Yarkovsky-O'Keefe-Radzievskii-Paddack Research Articles

Dynamical Characteristics of Active Asteroid 311P/PANSTARRS

311P/PANSTARRS is an active asteroid with characteristics of both asteroids and comets, and it is one of the targets of China's Tianwen-2 mission. Because of its small size of about 400 m, the Yarkovsky effect may have a significant influence on its long-term dynamics. This paper discussed the changes in the long-term motion of 311P/PANSTARRS caused by the Yarkovsky effect. By assuming different surface compositions, this simulation introduced the semi-major axis drift by propagating orbits of orbital clones. It also discusses non-gravitational effects such as close encounters, non-destructive impacts, and the YORP (Yarkovsky-O'Keefe-Radzievskii-Paddack) effect. The study calculates the probabilities of close encounters and impacts with major planets and estimates the timescale for 311P/PANSTARRS to reach its rotational period splitting limit. The results of the simulations show that the Yarkovsky effect may cause 311P/PANSTARRS to exit from the resonance region faster when compared to a purely gravitational model. 311P/PANSTARRS will leave the current resonance region after roughly 10 Myr, and have a chance to become a Mars-crossing asteroid through ν6 secular resonance due to the diurnal Yarkovsky effect if its surface is covered by a regolith layer. It is concluded that 311P/PANSTARRS is stable at least 10 Myr time scale even if taking the Yarkovsky effect and the YORP effect into account. Furthermore, the YORP effect may not significantly affect the semi-major axis drift of 311P/PANSTARRS.

Recent collisional history of (65803) Didymos

The Double Asteroid Redirection Test (DART, NASA) spacecraft revealed that the primary of the (65803) Didymos near-Earth asteroid (NEA) binary system is not exactly the expected spinning top shape observed for other km-size asteroids. Ground based radar observations predicted that such shape was compatible with the uncertainty along the direction of the asteroid spin axis. Indeed, Didymos shows crater and landslide features, and evidence for boulder motion at low equatorial latitudes. Altogether, the primary seems to have undergone sudden structural failure in its recent history, which may even result in the formation of the secondary. The high eccentricity of Didymos sets its aphelion distance inside the inner main belt, where it spends more than 1/3 of its orbital period and it may undergo many more collisions than in the NEA region. In this work, we investigate the collisional environment of this asteroid and estimate the probability of collision with multi-size potential impactors. We analyze the possibility that such impacts produced the surface features observed on Didymos by comparing collisional intervals with estimated times for surface destabilization by the Yarkovsky-O’Keefe-Radzievskii-Paddack (YORP) effect. We find that collisional effects dominate over potential local or global deformation due to YORP spin up.

Regolith resurfacing and shedding on spinning spheroidal asteroids: Dependence on the surface mechanical properties

The Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effect has been shown to effectively alter the rotational status of asteroids. The spin-up of the asteroid leads to surface instability and eventually triggers regolith failure, followed by landslide and mass shedding on the asteroid's surface. We explore the dynamics of the rotation-induced resurfacing and shedding, paying special attention to the dependence of post-shedding evolution on regolith mechanical properties, such as cohesion. We propose a qualitative semi-analytical model to explore the post-failure dynamics of a fast-rotating asteroid. We also consider the interaction between the surface mass rearrangement and the asteroid’s spin status. We used our model to investigate the surface region where the failure occurs, as well as the total mass shed from the surface and the spin-down of the asteroid in this process. Based on our model, all the possible avalanche events following a regolith failure can be classified into four basic types: resurfacing (ReS), shedding and resurfacing (S ReS), shed and bound (S-Bound), and shedding and escaping (S-Escp). Their corresponding regions in the parameter space are illustrated in this work. Our results show that although the regolith cohesion is very small ($ 1-2$Pa), cohesion plays an important role in the onset of the avalanche. Moreover, our model qualitatively reconstructs the links between the regolith’s properties and the dynamical fates of the shed material. The timescale of YORP-induced shedding events is also discussed in this work.

Finite Element Method approach 3-dimensional thermophysical model for YORP torque computation

We present a new thermophysical model suitable for simulating the thermal conditions of small celestial bodies, such as asteroids and comet nuclei, as well as local topographic features like rocks, boulders, and craters. The model employs a Finite Element Method (FEM) approach to solve the 3-dimensional heat conduction problem, explicitly accounting for heat conduction between neighboring FEM elements. This sets it apart from other thermophysical models that typically neglect lateral heat conduction. The model takes into account scattering sunlight, self-heating due to thermal radiation, and both horizon and cast shadows. We validated our model against an analytical solution for the transient temperature distribution of a sphere under convective boundary conditions. Additionally, we compared our results with earlier thermophysical modeling works and observational data of asteroid (101955) Bennu. Using the shape models of Bennu as well as scaled versions of (162173) Ryugu, (25143) Itokawa, and (6489) Golevka to match Bennu’s surface area, we investigated the effects of shape and lateral heat conduction on the Yarkovsky-O’Keefe-Radzievskii-Paddack (YORP) torque. Results indicate that contact binary and non-classified/irregular objects experience a stronger YORP torque compared to spheroidal objects. The lateral heat conduction can enhance or dampen the YORP torque. Further analysis is important to obtain more robust statistical conclusions.

Deficit of primitive compositions in binary asteroids and pairs

Context. Small binary asteroid systems and pairs are thought to form through fission induced by spin up via the Yarkovsky-O’Keefe-Radzievskii-Paddack (YORP) effect. This process is expected to depend on their structural strength and therefore composition. Aims. We aim to determine how taxonomic classes – used as a proxy for composition – are distributed amongst binary asteroids and asteroid pairs compared to the general population. Methods. We compared the distribution of taxonomic classes of binary systems and pairs with that of a reference sample of asteroids. We built this sample by selecting asteroids in a way that reproduces the orbital and size distribution of the binaries and pairs. We did this in order to minimize potential biases between samples. Results. A strong deficit of primitive compositions (C, B, P, D types) among binary asteroids and asteroid pairs is identified, as well as a strong excess of asteroids with mafic-silicate-rich surface compositions (S, Q, V, A types). Conclusions. Amongst low-mass, rapidly rotating asteroids, those with mafic-silicate-rich compositions are more likely to form multiple asteroid systems than their primitive counterparts.

A Detectable Candidate for the YORP Effect of Asteroids

The YORP (Yarkovsky-O’Keefe-Radzievskii-Paddack) effect is one of the mechanisms of the long-term dynamical evolution of asteroids. Compared with factors such as collision and gravitational perturbation, the YORP is of small magnitude, and the short-time scale observation effect is inconspicuous, which brings great difficulties to the direct measurement of the YORP. From the Asteroid Lightcurve Database, asteroids having a high confidence rotation period were selected for this study. Two subsample groups for identifying potential asteroids slowed by the YORP effect are provided by using the kernel density estimation method and the Kolmogorov-Smirnov test to analyze the rotation rate distribution characteristics of near-Earth asteroids and main belt asteroids; a screening model is proposed based on the light-curve data of seven YORP asteroids with YORP rotation acceleration, combined with the YORP intensity estimation method and the detection conditions of the YORP effect. Finally, ten candidates that can directly detect the YORP effect through light-curve data in the future are listed based on the screening model.

The crater-induced YORP effect

Context. The Yarkovsky–O’Keefe–Radzievskii–Paddack (YORP) effect plays an important role in the rotational properties and evolution of asteroids. While the YORP effect induced by the macroscopic shape of the asteroid and by the presence of surface boulders has been well studied, no investigation has been performed yet regarding how craters with given properties influence this effect. Aims. We introduce and estimate the crater-induced YORP effect (CYORP), which arises from the concave structure of the crater, to investigate the magnitude of the resulting torques as a function of varying properties of the crater and the asteroid by a semi-analytical method. Methods. By using a simple spherical shape model of the crater and assuming zero thermal inertia, we calculated the total YORP torque due to the crater, which was averaged over the spin and orbital motions of the asteroid, accounting for self-sheltering and self-sheltering effects. Results. The general form of the CYORP torque can be expressed in terms of the crater radius R0 and the asteroid radius Rast: 〈TCYORP〉 ~ WR02RastΦ/c, where W is an efficiency factor. We find that the typical values of W are about 0.04 and 0.025 for the spin and obliquity component, respectively, which indicates that the CYORP can be comparable to the normal YORP torque when the size of the crater is about one-tenth of the size of the asteroid, or equivalently when the crater/roughness covers one-tenth of the asteroid surface. Although the torque decreases with the crater size R0 as ~R02, the combined contribution of all small craters can become non-negligible due to their large number when the commonly used power-law crater size distribution is considered. The CYORP torque of small concave structures, usually considered as surface roughness, is essential to the accurate calculation of the complete YORP torque. Under the CYORP effect that is produced by collisions, asteroids go through a random walk in spin rate and obliquity, with a YORP reset timescale typically of 0.4 Myr. This has strong implications for the rotational evolution and orbital evolution of asteroids. Conclusions. Craters and roughness on asteroid surfaces, which correspond to concave structures, can influence the YORP torques and therefore the rotational properties and evolution of asteroids. We suggest that the CYORP effect should be considered in the future investigation of the YORP effect on asteroids.

Shape Model and Rotation Acceleration of (1685) Toro and (85989) 1999 JD6 from Optical Observations

The Yarkovsky-O’Keefe-Radzievskii-Paddack (YORP) effect is a net torque caused by solar radiation directly reflected and thermally re-emitted from the surface of small asteroids and is considered to be crucial in their dynamical evolution. By long-term photometric observations of selected near-Earth asteroids, it is hoped to enlarge asteroid samples with a detected YORP effect to facilitate the development of a theoretical framework. Archived light-curve data are collected and photometric observations are made for (1685) Toro and (85989) 1999 JD6, which enables measurement of their YORP effect by inverting the light curve to fit observations from a convex shape model. For (1685) Toro, a YORP acceleration υ = (3.2 ± 0.3) × 10−9 rad · day−2 (1σ error) is updated, which is consistent with previous YORP detection based on different light-curve data; for (85989) 1999 JD6, it is determined that the sidereal period is 7.667 749 ± 0.000009 hr, the rotation pole direction is located at λ = 232° ± 2°, β = − 59° ± 1°, the acceleration is detected to be υ = (2.4 ± 0.3) × 10−8 rad · day−2 (1σ error) and in addition to obtaining an excellent agreement between the observations and model. YORP should produce both spin-up and spin-down cases. However, including (85989) 1999 JD6, the dω/dt values of 11 near-Earth asteroids are positive totally, which suggests that there is either a bias in the sample of YORP detections or a real feature needs to be explained.

YORP Effect on Long-Term Rotational Dynamics of Debris in GEO

The Yarkovsky–O’Keefe–Radzievskii–Paddack (YORP) effect describes the torque induced on space objects produced by solar radiation and thermal re-emission. Previous analyses have demonstrated its influence on long-term rotational dynamics of space debris objects in Geostationary Orbit (GEO), where YORP becomes predominant with respect to other external perturbations (e.g., atmospheric drag, gravity gradient, eddy current torque), leading to a wide variety of possible behaviors. The capability of forecasting time windows of slow uniform rotation, if any, would bring significant advantages in operations of Active Debris Removal and on-orbit servicing, especially in the detumbling phase. Also, a non-negligible impact of the End-of-Life configuration, in terms of movable surfaces orientation and center of mass location, could lead to guidelines for future satellites to be easier targets in the disposal phase. In this work, a previously derived semi-analytical tumbling-averaged YORP rotational dynamics model is leveraged. Exploiting an averaged model, computational time is strongly reduced while maintaining sufficient accuracy compared to propagation of Euler’s equations of motion. First, a satellite of the Geostationary Operational Environmental Satellite (GOES) family is analyzed and compared to previous studies to verify the correct implementation of the model. A wider analysis is performed on simple geometric models, such as a box-wing satellite, a 3U CubeSat, and a rocket body. The impact of object size, surface optical properties, and center of mass position on long-term rotational behavior is investigated, providing a general insight into these phenomena with a possible future application to existing objects in GEO.

General Tumbling-Averaged Rotational Dynamics for Defunct Satellites

Understanding and predicting the long-term spin state evolution of defunct satellites and rocket bodies is important for solar radiation pressure modeling, space domain awareness, and active debris removal (ADR). Dynamical modeling and observations indicate that defunct geosynchronous satellite spin states are primarily driven by solar radiation torques via the Yarkovsky–O’Keefe–Radzievskii–Paddack (YORP) effect. In our two recent papers, we uncovered dynamically rich YORP-driven behavior including cycling between uniform rotation and non-principal axis tumbling, angular momentum sun tracking, and tumbling period resonances. These papers only considered the YORP effect. However, tumbling satellites are also subject to energy dissipation from residual fuel slosh and flexure. Gravitational torques and other environmental perturbations may affect long-term evolution as well. In this paper, the third in our series, we develop semi-analytical tumbling-averaged models for internal energy dissipation and gravity gradient torques and combine them with the earlier YORP models. Accounting for YORP and dissipation, we find asymptotically stable tumbling states with constant angular momentum and kinetic energy and a pole fixed in the rotating sun-satellite orbit frame. With gravity gradients, these asymptotic states become stable limit cycles with yearly periodicity. We discuss the implications of these findings for the space debris population, ADR, and satellite decommission procedures.

Video observations of tiny near-Earth objects with Tomo-e Gozen

Abstract We report the results of video observations of tiny (diameter less than 100 m) near-Earth objects (NEOs) with Tomo-e Gozen on the Kiso 105 cm Schmidt telescope. The rotational period of a tiny asteroid reflects its dynamical history and physical properties since smaller objects are sensitive to the Yarkovsky–O’Keefe–Radzievskii–Paddack (YORP) effect. We carried out video observations of 60 tiny NEOs at 2 fps from 2018 to 2021 and successfully derived the rotational periods and axial ratios of 32 NEOs including 13 fast rotators with rotational periods less than 60 s. The fastest rotator found during our survey is 2020 HS$_\mathsf {7}$ with a rotational period of 2.99 s. We statistically confirmed that there is a certain number of tiny fast rotators in the NEO population, which have been missed with all previous surveys. We have discovered that the distribution of the tiny NEOs in a diameter and rotational period (D–P) diagram is truncated around a period of 10 s. The truncation with a flat-top shape is not explained well by either a realistic tensile strength of NEOs or the suppression of YORP by meteoroid impacts. We propose that the dependence of the tangential YORP effect on the rotational period potentially explains the observed pattern in the D–P diagram.

Mercury and orbfit packages for numerical integration of planetary systems: implementation of the yarkovsky and yorp effects

For studies of the long-term evolution of small Solar System objects, it is fundamental to add the Yarkovsky and Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effects in the dynamical model. Still, implementations of these effects in publicly available N-body codes is either lacking, or the effects are implemented using significantly simplified models. In this paper, we present an implementation of the coupled Yarkovsky/YORP effects in the mercury and orbfit N-body codes. Along with these two effects, we also included the effects of non-destructive collisions and rotationally induced breakups to model the asteroid spin state properly. Given the stochastic nature of many incorporated effects, the software is suitable for statistical dynamical studies. Here we primarily explained the scientific aspect of the implementation, while technical details will be made freely available along with the source codes.

Rotation acceleration of asteroids (10115) 1992 SK, (1685) Toro, and (1620) Geographos due to the YORP effect

Context. The rotation state of small asteroids is affected by the Yarkovsky–O’Keefe–Radzievskii–Paddack (YORP) effect, which is a net torque caused by solar radiation directly reflected and thermally reemitted from the surface. Due to this effect, the rotation period slowly changes, which can be most easily measured in light curves because the shift in the rotation phase accumulates over time quadratically. Aims. By new photometric observations of selected near-Earth asteroids, we want to enlarge the sample of asteroids with a detected YORP effect. Methods. We collected archived light curves and carried out new photometric observations for asteroids (10115) 1992 SK, (1620) Geographos, and (1685) Toro. We applied the method of light curve inversion to fit observations with a convex shape model. The YORP effect was modeled as a linear change of the rotation frequency υ ≡ dω∕dt and optimized together with other spin and shape parameters. Results. We detected the acceleration υ = (8.3 ± 0.6) × 10−8 rad d−2 of the rotation for asteroid (10115) 1992 SK. This observed value agrees well with the theoretical value of YORP-induced spin-up computed for our shape and spin model. For (1685) Toro, we obtained υ = (3.3 ± 0.3) × 10−9 rad d−2, which confirms an earlier tentative YORP detection. For (1620) Geographos, we confirmed the previously detected YORP acceleration and derived an updated value of υ with a smaller uncertainty. We also included the effect of solar precession into our inversion algorithm, and we show that there are hints of this effect in Geographos’ data. Conclusions. The detected change of the spin rate of (10115) 1992 SK has increased the total number of asteroids with YORP detection to ten. In all ten cases, the dω∕dt value is positive, so the rotation of these asteroids is accelerated. It is unlikely to be just a statistical fluke, but it is probably a real feature that needs to be explained.

YORP Effect on Asteroid 162173 Ryugu: Implications for the Dynamical History

AbstractAsteroid 162173 Ryugu is a carbonaceous asteroid that was visited by Japan's Hayabusa2 spacecraft in 2018. The formation mechanism of the “spinning‐top” shape of Ryugu is a vital clue to the dynamical history of the near‐Earth asteroid. In this study, we address the long‐term evolution of its spin state induced by the Yarkovsky‐O’Keefe‐Radzievskii‐Paddack (YORP) effect, that is, the thermal recoil torque that changes the rotation period and spin‐pole direction. Given the current orbit, spin state, and three‐dimensional shape of Ryugu observed by Hayabusa2, we computed the YORP torque exerted on Ryugu using a simplified thermal model assuming zero thermal conductivity. Despite variations in the meter‐scaled topography, all 20 shape models that we examined indicate that the spin velocity of Ryugu is currently decreasing at a rate of deg/day2. Our findings also suggest that the thermal torque is responsible for maintaining the spin pole upright with respect to the orbital plane. Therefore, the YORP effect may explain the significant spin‐down from an earlier period of 3.5 hr to the present period of 7.6 hr. The corresponding time scale of the spin‐down is estimated to be 0.58–8.7 million years, depending on the input shape models. This time scale is comparable to the formation period of the largest crater, Urashima (5–12 Ma), or the western bulge (2–9 Ma) as derived from previous studies on crater statistics in Ryugu. Thus, its rotation may have started to decelerate as a consequence of major resurfacing events.

Resonance-Averaged Solar Torque Dynamics for Tumbling Satellites

Observations indicate that the spin states of retired and otherwise defunct satellites are diverse and can change significantly over time. Understanding defunct satellite spin state evolution is important for solar radiation pressure modeling, active debris removal, satellite servicing, and space situational awareness. Research has shown that many defunct satellites in geosynchronous earth orbit (GEO) are primarily driven by solar radiation torques via the Yarkovsky–O’Keefe–Radzievskii–Paddack (YORP) effect. Recent exploration of YORP-driven nonprincipal axis tumbling has uncovered rich dynamic behavior, including tumbling cycles, spin–orbit coupling, and tumbling period resonances. Radar and optical observations of the defunct Geostationary Operational Environmental Satellite (GOES) 8 strongly suggest that it has been captured in a tumbling resonance at least once since 2018. Motivated by these findings, we develop a numerical resonance-averaged dynamic model to understand YORP-driven resonance capture, building on our earlier nonresonant averaging framework. This resonance-averaged model illuminates resonance capture mechanisms. Also, by averaging over the satellite’s rotation, this model is roughly 20 times faster to propagate than the full (Euler) dynamics. Overall, this allows for rapid, broad exploration to determine resonance capture durations, spin states changes, and the influence of initial spin rate and resonance order on resonance strength. This resonance-averaged model can be easily applied to other environmental perturbations.

Detection of the YORP effect on the contact binary (68346) 2001 KZ66 from combined radar and optical observations

Abstract The Yarkovsky–O’Keefe–Radzievskii–Paddack (YORP) effect is a small thermal-radiation torque experienced by small asteroids, and is considered to be crucial in their physical and dynamical evolution. It is important to understand this effect by providing measurements of YORP for a range of asteroid types to facilitate the development of a theoretical framework. We are conducting a long-term observational study on a selection of near-Earth asteroids to support this. We focus here on (68346) 2001 KZ66, for which we obtained both optical and radar observations spanning a decade. This allowed us to perform a comprehensive analysis of the asteroid’s rotational evolution. Furthermore, radar observations from the Arecibo Observatory enabled us to generate a detailed shape model. We determined that (68346) is a retrograde rotator with its pole near the southern ecliptic pole, within a 15○ radius of longitude 170○ and latitude −85○. By combining our radar-derived shape model with the optical light curves, we developed a refined solution to fit all available data, which required a YORP strength of $(8.43\pm 0.69)\times 10^{-8} \rm ~rad ~d^{-2}$. (68346) has a distinct bifurcated shape comprising a large ellipsoidal component joined by a sharp neckline to a smaller non-ellipsoidal component. This object likely formed either from the gentle merging of a binary system or from the deformation of a rubble pile due to YORP spin-up. The shape exists in a stable configuration close to its minimum in topographic variation, where regolith is unlikely to migrate from areas of higher potential.

Limiting Behavior of Asteroid Obliquity and Spin Using a Semi-analytic Thermal Model of the YORP Effect

Abstract 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 nonzero 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 nontrivial 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.

(6478) Gault: physical characterization of an active main-belt asteroid

ABSTRACTIn 2018 December, the main-belt asteroid (6478) Gault was reported to display activity. Gault is an asteroid belonging to the Phocaea dynamical family and was not previously known to be active, nor was any other member of the Phocaea family. In this work, we present the results of photometric and spectroscopic observations that commenced soon after the discovery of activity. We obtained observations over two apparitions to monitor its activity, rotation period, composition, and possible non-gravitational orbital evolution. We find that Gault has a rotation period of P = 2.4929 ± 0.0003 h with a light-curve amplitude of 0.06 magnitude. This short rotation period close to the spin barrier limit is consistent with Gault having a density no smaller than ρ = 1.85 g cm−3 and its activity being triggered by the YORP (Yarkovsky–O’Keefe–Radzievskii–Paddack) spin-up mechanism. Analysis of the Gault phase curve over phase angles ranging from 0.4° to 23.6° provides an absolute magnitude of H = 14.81 ± 0.04, G1 = 0.25 ± 0.07, and G2 = 0.38 ± 0.04. Model fits to the phase curve find the surface regolith grain size constrained between 100 and 500 $\rm {\mu }$m. Using relations between the phase curve and albedo, we determine that the geometrical albedo of Gault is pv = 0.26 ± 0.05 corresponding to an equivalent diameter of $D = 2.8^{+0.4}_{-0.2}$ km. Our spectroscopic observations are all consistent with an ordinary chondrite-like composition (S, or Q-type in the Bus-DeMeo taxonomic classification). A search through archival photographic plate surveys found previously unidentified detections of Gault dating back to 1957 and 1958. Only the latter had been digitized, which we measured to nearly double the observation arc of Gault. Finally, we did not find any signal of activity during the 2020 apparition or non-gravitational effects on its orbit.

Averaged Solar Torque Rotational Dynamics for Defunct Satellites

Spin state predictions for defunct satellites in geosynchronous Earth orbit (GEO) are valuable for active debris removal and servicing missions as well as material shedding studies and attitude-dependent solar radiation pressure (SRP) modeling. Previous studies have shown that solar radiation torques can explain the observed spin state evolution of some GEO objects via the Yarkovsky–O’Keefe–Radzievskii–Paddack (YORP) effect. These studies have focused primarily on uniform rotation. Nevertheless, many objects are in nonprincipal axis rotation (i.e., tumbling). Recent exploration of the tumbling regime for the family of retired Geostationary Operational Environmental Satellite (GOES) 8–12 satellites has shown intriguing YORP-driven behavior including spin-orbit coupling, tumbling cycles, and tumbling period resonances. To better explore and understand the tumbling regime, a semi-analytical tumbling-averaged rotational dynamics model has been developed. The derivation requires analytically averaging over the satellite’s torque-free rotation, defined by Jacobi elliptic functions. Averaging is facilitated by a second-order Fourier series approximation of the facet illumination function. The averaged model is found to capture and explain the general long-term behavior of the full dynamics while reducing computation time by roughly three orders of magnitude. This improved computation efficiency promises to enable rapid exploration of general long-term rotational dynamics for defunct satellites and rocket bodies.

Spin Change of Asteroid 2012 TC4 Probably by Radiation Torques

Abstract Asteroid 2012 TC4 is a small (∼10 m) near-Earth object that was observed during its Earth close approaches in 2012 and 2017. Earlier analyses of light curves revealed its excited rotation state. We collected all available photometric data from the two apparitions to reconstruct its rotation state and convex shape model. We show that light curves from 2012 and 2017 cannot be fitted with a single set of model parameters; the rotation and precession periods are significantly different for these two data sets, and they must have changed between or during the two apparitions. Nevertheless, we could fit all light curves with a dynamically self-consistent model assuming that the spin states of 2012 TC4 in 2012 and 2017 were different. To interpret our results, we developed a numerical model of its spin evolution in which we included two potentially relevant perturbations: (i) gravitational torque due to the Sun and Earth and (ii) radiation torque, known as the Yarkovsky–O’Keefe–Radzievskii–Paddack (YORP) effect. Despite our model simplicity, we found that the role of gravitational torques is negligible. Instead, we argue that the observed change of its spin state may be plausibly explained as a result of the YORP torque. To strengthen this interpretation, we verify that (i) the internal energy dissipation due to material inelasticity and (ii) an impact with a sufficiently large interplanetary particle are both highly unlikely causes of its observed spin state change. If true, this is the first case where the YORP effect has been detected for a tumbling body.