Yarkovsky-O'Keefe-Radzievskii-Paddack Effect 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.

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.

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.

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.

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.

Spin rates of V-type asteroids

Context. Basaltic V-type asteroids play a crucial role in studies of Solar System evolution and planetesimal formation. Comprehensive studies of their physical, dynamical, and statistical properties provide insight into these processes. Thanks to wide surveys, currently there are numerous known V-type and putative V-type asteroids, allowing a detailed statistical analysis. Aims. Our main goal is to analyze the currently available large sample of V-type spin rates, to find signatures of the non-gravitational Yarkovsky–O’Keefe–Radzievskii–Paddack (YORP) effect among the different V-type populations, and to estimate the spin barrier and critical density for V-type asteroids. Our intention is to increase the pool of information about the intriguing V-types. Methods. We collected rotational periods from the literature for spectrally confirmed V-types, putative V-types, and Vesta family members. Through spectroscopic observations we confirmed their taxonomic type and verified the high confirmation rates of the putative V-types. We combined the collected periods with periods estimated in this manuscript and produced rotational frequency distributions. We determined the spin barrier in the frequency–light curve amplitude space for V-type asteroids. Results. We analyzed rotational periods of 536 asteroids in our sample. As expected, due to the small size of the objects analyzed, the frequency distributions for the Vesta family and the V-types outside the family are inconsistent with a Maxwellian shape. The Vesta family shows an excess of slow-rotators. V-types outside the family show an excess of both slow and fast rotators. Interestingly, we found that the population of V-types outside the Vesta family shows a significant excess of fast rotators compared to the Vesta family. The estimated critical density for V-type asteroids exceeds ρc = 2.0 g cm−3, which surpasses the previous estimates. Conclusions. We demonstrated that V-type asteroids have been influenced by the thermal radiation YORP effect and that their critical spin rate is higher than for C-type asteroids. The population of V-types outside the Vesta family shows a significant excess of fast rotators compared to the Vesta family. We hypothesize that the objects that evolved from the Vesta family though the Yarkovsky drift are also more susceptible to the YORP effect. Objects for which YORP has not yet had enough time to act and those that are more YORP resistant will be left in the family, which explains the relatively small proportion of fast rotators being left. The YORP timescale must thus be similar to the migration timescale for those objects.

‘Oumuamua’s Rotation with the Mechanical Torque Produced by Interstellar Medium

Abstract The first interstellar object ‘Oumuamua was discovered in 2017. When ‘Oumuamua travels in interstellar space, it keeps colliding with the interstellar medium (ISM). Given a sufficiently long interaction time, its rotation state may change significantly because of the angular momentum transfer with the interstellar medium. Using generated Gaussian random spheres with dimension ratios 6:1:1 and 5:5:1, this paper explores the ISM torque curve and proposes that ISM collision may account for ‘Oumuamua’s tumbling with the simple constant-torque analytical method. The statistic results show that the asymptotic obliquities distribute mostly at 0° and 180° and most cases spin down at the asymptotic obliquity, indicating that the ISM collision effect is similar to the Yarkovsky–O’Keefe–Radzievskii–Paddack (YORP) effect with zero heat conductivity assumed. Given a long time of deceleration of the spin rate, an initial major-axis rotation may evolve into tumbling motion under ISM torque. Using a constant-torque analytical model, the timescales of evolving into tumbling for the sample of 200 shapes are found to range from several gigayears to tens of gigayears, highly dependent on the chosen shape. The mean value is about 8.5 ± 0.5 Gyr for prolate shapes and 7.3 ± 0.4 Gyr for oblate shapes. Rotation of asteroids in the Oort cloud might also be dominated by the ISM collision effect since the YORP effect is quite weak at such a long distance from the Sun. Although this paper assumes an ideal mirror reflection and a constant relative velocity of ‘Oumuamua, the results still show the importance of the ISM collision effect.

Particle Ejection Contributions to the Rotational Acceleration and Orbit Evolution of Asteroid (101955) Bennu.

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.

Shape model and spin-state analysis of PHA contact binary (85990) 1999 JV6 from combined radar and optical observations

Context.The potentially hazardous asteroid (85990) 1999 JV6 has been a target of previously published thermal-infrared observations and optical photometry. It has been identified as a promising candidate for possible Yarkovsky-O’Keefe-Radzievskii-Paddack (YORP) effect detection.Aims.The YORP effect is a small thermal-radiation torque considered to be a key factor in spin-state evolution of small Solar System bodies. In order to detect YORP on 1999 JV6 we developed a detailed shape model and analysed the spin-state using both optical and radar observations.Methods.For 1999 JV6, we collected optical photometry between 2007 and 2016. Additionally, we obtained radar echo-power spectra and imaging observations with Arecibo and Goldstone planetary radar facilities in 2015, 2016, and 2017. We combined our data with published optical photometry to develop a robust physical model.Results.We determine that the rotation pole resides at negative latitudes in an area with a 5° radius close to the south ecliptic pole. The refined sidereal rotation period is 6.536787 ± 0.000007 h. The radar images are best reproduced with a bilobed shape model. Both lobes of 1999 JV6 can be represented as oblate ellipsoids with a smaller, more spherical component resting at the end of a larger, more elongated component. While contact binaries appear to be abundant in the near-Earth population, there are only a few published shape models for asteroids in this particular configuration. By combining the radar-derived shape model with optical light curves we determine a constant-period solution that fits all available data well. Using light-curve data alone we determine an upper limit for YORP of 8.5 × 10−8rad day−2.Conclusions.The bifurcated shape of 1999 JV6 might be a result of two ellipsoidal components gently merging with each other, or a deformation of a rubble pile with a weak-tensile-strength core due to spin-up. The physical model of 1999 JV6 presented here will enable future studies of contact binary asteroid formation and evolution.

A New Equilibrium State for Singly Synchronous Binary Asteroids

Abstract The evolution of rotation states of small asteroids is governed by the Yarkovsky–O’Keefe–Radzievskii–Paddack (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 binary YORP (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 BYORP compensate each other, and tidal torques distribute the angular momentum between the components of the system and dissipate energy. If unperturbed, such a system 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.

The YORP effect on the GOES 8 and GOES 10 satellites: A case study

The Yarkovsky-O’Keefe-Radzievskii-Paddack (YORP) effect is a proposed explanation for the observed rotation behavior of inactive satellites in Earth orbit. This paper further explores the YORP effect for highly asymmetric inactive satellites. Satellite models are developed to represent the GOES 8 and GOES 10 satellites, both of which are currently inactive in geosynchronous Earth orbit (GEO). A simple satellite model for the GOES 8 satellite is used to analyze the short period variations of the angular velocity and obliquity as a result of the YORP effect. A more complex model for the rotational dynamics of the GOES 8 and GOES 10 satellites are developed to probe their sensitivity and to match observed spin periods and states of these satellites. The simulated rotation periods are compared to observations for both satellites. The comparison between YORP theory and observed rotation rates for both satellites show that the YORP effect could be the cause for the observed rotational behavior. The YORP model also predicts a novel state for the GOES 8 satellite, namely that it could periodically fall into a tumbling rotation state. Recent observations of this satellite are consistent with this prediction.

Evolution of angular velocity for defunct satellites as a result of YORP: An initial study

Observations of defunct satellites show that these objects are generally rotating, with some having very fast rotation rates, yet the cause of these rapid rates is unknown. The observed secular change in the spin rate and spin axis orientation of asteroids is known to be caused by the Yarkovsky-O’Keefe-Radzievskii-Paddack (YORP) effect, however, its effect on inactive satellites in Earth orbit remains unexplored. This paper applies the YORP effect to defunct satellites and analyzes its effect on the spin rate and obliquity of these objects. This work uses two different satellite geometries to explore the secular change of the spin rate and obliquity caused by the YORP effect for inactive Geostationary Earth Orbit (GEO) satellites. One of the model satellites has an asymmetric geometry, which leads to the classical YORP effect as originally formulated for asteroids. The other model satellite is geometrically symmetric, but relies on mass distribution asymmetry to generate the YORP effect. For both models the secular change is explored with averaged dynamics, and the solutions of the averaged theory are compared with numerical integrations of the non-averaged equations of motion. Additionally, previously published observations of inactive GEO satellites are used to estimate the YORP torque acting on those bodies. A comparison between this torque and the expected torque on a defunct satellite shows that the two are of the same order of magnitude. These results motivate further study on the YORP effect in the realm of inactive satellites.

Meteoroid impacts onto asteroids: A competitor for Yarkovsky and YORP

The impact of a meteoroid onto an asteroid transfers linear and angular momentum to the larger body, which may affect its orbit and its rotational state. Here we show that the meteoroid environment of our Solar System can have an effect on small asteroids that is comparable to the Yarkovsky and Yarkovsky–O’Keefe–Radzievskii–Paddack (YORP) effects under certain conditions.The momentum content of the meteoroids themselves is expected to generate an effect much smaller than that of the Yarkovsky effect. However, momentum transport by ejecta may increase the net effective force by one order of magnitude for iron or regolith surfaces, and two orders of magnitude for impacts into bare rock surfaces. The result is sensitive to the extrapolation of laboratory microcratering experiment results to real meteoroid-asteroid collisions and needs further study. If this extrapolation holds, then meteoroid impacts are more important to the dynamics of small rocky asteroids than had previously been considered.Asteroids orbiting on prograde orbits near the Earth encounter an anisotropic meteoroid environment, including a population of particles on retrograde orbits generally accepted to be material from long-period comets spiralling inwards under Poynting–Robertson drag. High relative speed (60kms−1) impacts by meteoroids provide a small effective drag force that decreases asteroid semimajor axes and which is independent of their rotation pole. If small asteroids are bare instead of regolith covered, as is perhaps to be expected given their rapid rotation rates (Harris, A.W., Pravec, P. [2006]. In: Daniela, L., Sylvio Ferraz, M., Angel, F.J. (Eds.), Asteroids, Comets, Meteors. IAU Symposium, vol. 229, pp. 439–447), this effect may exceed the instantaneous Yarkovsky drift at sizes near and below one meter. Since one meter objects are the most abundant meteorite droppers at the Earth, the delivery of these important objects may be controlled by drag against the meteoroid environment.The rate of reorientation of asteroid spins is also substantially increased when momentum transport by ejecta is included. This has an indirect effect on the net Yarkovsky drift, particularly the diurnal variant, as the sign of the drift it creates depends on its rotational state. The net drift of an asteroid towards a resonance under the diurnal Yarkovsky effect can be slowed by more frequent pole reorientations or induced tumbling. This may make the effect of the meteoroid environment more important than the Yarkovsky effect at sizes even above one meter.Meteoroid impacts also affect asteroid spins at a level comparable to that of YORP at sizes smaller than tens of meters. Here the effect comes primarily from a small number of impacts by centimeter size particles. We conclude that recent measurements of the YORP effect have probably not been compromised, because of the targets’ large sizes and because they are known or likely to be regolith-covered rather than bare rock. However, the effect of impacts increases sharply with decreasing size, and will likely become important for asteroids smaller than a few tens of meters in radius.