arXiv subjects

Derek C. Richardson

Publications and source records attributed to Derek C. Richardson.

At least 19 recordsLinked to original sources

arXiv2026

A change of the rotation period of asteroid (65803) Didymos caused by the DART impact

On 26 September 2022, the NASA Double Asteroid Redirection Test (DART) spacecraft impacted Dimorphos, the secondary component of the binary asteroid (65803)~Didymos. This experiment tested the Kinetic Impactor technology for diverting dangerous asteroids. Due to the impact, the binary system's angular momentum has changed, resulting in a significant change in the orbital period of Dimorphos. Precise values of the pre- and post-impact orbital periods were derived from a large set of photometric light curves measured for the Didymos-Dimorphos system during six apparitions from 2003 to 2023. We used these data to detect a possible change in the rotation period of the primary as a consequence of the impact. We analyzed the binary system's light curves using the binary asteroid light curve decomposition method. We selected parts of the light curves covering orbital phases outside mutual events, which represent the primary rotational light curves. We applied the light curve inversion method to construct a convex shape model of Didymos and determine its rotation period before and after the impact. These two periods were treated as independent free parameters of the modeling. We found a value of 2.2603891 +/- 0.0000002 h for the pre-impact period and 2.260440 +/- 0.000008 h for the post-impact period. Their difference 0.18 +/- 0.03 s is small yet significant, indicating that the rotation of Didymos became slower after the DART impact. The most plausible physical explanation is Didymos's post-impact reshaping, making its shape more oblate.

astro-ph.EP↗

arXiv2025

The Dynamical State of the Didymos System Before and After the DART Impact

NASA's Double Asteroid Redirection Test (DART) spacecraft impacted Dimorphos, the natural satellite of (65803) Didymos, on 2022 September 26, as a first successful test of kinetic impactor technology for deflecting a potentially hazardous object in space. The experiment resulted in a small change to the dynamical state of the Didymos system consistent with expectations and Level 1 mission requirements. In the pre-encounter paper Richardson (2022), predictions were put forward regarding the pre- and post-impact dynamical state of the Didymos system. Here we assess these predictions, update preliminary findings published after the impact, report on new findings related to dynamics, and provide implications for ESA's Hera mission to Didymos, scheduled for launch in 2024 with arrival in late December 2026. Pre-encounter predictions tested to date are largely in line with observations, despite the unexpected, flattened appearance of Didymos compared to the radar model and the apparent pre-impact oblate shape of Dimorphos (with implications for the origin of the system that remain under investigation). New findings include that Dimorphos likely became prolate due to the impact and may have entered a tumbling rotation state. A possible detection of a post-impact transient secular decrease in the binary orbital period suggests possible dynamical coupling with persistent ejecta. Timescales for damping of any tumbling and clearing of any debris are uncertain. The largest uncertainty in the momentum transfer enhancement factor of the DART impact remains the mass of Dimorphos, which will be resolved by the Hera mission.

astro-ph.EP↗

arXiv2025

Surface dynamics and geophysical environment of asteroid (3200) Phaethon

Context. (3200) Phaethon is a ~5-km-diameter near-Earth asteroid with a small perihelion distance of 0.14 au and is the parent body of the Geminids. JAXA's DESTINY+ mission will fly by Phaethon in the near future. Aims. We aim to support the pre-flight planning for the DESTINY+ mission by performing a geophysical analysis on Phaethon's surface and near-surface environment utilizing the latest shape model from numerous observations. Methods. We employed the soft-sphere discrete element method code PKDGRAV to construct a "mascon" model of Phaethon and determine its gravity. We then computed the geopotential on Phaethon and derived various physical quantities related to its surface and near-surface dynamics. Results. We calculated geophysical quantities for the surface, including surface acceleration and slope. To assess whether surface objects could be launched off the surface, we computed the escape speed, return speed, Jacobi speed, and the location and stability of equilibrium points around Phaethon, and conducted a simple dynamical simulation of launched particles. Conclusions. Our results suggest that a large depression feature in the northern hemisphere could harbor exposed subsurface material and the freshest material on Phaethon. We propose that this depression be considered a key area for observation by the DESTINY+ mission

astro-ph.EP↗

arXiv2024

Dimorphos orbit determination from mutual events photometry

The NASA Double Asteroid Redirection Test (DART) spacecraft successfully impacted the Didymos-Dimorphos binary asteroid system on 2022 September 26 UTC. We provide an update to its pre-impact mutual orbit and estimate the post-impact physical and orbital parameters, derived using ground-based photometric observations taken from July 2022 to February 2023. We found that the total change of the orbital period was $-33.240 \pm 0.072$ min. (all uncertainties are 3$σ$). We obtained the eccentricity of the post-impact orbit to be $0.028 \pm 0.016$ and the apsidal precession rate of $7.3 \pm 2.0$ deg./day from the impact to 2022 December 2. The data taken later in December to February suggest that the eccentricity dropped close to zero or the orbit became chaotic approximately 70 days after the impact. Most of the period change took place immediately after the impact but in a few weeks following the impact it was followed by additional change of $-27^{+19}_{-58}$ seconds or $-19 \pm 18$ seconds (the two values depend on the approach we used to describe the evolution of the orbital period after the impact -- an exponentially decreasing angular acceleration or an assumption of a constant orbital period, which changed abruptly some time after the impact, respectively). We estimate the pre-impact Dimorphos-Didymos size ratio was $0.223 \pm 0.012$ and the post-impact is $0.202 \pm 0.018$, which indicates a marginally significant reduction of Dimorphos' volume by ($9 \pm 9) \%$ as the result of the impact.

astro-ph.EP↗

arXiv2024

Direct $N$-body simulations of satellite formation around small asteroids: insights from DART's encounter with the Didymos system

We explore binary asteroid formation by spin-up and rotational disruption considering the NASA DART mission's encounter with the Didymos-Dimorphos binary, which was the first small binary visited by a spacecraft. Using a suite of $N$-body simulations, we follow the gravitational accumulation of a satellite from meter-sized particles following a mass-shedding event from a rapidly rotating primary. The satellite's formation is chaotic, as it undergoes a series of collisions, mergers, and close gravitational encounters with other moonlets, leading to a wide range of outcomes in terms of the satellite's mass, shape, orbit, and rotation state. We find that a Dimorphos-like satellite can form rapidly, in a matter of days, following a realistic mass-shedding event in which only ${\sim}2-3\%$ of the primary's mass is shed. Satellites can form in synchronous rotation due to their formation near the Roche limit. There is a strong preference for forming prolate (elongated) satellites, although some simulations result in oblate spheroids like Dimorphos. The distribution of simulated secondary shapes is broadly consistent with other binary systems, measured through radar or lightcurves. Unless Dimorphos's shape is an outlier, and considering the observational bias against lightcurve-based determination of secondary elongations for oblate bodies, we suggest there could be a significant population of oblate secondaries. If these satellites initially form with elongated shapes, a yet-unidentified pathway is needed to explain how they become oblate. Finally, we show that this chaotic formation pathway occasionally forms asteroid pairs and stable triples, including co-orbital satellites and satellites in mean motion resonances.

astro-ph.EP↗

arXiv2023

An efficient numerical approach to modeling the effects of particle shape on rubble-pile dynamics

We present an approach for the inclusion of non-spherical constituents in high-resolution N-body discrete element method (DEM) simulations. We use aggregates composed of bonded spheres to model non-spherical components. Though the method may be applied more generally, we detail our implementation in the existing N-body code pkdgrav. It has long been acknowledged that non-spherical grains confer additional shear strength and resistance to flow when compared with spheres. As a result, we expect that rubble-pile asteroids will also exhibit these properties and may behave differently than comparable rubble piles composed of idealized spheres. Since spherical particles avoid some significant technical challenges, most DEM gravity codes have used only spherical particles, or have been confined to relatively low resolutions. We also discuss the work that has gone into improving performance with non-spherical grains, building on pkdgrav's existing leading-edge computational efficiency among DEM gravity codes. This allows for the addition of non-spherical shapes while maintaining the efficiencies afforded by pkdgrav's tree implementation and parallelization. As a test, we simulated the gravitational collapse of 25,000 non-spherical bodies in parallel. In this case, the efficiency improvements allowed for an increase in speed by nearly a factor of three when compared with the naive implementation. Without these enhancements, large runs with non-spherical components would remain prohibitively expensive. Finally, we present the results of several small-scale tests: spinup due to the YORP effect, tidal encounters, and the Brazil-nut Effect. In all cases, we find that the inclusion of non-spherical constituents has a measurable impact on simulation outcomes.

astro-ph.EP↗

arXiv2023

The Perturbed Full Two-Body Problem: Application to Post-DART Didymos

With the successful impact of the NASA DART spacecraft in the Didymos-Dimorphos binary asteroid system, we provide an initial analysis of the post-impact perturbed binary asteroid dynamics. To compare our simulation results with observations, we introduce a set of "observable elements" calculated using only the physical separation of the binary asteroid, rather than traditional Keplerian elements. Using numerical methods that treat the fully spin-orbit-coupled dynamics, we estimate the system's mass and the impact-induced changes in orbital velocity, semimajor axis, and eccentricity. We find that the changes to the mutual orbit depend strongly on the separation distance between Didymos and Dimorphos at the time of impact. If Dimorphos enters a tumbling state after the impact, this may be observable through changes in the system's eccentricity and orbit period. We also find that any DART-induced reshaping of Dimorphos would generally reduce the required change in orbital velocity to achieve the measured post-impact orbit period and will be assessed by the ESA Hera mission in 2027.

astro-ph.EP↗

arXiv2023

Momentum Transfer from the DART Mission Kinetic Impact on Asteroid Dimorphos

The NASA Double Asteroid Redirection Test (DART) mission performed a kinetic impact on asteroid Dimorphos, the satellite of the binary asteroid (65803) Didymos, at 23:14 UTC on September 26, 2022 as a planetary defense test. DART was the first hypervelocity impact experiment on an asteroid at size and velocity scales relevant to planetary defense, intended to validate kinetic impact as a means of asteroid deflection. Here we report the first determination of the momentum transferred to an asteroid by kinetic impact. Based on the change in the binary orbit period, we find an instantaneous reduction in Dimorphos's along-track orbital velocity component of 2.70 +/- 0.10 mm/s, indicating enhanced momentum transfer due to recoil from ejecta streams produced by the impact. For a Dimorphos bulk density range of 1,500 to 3,300 kg/m$^3$, we find that the expected value of the momentum enhancement factor, $β$, ranges between 2.2 and 4.9, depending on the mass of Dimorphos. If Dimorphos and Didymos are assumed to have equal densities of 2,400 kg/m$^3$, $β$= 3.61 +0.19/-0.25 (1 $σ$). These $β$ values indicate that significantly more momentum was transferred to Dimorphos from the escaping impact ejecta than was incident with DART. Therefore, the DART kinetic impact was highly effective in deflecting the asteroid Dimorphos.

astro-ph.EP↗

arXiv2022

Experimentally measuring rolling and sliding in three-dimensional dense granular packings

We experimentally measure a three-dimensional (3D) granular system's reversibility under cyclic compression. We image the grains using a refractive-index-matched fluid, then analyze the images using the artificial intelligence of variational autoencoders. These techniques allow us to track all the grains' translations and 3D rotations with accuracy sufficient to infer sliding and rolling displacements. Our observations reveal unique roles played by 3D rotational motions in granular flows. We find that rotations and contact-point motion dominate the dynamics in the bulk, far from the perturbation's source. Furthermore, we determine that 3D rotations are irreversible under cyclic compression. Consequently, contact-point sliding, which is dissipative, accumulates throughout the cycle. Using numerical simulations whose accuracy our experiment supports, we discover that much of the dissipation occurs in the bulk, where grains rotate more than they translate. Our observations suggest that the analysis of 3D rotations is needed for understanding granular materials' unique and powerful ability to absorb and dissipate energy.

cond-mat.soft↗

arXiv2022

Rotation-induced granular motion on the secondary component of binary asteroids: Application to the DART impact on Dimorphos

NASA's Double Asteroid Redirection Test (DART) mission will kinetically impact Dimorphos, the secondary component of the Didymos binary asteroid system, which will excite Dimorphos's dynamical state and lead to significant libration about the synchronous state and possibly chaotic non-principal axis rotation. Although this particular outcome is human caused, many other secondary components of binary systems are also prone to such exotic spin states. For a satellite in an excited spin state, the time-varying tidal and rotational environment can lead to significant surface accelerations. Depending on the circumstances, this mechanism may drive granular motion on the surface of the secondary. We modeled the dynamical evolution of a Didymos-like binary asteroid system using a fully coupled, three-dimensional simulation code. Then, we computed the time-varying gravitational and rotational accelerations felt over the entire surface resulting from the secondary's perturbed dynamical state. We find that an excited spin and orbit can induce large changes in the effective surface slope, potentially triggering granular motion and surface refreshment. However, for the case of the DART impact, this effect is highly dependent on many unknowns, such as Dimorphos's detailed shape, bulk density, surface geology, and the momentum transferred. Aside from the Didymos system and the DART mission, this effect also has important implications for binary systems in general.

astro-ph.EP↗

arXiv2022

Dynamical Evolution of the Didymos-Dimorphos Binary Asteroid as Rubble Piles following the DART Impact

Previous efforts have modeled the Didymos system as two irregularly shaped rigid bodies, although it is likely that one or both components are in fact rubble piles. Here, we relax the rigid-body assumption to quantify how this affects the spin and orbital dynamics of the system following the DART impact. Given known fundamental differences between our simulation codes, we find that faster rigid-body simulations produce nearly the same result as rubble-pile models in scenarios with a moderate value for the momentum enhancement factor, $β$ ($β{\sim}3$) and an ellipsoidal secondary. This indicates that the rigid-body approach is likely adequate for propagating the post-impact dynamics necessary to meet DART Mission requirements. Although, if Dimorphos has a highly-irregular shape or structure, or if $β$ is unexpectedly large, then rubble-pile effects may become important. If Dimorphos's orbit and spin state are sufficiently excited, then surface particle motion is also possible. However, these simulations are limited in their resolution and range of material parameters, so they serve as a demonstration of principle, and Future work is required to fully understand the likelihood and magnitude of surface motion.

astro-ph.EP↗

arXiv2022

Predictions for the Dynamical States of the Didymos System before and after the Planned DART Impact

NASA's Double Asteroid Redirection Test (DART) spacecraft is planned to impact the natural satellite of (65803) Didymos, Dimorphos, around 23:14 UTC on 26 September 2022, causing a reduction in its orbital period that will be measurable with ground-based observations. This test of kinetic impactor technology will provide the first estimate of the momentum transfer enhancement factor $β$ at a realistic scale, wherein ejecta from the impact provides an additional deflection to the target. Earth-based observations, the LICIACube spacecraft (to be detached from DART prior to impact), and ESA's follow-up Hera mission to launch in 2024, will provide additional characterization of the deflection test. Together Hera and DART comprise the Asteroid Impact and Deflection Assessment (AIDA) cooperation between NASA and ESA. Here the predicted dynamical states of the binary system upon arrival and after impact are presented. The assumed dynamically relaxed state of the system will be excited by the impact, leading to an increase in eccentricity and slight tilt of the orbit together with enhanced libration of Dimorphos with amplitude dependent on the currently poorly known target shape. Free rotation around the moon's long axis may also be triggered and the orbital period will experience variations from seconds to minutes over timescales of days to months. Shape change of either body due to cratering or mass wasting triggered by crater formation and ejecta may affect $β$ but can be constrained through additional measurements. Both BYORP and gravity tides may cause measurable orbital changes on the timescale of Hera's rendezvous.

astro-ph.EP↗

arXiv2022

Surface Properties of Near-Sun Asteroids

Near-Earth Asteroids (NEAs) with small perihelion distances reach sub-solar temperatures of > 1000 K. They are hypothesized to undergo "super-catastrophic" disruption, potentially caused by near-Sun processes such as thermal cracking, spin-up, meteoroid impacts, and subsurface volatile release; all of which are likely to cause surface alteration, which may change the spectral slope of the surface. We attempted to observe 35 of the 53 known near-Sun asteroids with q < 0.15 au from January 2017 to March 2020 to search for trends related to near-Sun processes. We report the optical colors and spectral slopes of 22 objects that we successfully observed and the measured rotation periods for three objects. We find the distribution of colors to be overall bluer than the color distribution of NEAs, though there is large overlap. We attribute large scatter to unknown dynamical histories and compositions for individual objects, as well as competing surface altering processes. We also investigated potential correlations between colors and other properties (e.g., perihelion distance, Tisserand parameter, rotation period), and searched for evidence of activity. Finally, we have compiled all known physical and dynamical properties of these objects, including probabilistic source regions and dwell times with q < 0.15 au.

astro-ph.EP↗

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.

astro-ph.EP↗

arXiv2021

Memory in 3D cyclically driven granular material

We perform experimental and numerical studies of a granular system under cyclic-compression to investigate reversibility and memory effects. We focus on the quasi-static forcing of dense systems, which is most relevant to a wide range of geophysical, industrial, and astrophysical problems. We find that soft-sphere simulations with proper stiffness and friction quantitatively reproduce both the translational and rotational displacements of the grains. We then utilize these simulations to demonstrate that such systems are capable of storing the history of previous compressions. While both mean translational and rotational displacements encode such memory, the response is fundamentally different for translations compared to rotations. For translational displacements, this memory of prior forcing depends on the coefficient of static inter-particle friction, but rotational memory is not altered by the level of friction.

cond-mat.soft↗

arXiv2021

Effects of interparticle friction on the response of 3D cyclically compressed granular material

We numerically study the effect of inter-particle friction coefficient on the response to cyclical pure shear of spherical particles in three dimensions. We focus on the rotations and translations of grains and look at the spatial distribution of these displacements as well as their probability distribution functions. We find that with increasing friction, the shear band becomes thinner and more pronounced. At low friction, the amplitude of particle rotations is homogeneously distributed in the system and is therefore mostly independent from both the affine and non-affine particle translations. In contrast, at high friction, the rotations are strongly localized in the shear zone. This work shows the importance of studying the effects of inter-particle friction on the response of granular materials to cyclic forcing, both for a better understanding of how rotations correlate to translations in sheared granular systems, and due to the relevance of cyclic forcing for most real-world applications in planetary science and industry.

cond-mat.soft↗

arXiv2020

Binary Planetesimal Formation from Gravitationally Collapsing Pebble Clouds

Planetesimals are compact astrophysical objects roughly 1-1000 km in size, massive enough to be held together by gravity. They can grow by accreting material to become full-size planets. Planetesimals themselves are thought to form by complex physical processes from small grains in protoplanetary disks. The streaming instability (SI) model states that mm/cm-size particles (pebbles) are aerodynamically collected into self-gravitating clouds which then directly collapse into planetesimals. Here we analyze ATHENA simulations of the SI to characterize the initial properties (e.g., rotation) of pebble clouds. Their gravitational collapse is followed with the PKDGRAV N-body code, which has been modified to realistically account for pebble collisions. We find that pebble clouds rapidly collapse into short-lived disk structures from which planetesimals form. The planetesimal properties depend on the cloud's scaled angular momentum, l=L/(M R_H^2 Omega, where L and M are the angular momentum and mass, R_H is the Hill radius, and Omega is the orbital frequency. Low-l pebble clouds produce tight (or contact) binaries and single planetesimals. Compact high-l clouds give birth to binary planetesimals with attributes that closely resemble the equal-size binaries found in the Kuiper belt. Significantly, the SI-triggered gravitational collapse can explain the angular momentum distribution of known equal-size binaries -- a result pending verification from studies with improved resolution. About 10% of collapse simulations produce hierarchical systems with two or more large moons. These systems should be found in the Kuiper belt when observations reach the threshold sensitivity.

astro-ph.EP↗

arXiv2020

Critical spin periods of sub-km-sized cohesive rubble-pile asteroids: dependencies on material parameters

In this work, we employ a soft-sphere discrete element method with a cohesion implementation to model the dynamical process of sub-km-sized cohesive rubble piles under continuous spinup. The dependencies of critical spin periods $T_c$ on several material parameters for oblate rubble piles with different bulk diameters $D$ are explored. Our numerical simulations show that both the increase of interparticle cohesion and particle shape parameter in our model can strengthen the bodies, especially for the smaller ones. In addition, we find there exists some critical diameter $D_{cri,ρ}$ at which the variation trend of $T_c$ with the bulk density $ρ$ reverses. Though a greater static friction coefficient $μ_S$ can strengthen the body, this effect attains a minimum at a critical diameter $D_{cri,ϕ}$ close to $D_{cri,ρ}$. The continuum theory (analytical method) is used for comparison and two equivalent critical diameters are obtained. The numerical results were fitted with the analytical method and the ratio of the interparticle cohesion $c$ to the bulk cohesion $C$ is estimated to be roughly 88.3. We find this ratio keeps constant for different $c$ and $ρ$, while it strongly depends on the friction angle $ϕ$. Also, our numerical results further show that the dependency of $T_c$ on $ϕ$ is opposite from that predicted by the continuum theory when $D$ < $D_{cri,ϕ}$. Finally, we find that the two critical diameters happen to be close to the diameter when the mean normal stress of the body equals zero, which is the separation between the compressive regime and the tensile regime.

astro-ph.EP↗