arXiv subjects

Daniel J. Scheeres

Publications and source records attributed to Daniel J. Scheeres.

At least 37 records · Page 2Linked to original sources

arXiv2021

Libration-induced Orbit Period Variations Following the DART Impact

The Double Asteroid Redirection Test (DART) mission will be the first test of a kinetic impactor as a means of planetary defense. In late 2022, DART will collide with Dimorphos, the secondary in the Didymos binary asteroid system. The impact will cause a momentum transfer from the spacecraft to the binary asteroid, changing the orbit period of Dimorphos and forcing it to librate in its orbit. Owing to the coupled dynamics in binary asteroid systems, the orbit and libration state of Dimorphos are intertwined. Thus, as the secondary librates, it also experiences fluctuations in its orbit period. These variations in the orbit period are dependent on the magnitude of the impact perturbation, as well as the system's state at impact and the moments of inertia of the secondary. In general, any binary asteroid system whose secondary is librating will have a non-constant orbit period on account of the secondary's fluctuating spin rate. The orbit period variations are typically driven by two modes: a long-period and short-period, each with significant amplitudes on the order of tens of seconds to several minutes. The fluctuating orbit period offers both a challenge and an opportunity in the context of the DART mission. Orbit period oscillations will make determining the post-impact orbit period more difficult, but can also provide information about the system's libration state and the DART impact.

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arXiv2021

The Excited Spin State of Dimorphos Resulting from the DART Impact

The NASA Double Asteroid Redirection Test (DART) mission is a planetary defense-driven test of a kinetic impactor on Dimorphos, the satellite of the binary asteroid 65803 Didymos. DART will intercept Dimorphos at a relative speed of ${\sim}6.5 \text{ km s}^{-1}$, perturbing Dimorphos's orbital velocity and changing the binary orbital period. We present three independent methods (one analytic and two numerical) to investigate the post-impact attitude stability of Dimorphos as a function of its axial ratios, $a/b$ and $b/c$ ($a \ge b \ge c$), and the momentum transfer efficiency $β$. The first method uses a novel analytic approach in which we assume a circular orbit and a point-mass primary that identifies four fundamental frequencies of motion corresponding to the secondary's mean motion, libration, precession, and nutation frequencies. At resonance locations among these four frequencies, we find that attitude instabilities are possible. Using two independent numerical codes, we recover many of the resonances predicted by the analytic model and indeed show attitude instability. With one code, we use fast Lyapunov indicators to show that the secondary's attitude can evolve chaotically near the resonance locations. Then, using a high-fidelity numerical model, we find that Dimorphos enters a chaotic tumbling state near the resonance locations and is especially prone to unstable rotation about its long axis, which can be confirmed by ESA's Hera mission arriving at Didymos in late 2026. We also show that a fully coupled treatment of the spin and orbital evolution of both bodies is crucial to accurately model the long-term evolution of the secondary's spin state and libration amplitude. Finally, we discuss the implications of a post-impact tumbling or rolling state, including the possibility of terminating BYORP evolution if Dimorphos is no longer in synchronous rotation.

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arXiv2021

Limiting behavior of asteroid obliquity and spin using a semi-analytic thermal model of the YORP effect

The Yarkovsky--O'Keefe--Radzievskii--Paddack (YORP) effect governs the spin evolution of small asteroids. The axial component of YORP, which alters the rotation rate of the asteroid, is mostly independent of its thermal inertia, while the obliquity component is very sensitive to the thermal model of the asteroid. Here we develop a semi-analytic theory for the obliquity component of YORP. We integrate an approximate thermal model over the surface of an asteroid, and find an analytic expression for the obliquity component in terms of two YORP coefficients. This approach allows us to investigate the overall evolution of asteroid rotation state, and to generalize the results previously obtained in the case of zero thermal inertia. The proposed theory also explains how a non-zero obliquity component of YORP originates even for a symmetric asteroid due to its finite thermal inertia. In many cases, this causes equatorial planes of asteroids to align with their orbital planes. The studied non-trivial behavior of YORP as a function of thermal model allows for a new kind of rotational equilibria, which can have important evolutionary consequences for asteroids.

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arXiv2020

King-Hele orbit theory for periodic orbit and attitude variations

The analytical theory of satellite orbits in an atmosphere developed by King-Hele remains widely in use for satellite mission design because of its accurate approximation to numerical integration under simplifying assumptions. Over the course of six decades, modifications to the theory have addressed many of its weaknesses. However, in all subsequent modifications of the original theory, the assumption of a constant drag-coefficient has been retained. The drag-coefficient is a dynamic parameter that governs the physical interaction between the atmosphere and the satellite and depends on ambient as well as satellite specific factors. In this work, Fourier series expansion models of the drag-coefficient are incorporated in the original King-Hele theory to capture time-variations of the drag-coefficient in averaging integrals. The modified theory is validated through simulations that demonstrate the attained improvements in approximating numerical results over the original King-Hele formulation.

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arXiv2020

Spin-driven evolution of asteroids' top-shapes at fast and slow spins seen from (101955) Bennu and (162173) Ryugu

Proximity observations by OSIRIS-REx and Hayabusa2 provided clues on the shape evolution processes of the target asteroids, (101955) Bennu and (162173) Ryugu. Their oblate shapes with equatorial ridges, or the so-called top shapes, may have evolved due to their rotational conditions at present and in the past. Different shape evolution scenarios were previously proposed; Bennu's top shape may have been driven by surface processing, while Ryugu's may have been developed due to large deformation. These two scenarios seem to be inconsistent. Here, we revisit the structural analyses in earlier works and fill a gap to connect these explanations. We also apply a semi-analytical technique for computing the cohesive strength distribution in a uniformly rotating triaxial ellipsoid to characterize the global failure of top-shaped bodies. Assuming that the structure is uniform, our semi-analytical approach describes the spatial variations in failed regions at different spin periods; surface regions are the most sensitive at longer spin periods, while interiors fail structurally at shorter spin periods. This finding suggests that the shape evolution of a top shape may vary due to rotation and internal structure, which can explain the different evolution scenarios of Bennu's and Ryugu's top shapes. We interpret our results as the indications of top shapes' various evolution processes.

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arXiv2020

Post-main-sequence debris from rotation-induced YORP break-up of small bodies II: multiple fissions, internal strengths and binary production

Over one quarter of white dwarfs contain observable metallic debris from the breakup of exo-asteroids. Understanding the physical and orbital history of this debris would enable us to self-consistently link planetary system formation and fate. One major debris reservoir is generated by YORP-induced rotational fission during the giant branch phases of stellar evolution, where the stellar luminosity can exceed the Sun's by four orders of magnitude. Here, we determine the efficacy of the giant branch YORP effect for asteroids with nonzero internal strength, and model post-fission evolution by imposing simple analytic fragmentation prescriptions. We find that even the highest realistic internal strengths cannot prevent the widespread fragmentation of asteroids and the production of a debris field over 100 au in size. We compute the number of successive fission events as they occur in progressively smaller time intervals as the star ascends the giant branches, providing a way to generate size distributions of asteroid fragments. The results are highly insensitive to progenitor stellar mass. We also conclude that the ease with which giant branch YORP breakup can generate binary asteroid subsystems is strongly dependent on internal strength. Formed binary subsystems in turn could be short-lived due to the resulting luminosity-enhanced BYORP effect.

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arXiv2019

Disassociation energies for the finite density N-body problem

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.

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arXiv2019

Doubly Synchronous Binary Asteroid Mass Parameter Observability

The full two-body problem (F2BP) is often used to model binary asteroid systems, representing the bodies as two finite mass distributions whose dynamics are influenced by their mutual gravity potential. The emergent behavior of the F2BP is highly coupled translational and rotational mutual motion of the mass distributions. A large fraction of characterized binary asteroids appear to be at, or near, the doubly synchronous equilibrium, which occurs when both bodies are tidally-locked and in a circular co-orbit. Stable oscillations about this equilibrium can be shown, for the nonplanar system, to be combinations of seven fundamental frequencies of the system and the mutual orbit rate. The fundamental frequencies arise as the linear periods of center manifolds identified about the equilibrium which are heavily influenced by each body's mass parameters. We leverage these eight dynamical constraints to investigate the observability of binary asteroid mass parameters via dynamical observations. This is accomplished by deriving a relationship between the fundamental frequencies and mass parameters for doubly synchronous systems. This relationship allows us to show the sensitivity of the dynamics to changes in the mass parameters, first for the planar dynamics, and then for the nonplanar dynamics. In so doing we are able to predict the idealized estimation covariance of the mass parameters based on observation quality and define idealized observation accuracies for desired mass parameter certainties. We apply these tools to 617 Patroclus, a doubly synchronous Trojan binary and flyby target of the LUCY mission, as well as the Pluto and Charon system in order to predict mutual behavior

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arXiv2019

Cohesive Regolith on Fast Rotating Asteroids

The migration of cohesive regolith on the surface of an otherwise monolithic or strong asteroid is studied using theoretical and simulation models. The theory and simulations show that under an increasing spin rate (such as due to the YORP effect), the regolith covering is preferentially lost across certain regions of the body. For regolith with little or no cohesive strength, failure occurs by landsliding from the mid latitudes of the body at high enough spin rates. As the cohesive strength of the regolith increases, failure occurs by fission of grains (or coherent chunks of grains) across a greater extent of latitudes and eventually will first occur at the equator. As the spin rate is further increased, failure regions migrate from the first failure point to higher and lower latitudes. Eventually failure will encompass the equatorial region, however there always remains a region of high latitudes (around the poles) that will not undergo failure for arbitrarily high spin rates (unless disturbed by some other phenomenon). With these results a scaling law is derived that can be used to determine whether observed asteroids could retain surface regolith grains of a given size. The implications of this for the interpretation of spectral observations of small asteroids and boulder migration on large asteroids are discussed.

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arXiv2019

The Western Bulge of 162173 Ryugu Formed as a Result of a Rotationally Driven Deformation Process

162173 Ryugu, the target of Hayabusa2, has a round shape with an equatorial ridge, which is known as a spinning top-shape. A strong centrifugal force is a likely contributor to Ryugu's top-shaped features. Observations by Optical Navigation Camera onboard Hayabusa2 show a unique longitudinal variation in geomorphology; the western side of this asteroid, later called the western bulge, has a smooth surface and a sharp equatorial ridge, compared to the other side. Here, we propose a structural deformation process that generated the western bulge. Applying the mission-derived shape model, we employ a finite element model technique to analyze the locations that experience structural failure within the present shape. Assuming that materials are uniformly distributed, our model shows the longitudinal variation in structurally failed regions when the spin period is shorter than ~3.75 h. Ryugu is structurally intact in the subsurface region of the western bulge while other regions are sensitive to structural failure. We infer that this variation is indicative of the deformation process that occurred in the past, and the western bulge is more relaxed structurally than the other region. Our analysis also shows that this deformation process might occur at a spin period between ~3.5 h and ~3.0 h, providing the cohesive strength ranging between ~4 Pa and ~10 Pa.

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arXiv2019

Detection of Rotational Acceleration of Bennu using HST Lightcurve Observations

We observed the near-Earth asteroid (101955) Bennu from the ground in 1999 and 2005, and with the Hubble Space Telescope in 2012, to constrain its rotation rate. The data reveal an acceleration of $2.64 \pm 1.05 \times 10^{-6} \mathrm{deg\ day}^{-2}$, which could be due to a change in the moment of inertia of Bennu or to spin up from the YORP effect or other source of angular momentum. The best solution is within 1 sigma of the period determined by Nolan et al. (2013). The 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, for example, to the YORP 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.

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arXiv2019

Systematic structure and sinks in the YORP effect

There is a correlation between the components of the YORP effect of most asteroids, which drives the obliquity and spin rate of the affected bodies in a consistent pattern. This allows for a clear and unambiguous picture for how the spin rates and poles of asteroids affected by YORP will evolve and simplifies the overall picture for how populations will migrate on average. The YORP effect can also lead to a previously unexplored equilibrium state for affected bodies. This equilibrium state is a function of the usual "normal YORP" effect (which arises due to the global shape asymmetry of the asteroid) and the "tangential YORP" (which arises due the transport of thermal energy through rocky surface features). Estimates from current shape models show that 10-20\% of asteroids have the proper condition to be captured in this equilibrium state, indicating that the occurrence of this state may be significant. The existence of this attractor for the asteroid population means that objects affected by YORP may leave their usual YORP cycles and maintain a constant spin rate over long time periods -- this has significant implications for our interpretation of asteroid spin rate evolution and related theories for their physical evolution.

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arXiv2018

Rotationally induced failure of irregularly shaped asteroids

Many asteroids are rubble piles with irregular shapes. While the irregular shapes of large asteroids may be attributed to collisional events, those of small asteroids may result from not only impact events but also rotationally induced failure, a long-term consequence of small torques caused by, for example, solar radiation pressure. A better understanding of shape deformation induced by such small torques will allow us to give constraints on the evolution process of an asteroid and its structure. However, no quantitative study has been reported to provide the relationship between an asteroid's shape and its failure mode due to its fast rotation. Here, we use a finite element model (FEM) technique to analyze the failure modes and conditions of 24 asteroids with diameters less than 30 - 40 km, which were observed at high resolution by ground radar or asteroid exploration missions. Assuming that the material distribution is uniform, we investigate how these asteroids fail structurally at different spin rates. Our FEM simulations describe the detailed deformation mode of each irregularly shaped asteroid at fast spin. The failed regions depend on the original shape. Spheroidal objects structurally fail from the interior, while elongated objects experience structural failure on planes perpendicular to the minimum moment of inertia axes in the middle of their structure. Contact binary objects have structural failure across their most sensitive cross sections. We further investigate if our FEM analysis is consistent with earlier works that theoretically explored a uniformly rotating triaxial ellipsoid. The results show that global shape variations may significantly change the failure condition of an asteroid. Our work suggests that it is critical to take into account the actual shapes of asteroids to explore their failure modes in detail.

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arXiv2018

A new equilibrium state for singly synchronous binary asteroids

The evolution of rotation states of small asteroids is governed by the YORP effect, nonetheless some asteroids can stop their YORP evolution by attaining a stable equilibrium. The same is true for binary asteroids subjected to the BYORP effect. Here we discuss a new type of equilibrium that combines these two, which is possible in a singly synchronous binary system. This equilibrium occurs when the normal YORP, the tangential YORP and the binary YORP compensate each other, and tidal torques distribute the angular momentum between the components of the system and dissipate energy. Such a system if unperturbed would remain singly synchronous in perpetuity with constant spin and orbit rates, as the tidal torques dissipate the incoming energy from impinging sunlight at the same rate. The probability of the existence of this kind of equilibrium in a binary system is found to be on the order of a few percent.

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arXiv2017

Equilibrium rotation states of doubly synchronous binary asteroids

A doubly synchronous binary asteroid simultaneously experiences YORP and BYORP, the former being independent of the radius of the orbit, while the latter linearly dependent on the radius. In many systems YORP and BYORP can compensate each other at some radius, causing an equilibrium state, to which other orbits converge in the course of their evolution. We derive mathematical formalism of such equilibria in terms of dimensionless YORP and BYORP coefficients. We compute YORP and BYORP coefficients for a set of photometric and radar shape models, and find equilibria to be relatively common.

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arXiv2017

Constraints on the perturbed mutual motion in Didymos due to impact-induced deformation of its primary after the DART impact

Binary near-Earth asteroid (65803) Didymos is the target of the proposed NASA Double Asteroid Redirection Test (DART), part of the Asteroid Impact & Deflection Assessment (AIDA) mission concept. In this mission, the DART spacecraft is planned to impact the secondary body of Didymos, perturbing mutual dynamics of the system. The primary body is currently rotating at a spin period close to the spin barrier of asteroids, and materials ejected from the secondary due to the DART impact are likely to reach the primary. These conditions may cause the primary to reshape, due to landslides, or internal deformation, changing the permanent gravity field. Here, we propose that if shape deformation of the primary occurs, the mutual orbit of the system would be perturbed due to a change in the gravity field. We use a numerical simulation technique based on the full two-body problem to investigate the shape effect on the mutual dynamics in Didymos after the DART impact. The results show that under constant volume, shape deformation induces strong perturbation in the mutual motion. We find that the deformation process always causes the orbital period of the system to become shorter. If surface layers with a thickness greater than ~0.4 m on the poles of the primary move down to the equatorial region due to the DART impact, a change in the orbital period of the system and in the spin period of the primary will be detected by ground-based measurement.

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arXiv2016

Matching asteroid population characteristics with a model constructed from the YORP-induced rotational fission hypothesis

From the results of a comprehensive asteroid population evolution model, we conclude that the YORP-induced rotational fission hypothesis can be consistent with the observed population statistics of small asteroids in the main belt including binaries and contact binaries. The foundation of this model is the asteroid rotation model of Marzari et al. (2011), which incorporates both the YORP effect and collisional evolution. This work adds to that model the rotational fission hypothesis and the binary evolution model of Jacobson & Scheeres (2011). The asteroid population evolution model is highly constrained by these and other previous works, and therefore it has only two significant free parameters: the ratio of low to high mass ratio binaries formed after rotational fission events and the mean strength of the binary YORP (BYORP) effect. We successfully reproduce characteristic statistics of the small asteroid population: the binary fraction, the fast binary fraction, steady-state mass ratio fraction and the contact binary fraction. We find that in order for the model to best match observations, rotational fission produces high mass ratio ($> 0.2$) binary components with four to eight times the frequency as low mass ratio ($< 0.2$) components, where the mass ratio is the mass of the secondary component divided by the mass of the primary component. This is consistent with post-rotational fission binary system mass ratio being drawn from either a flat or a positive and shallow distribution, since the high mass ratio bin is four times the size of the low mass ratio bin; this is in contrast to the observed steady-state binary mass ratio, which has a negative and steep distribution. This can be understood in the context of the BYORP-tidal equilibrium hypothesis, which predicts that low mass ratio binaries survive for a significantly longer period of time than high mass ratio systems.

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arXiv2015

Internal Structure of Asteroids Having Surface Shedding due to Rotational Instability

Surface shedding of an asteroid is a failure mode where surface materials fly off due to strong centrifugal forces beyond the critical spin period, while the internal structure does not deform significantly. This paper proposes a possible structure of an asteroid interior that leads to such surface shedding due to rapid rotation rates. A rubble pile asteroid is modeled as a spheroid composed of a surface shell and a concentric internal core, the entire assembly called the test body. The test body is assumed to be uniformly rotating around a constant rotation axis. We also assume that while the bulk density and the friction angle are constant, the cohesion of the surface shell is different from that of the internal core. First, developing an analytical model based on limit analysis, we provide the upper and lower bounds for the actual surface shedding condition. Second, we use a Soft-Sphere Discrete Element Method (SSDEM) to study dynamical deformation of the test body due to a quasi-static spin-up. In this paper we show the consistency of both approaches. Additionally, the SSDEM simulations show that the initial failure always occurs locally and not globally. In addition, as the core becomes larger, the size of lofted components becomes smaller. These results imply that if there is a strong enough core in a progenitor body, surface shedding is the most likely failure mode.

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