal to a fundamental limit, called the symplectic width. This implies that there is always a fundamental limit to which we can know a spacecraft's future location in its coordinate and conjugate momentum space when mapped forward in time from an initial covariance distribution. This serves as an "uncertainty" principle for spacecraft uncertainty distributions. [ABSTRACT FROM AUTHOR]

We study spacecraft motion near a binary asteroid by means of theoretical and computational tools from geometric mechanics and dynamical systems. We model the system assuming that one of the asteroids is a rigid body (ellipsoid) and the other a sphere. In particular, we are interested in finding periodic and quasi-periodic orbits for the spacecraft near the asteroid pair that are suitable for observations and measurements. First, using reduction theory, we study the full two body problem (gravitational interaction between the ellipsoid and the sphere) and use the energy-momentum method to prove nonlinear stability of certain relative equilibria. This study allows us to construct the restricted full three-body problem (RF3BP) for the spacecraft motion around the binary, assuming that the asteroid pair is in relative equilibrium. Then, we compute the modified Lagrangian fixed points and study their spectral stability. The fixed points of the restricted three-body problem are modified in the RF3BP because one of the primaries is a rigid body and not a point mass. A systematic study depending on the parameters of the problem is performed in an effort to understand the rigid body effects on the Lagrangian stability regions. Finally, using frequency analysis, we study the global dynamics near these modified Lagrangian points. From this global picture, we are able to identify (almost-) invariant tori in the stability region near the modified Lagrangian points. Quasi-periodic trajectories on these invariant tori are potentially convenient places to park the spacecraft while it is observing the asteroid pair. [ABSTRACT FROM AUTHOR]

Equilibrium conditions for a mutually attracting general mass distribution and point mass are stated. The equilibrium conditions can be reduced to six equations in six unknowns, plus the existence of integrals of motion consisting of the total angular momentum and energy of the system. The equilibrium conditions are further reduced to two independent equations, and their theoretical properties are studied. We state a set of necessary and sufficient conditions for an equilibrium that is well suited to the computation of certain classes of equilibria. These equations are solved for nonsymmetric gravity fields of interest, using a real asteroid shape model for the general gravity fields. The stability of the resulting equilibria are also noted. [ABSTRACT FROM AUTHOR]

The Restricted Hill Full 4-Body Problem (RHF4BP) models the motion of a spacecraft or particle about two mutually orbiting distributed bodies in the tidal gravity field of a larger body. The practical application of this problem is to the motion of a spacecraft or particle about a binary asteroid system. Current estimates are that up to 16% of near-Earth asteroids (NEAs) may be binary asteroids, thus this is an extremely relevant topic for future missions to NEAs. It is also an interesting topic from an academic point of view, as this problem integrates four classical problems of astrodynamics: the Hill problem, the restricted 3-body problem, the non-spherical orbiter problem, and the full 2-body problem. In this paper, we define the RHF4BP in terms of these classical models and present results that the RHF4BP inherits from these classical problems. Some initial steps towards the analysis of this problem are also given, relating to the stability of motion about the Lagrange points in the Restricted Full 3-Body Problem and the Restricted Hill 4-Body Problem, both one-stage simplifications of the RHF4BP. [ABSTRACT FROM AUTHOR]

The fuel optimality of third-body driven plane changes (i.e., plane changes performed by using third-body forces) over one-impulse transfers is investigated numerically and analytically. In particular, the range of third-body driven plane changes that are realizable is shown to be restricted and one impulse must be used in the uncovered regions. However, when third-body driven plane changes are realizable, it is shown that they are always optimal above a certain critical value (about 40° ) that depends on the initial condition. Contour plots of optimal ΔV values to perform a desired plane changes are given. [ABSTRACT FROM AUTHOR]

Presents research which simulated energetic impacts into small planetary bodies with varying internal structures. Prevalence of so-called rubble-pile asteroids in the Solar System; Importance of predicting how small asteroids evolve through impact; Factors influencing the outcome of a collision; Results from porous and multiple-component asteroids.

The dynamics and control of a satellite in orbit about the asteroid Apophis through its Earth close approach in 2029 is evaluated and investigated. First, the feasibility of carrying out close proximity operations about Apophis when in its heliocentric orbit phase is evaluated and shown to be feasible. Then three different types of close proximity motion relative to Apophis are analyzed that will enable a spacecraft to take observations throughout the Earth close approach. These are maintaining a relative orbit that is somewhat distant from Apophis, hovering along the Earth-Apophis line, or maintaining orbit about Apophis through the flyby. Each of these are shown to be feasible, albeit challenging, and some basic aspects of these operations are noted and discussed. [ABSTRACT FROM AUTHOR]

Asteroids and other Small Solar System Bodies (SSSBs) are of high general and scientific interest in many aspects. The origin, formation, and evolution of our Solar System (and other planetary systems) can be better understood by analysing the constitution and physical properties of small bodies in the Solar System. Currently, two space missions (Hayabusa2, OSIRIS-REx) have recently arrived at their respective targets and will bring a sample of the asteroids back to Earth. Other small body missions have also been selected by, or proposed to, space agencies. The threat posed to our planet by near-Earth objects (NEOs) is also considered at the international level, and this has prompted dedicated research on possible mitigation techniques. The DART mission, for example, will test the kinetic impact technique. Even ideas for industrial exploitation have risen during the last years. Lastly, the origin of water and life on Earth appears to be connected to asteroids. Hence, future space mission projects will undoubtedly target some asteroids or other SSSBs. In all these cases and research topics, specific knowledge of the structure and mechanical behaviour of the surface as well as the bulk of those celestial bodies is crucial. In contrast to large telluric planets and dwarf planets, a large proportion of such small bodies is believed to consist of gravitational aggregates ('rubble piles') with no—or low—internal cohesion, with varying macro-porosity and surface properties (from smooth regolith covered terrain, to very rough collection of boulders), and varying topography (craters, depressions, ridges). Bodies with such structure can sustain some plastic deformation without being disrupted in contrast to the classical visco-elastic models that are generally valid for planets, dwarf planets, and large satellites. These SSSBs are hence better described through granular mechanics theories, which have been a subject of intense theoretical, experimental, and numerical research over the last four decades. This being the case, it has been necessary to use the theoretical, numerical and experimental tools developed within soil mechanics, granular dynamics, celestial mechanics, chemistry, condensed matter physics, planetary and computer sciences, to name the main ones, in order to understand the data collected and analysed by observational astronomy (visible, thermal, and radio), and different space missions. In this paper, we present a review of the multi-disciplinary research carried out by these different scientific communities in an effort to study SSSBs. [ABSTRACT FROM AUTHOR]

Due to an error in a supporting algorithm used in writing the paper there was an incorrect conclusion given which is corrected here. [ABSTRACT FROM AUTHOR]

Tangential YORP, or TYORP, has recently been demonstrated to be an important factor in the evolution of an asteroid's rotation state. It is complementary to normal YORP, or NYORP, which used to be considered previously. While NYORP is produced by non-symmetry in the large-scale geometry of an asteroid, TYORP is due to heat conductivity in stones on the surface of the asteroid. To date, TYORP has been studied only in a simplified one-dimensional model, substituting stones with high long walls. This article for the first time considers TYORP in a realistic three-dimensional model, also including shadowing and self-illumination effects via ray tracing. TYORP is simulated for spherical stones lying on regolith. The model includes only five free parameters and the dependence of the TYORP on each of them is studied. The TYORP torque appears to be smaller than previous estimates from the one-dimensional model, but is still comparable to the NYORP torques. These results can be used to estimate TYORP of different asteroids and also as a basis for more sophisticated models of TYORP. [ABSTRACT FROM AUTHOR]