Spin Pole Research Articles

The Yarkovsky Effect on the Long-term Evolution of Binary Asteroids

We explore the Yarkovsky effect on small binary asteroids. While significant attention has been given to the binary YORP effect, the Yarkovsky effect is often overlooked. We develop an analytical model for the binary Yarkovsky effect, considering both the Yarkovsky–Schach and planetary Yarkovsky components, and verify it against thermophysical numerical simulations. We find that the Yarkovsky force could change the mutual orbit when the asteroid’s spin period is unequal to the orbital period. Our analysis predicts new evolutionary paths for binaries. For a prograde asynchronous secondary, the Yarkovsky force will migrate the satellite toward the location of the synchronous orbit on ∼100 kyr timescales, which could be faster than other synchronization processes such as YORP and tides. For retrograde secondaries, the Yarkovsky force always migrates the secondary outward, which could produce asteroid pairs with opposite spin poles. Satellites spinning faster than the Roche limit orbit period (e.g., from ∼4 hr to ∼10 hr) will migrate inward until they disrupt, reshape, or form a contact binary. We also predict a short-lived equilibrium state for asynchronous secondaries where the Yarkovsky force is balanced by tides. We provide calculations of the Yarkovsky-induced drift rate for known asynchronous binaries. If the NASA DART impact broke Dimorphos from synchronous rotation, we predict that Dimorphos’s orbit will shrink by ȧ∼7 cm yr−1, which can be measured by the Hera mission. We also speculate that the Yarkovsky force may have synchronized the Dinkinesh–Selam system after a possible merger of Selam’s two lobes.

The Hera Radio Science Experiment at Didymos

Hera represents the European Space Agency's inaugural planetary defense space mission and plays a pivotal role in the Asteroid Impact and Deflection Assessment international collaboration with NASA DART mission that performed the first asteroid deflection experiment using the kinetic impactor techniques. With the primary objective of conducting a detailed post-impact survey of the Didymos binary asteroid following the DART impact on its small moon called Dimorphos, Hera aims to comprehensively assess and characterize the feasibility of the kinetic impactor technique in asteroid deflection while conducting an in-depth investigation of the asteroid binary, including its physical and compositional properties as well as the effect of the impact on the surface and shape of Dimorphos. In this work, we describe the Hera radio science experiment, which will allow us to precisely estimate critical parameters, including the mass, which is required to determine the momentum enhancement resulting from the DART impact, mass distribution, rotational states, relative orbits, and dynamics of the asteroids Didymos and Dimorphos. Through a multi-arc covariance analysis, we present the achievable accuracy for these parameters, which consider the full expected asteroid phase and are based on ground radiometric, Hera optical images, and Hera to CubeSats InterSatellite Link radiometric measurements. The expected formal uncertainties for Didymos and Dimorphos GM are better than 0.01% and 0.1%, respectively, while their J2 formal uncertainties are better than 0.1% and 10%, respectively. Regarding their rotational state, the absolute spin pole orientations of the bodies can be recovered to better than 1°, and Dimorphos' spin rate to better than 10−3%. Dimorphos reconstructed relative orbit can be estimated at the sub-m level. Preliminary results, using a higher-fidelity dynamical model of the coupled motion between rotational and orbital dynamics, show uncertainties in the main parameters of interest that are comparable to those in standard radio science models. A first-order estimate of the expected uncertainty in the momentum transfer efficiency from DART's impact, obtainable with Hera, yields a value of about 0.25. This represents a significant improvement compared to current estimates. Overall, the retrieved values meet the Hera radio science requirements and goals, and remain valid under the condition that the system is determined to be in an excited but non-chaotic (or tumbling) state. The Hera radio science experiment will play an integral role in the exploration of the Didymos binary asteroid system and will provide unique scientific measurements, which, when combined with other observables such as optical images, altimetry measurements, and satellite-to-satellite tracking of the CubeSats, will support the mission's overarching goals in planetary defense and the deep understanding of binary asteroids.

Beyond Point Masses. III. Detecting Haumea’s Nonspherical Gravitational Field

The dwarf planet Haumea is one of the most compelling trans-Neptunian objects to study, hosting two small, dynamically interacting satellites, a family of nearby spectrally unique objects, and a ring system. Haumea itself is extremely oblate due to its 3.9 hr rotation period. Understanding the orbits of Haumea’s satellites, named Hi’iaka and Namaka, requires detailed modeling of both satellite–satellite gravitational interactions and satellite interactions with Haumea’s nonspherical gravitational field (parameterized here as J 2). Understanding both of these effects allows for a detailed probe of the satellites’ masses and Haumea’s J 2 and spin pole. Measuring Haumea’s J 2 provides information about Haumea’s interior, possibly determining the extent of past differentation. In an effort to understand the Haumea system, we have performed detailed non-Keplerian orbit fitting of Haumea’s satellites using a decade of new, ultra-precise observations. Our fits detect Haumea’s J 2 and spin pole at ≳2.5σ confidence. Degeneracies present in the dynamics prevent us from precisely measuring Haumea’s J 2 with the current data, but future observations should enable a precise measurement. Our dynamically determined spin pole shows excellent agreement with past results, illustrating the strength of non-Keplerian orbit fitting. We also explore the spin–orbit dynamics of Haumea and its satellites, showing that axial precession of Hi’iaka may be detectable over decadal timescales. Finally, we present an ephemeris of the Haumea system over the coming decade, enabling high-quality observations of Haumea and its satellites for years to come.

Seasonally varying outgassing as an explanation for dark comet accelerations

Significant nonradial, nongravitational accelerations with magnitudes incompatible with radiation-driven effects have been reported in seven photometrically inactive near-Earth objects. Two of these objects exhibit large transverse accelerations (i.e., within the orbital plane but orthogonal to the radial direction), and six exhibit significant out-of-plane accelerations. Here, we find that anisotropic outgassing resulting from differential heating on a nucleus with nonzero spin-pole obliquity, averaged over an eccentric orbit, can explain these accelerations for most of the objects. This balanced outgassing model depends on three parameters — the spin pole orientation (R.A. and Dec.) and an acceleration magnitude. For these “dark comets” (excepting 2003 RM), we obtain parameter values that reproduce the observed nongravitational accelerations. We derive formulae for the component accelerations under certain assumptions for the acceleration scaling over heliocentric distance. Although we lack estimates of these objects’ spin axes to confirm our values, this mechanism is nevertheless a plausible explanation for the observed accelerations, and produces accurate perturbations to the heliocentric motions of most of these objects. This model may also be applied to active objects outside of the dark comets group.

Multi‐color photometric observations of three asteroids in the vicinity of Vesta family

AbstractThe asteroid (4) Vesta, Vesta dynamic family members and asteroids residing in their vicinity, as the important informational carriers, can supply us with abundant information on the evolution of the inner solar system, such as the collision evolution process and the solar irradiation influence on the changes of the inner belt asteroidal orbits and their spin states. There are significant prospects for investigating the spin and color properties of these asteroids through multi‐color photometric observations. We developed a long‐term observational research plan, and have carried out the first implementation of this plan by using two telescopes who are equipped with the three‐channel system and the SDSS filters. In this paper, we report the corresponding observational results and the determinations of spin pole orientations for three asteroids (556) Phyllis, (620) Drakonia, and (1152) Pawona who reside in the vicinity of Vesta family, and meanwhile estimate the color indexes of Phyllis and Pawona.

Asteroid spin-states of a 4 Gyr collisional family

Context. Families of asteroids generated by the collisional fragmentation of a common parent body have been identified using clustering methods of asteroids in their proper orbital element space. However, there is growing evidence that some of the real families are larger than the corresponding cluster of objects in orbital elements, and there are families that escaped identification by clustering methods. An alternative method has been developed in order to identify collisional families from the correlation between the asteroid fragment sizes and their proper semi-major axis distance from the family centre (V-shape). This method has been shown to be effective in the cases of the very diffuse families that formed billions of years ago. Aims. Here we use multiple techniques for observing asteroids to provide corroborating evidence that one of the groups of asteroids identified as a family from the correlation between size and proper semi-major axis of asteroids are real fragments of a common parent body, and thus form a collisional family. Methods. We obtained photometric observations of asteroids in order to construct their rotational light curves; we combine them with the literature light curves and sparse-in-time photometry; we input these data in the light curve inversion methods, which allow us to determine a convex approximation to the 3D shape of the asteroids and their orientation in space, from which we extract the latitude (or obliquity) of the spin pole in order to assess whether an object is prograde or retrograde. We included in the analysis spin pole solutions already published in the literature aiming to increase the statistical significance of our results. The ultimate goal is to assess whether we find an excess of retrograde asteroids on the inward side of the V-shape of a 4 Gyr asteroid family identified via the V-shape method. This excess of retrograde rotators is predicted by the theory of asteroid family evolution. Results. We obtained the latitude of the spin poles for 55 asteroids claimed to belong to a 4 Gyr collisional family of the inner main belt that consists of low-albedo asteroids. After re-evaluating the albedo and spectroscopic information, we found that nine of these asteroids are interlopers in the 4 Gyr family. Of the 46 remaining asteroids, 31 are found to be retrograde and 15 prograde. We also found that these retrograde rotators have a very low probability (1.29%) of being due to random sampling from an underlying uniform distribution of spin poles. Conclusions. Our results constitute corroborating evidence that the asteroids identified as members of a 4 Gyr collisional family have a common origin, thus strengthening their family membership.

Rotation models for the Galilean satellites

The primary objective of the present study is to develop and present improved models of the rotational motions of the Galilean satellites Io, Europa, Ganymede, and Callisto. The models include both precessions and nutations of the spin poles, and forced librational oscillations of the rotation rates. Gravitational torques acting on the triaxial figures of these bodies cause their spin poles to precess about their instantaneous orbit poles, whose orientations are quite well known. It is generally expected that the obliquity, or angular separation between spin and orbit poles, for these bodies is small. As a result, there are not yet any good measurements of those angles and thus, the current IAU models for the spin pole motions of these bodies assume zero obliquity. Those models also ignore long period forced librations, driven by deviations of the orbital mean longitudes from linear trends in time. However, near-term future missions to Europa and Ganymede will soon change that situation for the better. We employ a simple model in which the spin pole precessional motion is assumed to be fully damped, and well-known variations in orbital mean longitude drive the librations. Our intent is to both present current estimates of the relevant parameters, and to describe the process used to obtain them, in enough detail to aid in developing better models when the relevant data become available.

Globally optimal shape and spin pole determination with light-curve inversion

ABSTRACT Light-curve inversion is an established technique in determining the shape and spin states of an asteroid. However, the front part of the processing pipeline, which recovers the spin pole and area of each facet, is a non-convex optimization problem. Hence, any local iterative optimization scheme can only promise a locally optimal solution. Apart from the obvious downsides of getting a non-optimal solution and the need for an initialization scheme, another major implication is that it creates an ambiguous scenario – which is to be blamed for the remaining residual? The inaccuracy of the modelling, the integrity of the data, or the non-global algorithm? We address the last uncertainty in this paper by embedding the spin pole and area vector determination module in a deterministic global optimization framework. To the best of our knowledge, this is the first attempt to solve these parameters globally. Specifically, given calibrated light-curve data, a scattering model for the object, and spin period, our method outputs the globally optimal spin pole and area vector solutions. One theoretical contribution of this paper is the introduction of a lower bound error function that is derived based on (1) the geometric relationship between the incident and scattered light on a surface and (2) the uncertainty of the gap between the observed and estimated brightness at a particular epoch in a light curve. We validated our method’s ability in achieving global minimum with both simulated and real light-curve data. We also tested our method on the real light curves of four asteroids.

Influence of Energy Dissipation on Spin Pole Precession Trajectories for Synchronous Rotators

Abstract We present an analysis of the influence of tidal energy dissipation on the precessional motion of the spin pole of a synchronously rotating body, whose orbit pole is also precessing. In the absence of dissipation, this problem has been frequently analyzed in a Hamiltonian context. The Cassini states, or fixed points of the motion of the spin pole, correspond to tangent intersections of the Hamiltonian function with the unit sphere. When dissipation is added to the dynamics, the locations of the fixed points change. We present a new geometrical characterization of the nullclines of the dissipative flow, or motion of the spin pole, and use it to find the locations of the dissipative fixed points. Using the Poincaré−Hopf index theorem, we show that in the case where there are four fixed points, one is a saddle, and depending on the sign of the dissipation rate parameter, the other three comprise either two sources and one sink or one source and two sinks. We also examine the domains of attraction of the sinks and present an analysis of their stability to initial conditions and model parameters.

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.

V-band photometry of asteroids from ASAS-SN

We present V-band photometry of the 20 000 brightest asteroids using data from the All-Sky Automated Survey for Supernovae (ASAS-SN) between 2012 and 2018. We were able to apply the convex inversion method to more than 5000 asteroids with more than 60 good measurements in order to derive their sidereal rotation periods, spin axis orientations, and shape models. We derive unique spin state and shape solutions for 760 asteroids, including 163 new determinations. This corresponds to a success rate of about 15%, which is significantly higher than the success rate previously achieved using photometry from surveys. We derive the first sidereal rotation periods for additional 69 asteroids. We find good agreement in spin periods and pole orientations for objects with prior solutions. We obtain a statistical sample of asteroid physical properties that is sufficient for the detection of several previously known trends, such as the underrepresentation of slow rotators in current databases, and the anisotropic distribution of spin orientations driven by the nongravitational forces. We also investigate the dependence of spin orientations on the rotation period. Since 2018, ASAS-SN has been observing the sky with higher cadence and a deeper limiting magnitude, which will lead to many more new solutions in just a few years.

Size and Shape of (11351) Leucus from Five Occultations

Abstract We present observations of five stellar occultations for (11351) Leucus and reports from two efforts on (21900) Orus. Both objects are prime mission candidate targets for the Lucy Discovery mission. Combined results for Leucus indicate a very dark surface with p V = 0.037 ± 0.001, which is derived from the average of the multichord occultations. Our estimate of the triaxial ellipsoidal shape is for axial diameters of 63.8 × 36.6 × 29.6 km assuming that the spin pole is normal to the line of sight. The actual shape of the object is only roughly elliptical in profile at each epoch. Significant topography is seen with horizontal scales up to 30 km and vertical scales up to 5 km. The most significant feature is a large depression on the southern end of the object as seen from a terrestrial viewpoint. For this work we developed a method to correct for differential refraction, accounting for the difference in color between the target object and the reference stars for astrometry derived from ground-based images.

Obliquity, Precession, and Fracture Mechanics: Implications of Europa's Global Cycloid Population

AbstractWe catalog the global inventory of Europa's cycloids, arcuate fractures whose paths have been linked to diurnal tidal stress, and use the locations and orientations of their cusps to further test the formation mechanism of cycloids and constrain Europa's rotation state. We find that the global distribution of cycloids is better explained by a precessing spin pole than longitude translation due to nonsynchronous rotation, which is consistent with studies of Europa's strike‐slip faults and linear fractures. We also find that a small obliquity can reproduce the orientations of most cycloid cusps at their current locations, outperforming a model using stress from eccentricity alone. Matching cycloid locations and cusp orientations under these conditions implies a variable failure threshold and that most cusps form at stresses that are 50%–90% of the local peak tidal stress, suggesting that periodic deformation is causing failure through fatigue. The fact that cycloids are not observed in some regions, despite the low failure stresses implied by some cusp orientations, suggests an additional control on cusp formation that was not included in our simplified model. We hypothesize that the larger amplitude of tidal stress in some regions leads to fatigue‐induced failure after fewer tidal cycles, leading to a build‐up of cycloids in those regions. Why more linear fractures do not seem limited in location or density is still unknown. More physically informed constraints on how ice fails under low, periodic deformation and across generations of fractures would be helpful in interpreting Europa's cycloids.

Multi-solitons of the half-wave maps equation and Calogero–Moser spin–pole dynamics

We consider the half-wave maps (HWM) equation which provides a continuum description of the classical Haldane–Shastry spin chain on the real line. We present exact multi-soliton solutions of this equation. Our solutions describe solitary spin excitations that can move with different velocities and interact in a non-trivial way. We make an ansatz for the solution allowing for an arbitrary number of solitons, each described by a pole in the complex plane and a complex spin variable, and we show that the HWM equation is satisfied if these poles and spins evolve according to the dynamics of an exactly solvable spin Calogero–Moser (CM) system with certain constraints on initial conditions. We also find first order equations providing a Bäcklund transformation of this spin CM system, generalize our results to the periodic HWM equation, and provide plots that visualize our soliton solutions.

Seasonal Polar Temperatures on the Moon

AbstractThe Diviner Lunar Radiometer Experiment on the Lunar Reconnaissance Orbiter has been acquiring visible and infrared radiance measurements of the Moon for nearly 10 years. These data have been compiled into polar stereographic maps of temperatures poleward of 80° latitude at fixed local times and fixed subsolar longitudes to provide an overview of diurnal temperatures of the polar regions. The data have been divided into winter and summer seasons, defined by the times of year when the subsolar latitude is above or below the equator, to characterize the variations in seasonal temperatures that result from the 1.54° angle between the Moon's spin pole and the ecliptic plane. Since the illumination in the polar regions is perpetually at grazing angles, topography plays a dominate role in surface temperatures. Consequently, the surface and near‐surface thermal environment can vary in complex ways with time of day and season, which produces areas that are seasonally shadowed for prolonged periods and that are much more extensive than the permanently shadowed regions (PSRs). We find that surfaces below 110 K capable of cold trapping water over 1 Gyr increases by factors of 2.8 and 4.3 in the winter for the south and north polar regions, respectively, with seasonal residence times of adsorbed water molecules occurring at higher temperatures and thus larger areas.

Stellar Winds As a Mechanism to Tilt the Spin Axes of Sun-like Stars

Abstract The rotation axis of the Sun is misaligned from the mean angular momentum plane of the solar system by about 6°. This obliquity significantly exceeds the ∼1°–2° distribution of inclinations among the planetary orbits and therefore requires a physical explanation. In concert, Sun-like stars are known to spin down by an order of magnitude throughout their lifetimes. This spindown is driven by the stellar wind, which carries angular momentum from the star. If the mean angular momentum axis of the stellar wind deviates from that of the stellar spin axis, it will lead to a component of the spindown torque that acts to tilt the star. Here, we show that solar-like tilts of 6° naturally arise during the first 10–100 Myr after planet formation as a result of stellar winds that deviate by about 10° from the star’s spin axis. These results apply to the idealized case of a dipole field, mildly inclined to the spin axis. Time-variability in the misalignment between the magnetic and spin poles is modeled as stochastic fluctuations, autocorrelated over timescales comparable to the primordial spindown time of several million years. In addition to wind direction, time-variability in mass-loss rate and magnetic topology over the stellar lifetime may alternatively generate obliquity. We hypothesize that the gaseous environments of young, open clusters may provide forcing over sufficient timescales to tilt the astrospheres of young stars, exciting modest obliquities. The more extreme, retrograde stellar obliquities of extrasolar planetary systems likely arise through separate mechanisms.

Asteroid pairs: A complex picture

We studied a sample of 93 asteroid pairs, i.e., pairs of genetically related asteroids that are on highly similar heliocentric orbits. We estimated times elapsed since separation of pair members (i.e., pair age) that are between 7 × 103 yr and a few 106 yr. With photometric observations, we derived the rotation periods P1 for all the primaries (i.e., the larger members of asteroid pairs) and a sample of secondaries (the smaller pair members). We derived the absolute magnitude differences of the studied asteroid pairs that provide their mass ratios q. For a part of the studied pairs, we refined their WISE geometric albedos and collected or estimated their taxonomic classifications. For 17 asteroid pairs, we also determined their pole positions. In two pairs where we obtained the spin poles for both pair components, we saw the same sense of rotation for both components and constrained the angles between their original spin vectors at the time of their separation. We found that the primaries of 13 asteroid pairs in our sample are actually binary or triple systems, i.e., they have one or two bound, orbiting secondaries (satellites). As a by-product, we found also 3 new young asteroid clusters (each of them consisting of three known asteroids on highly similar heliocentric orbits). We compared the obtained asteroid pair data with theoretical predictions and discussed their implications. We found that 86 of the 93 studied asteroid pairs follow the trend of primary rotation period vs mass ratio that was found by Pravec et al. (2010). Of the 7 outliers, 3 appear insignificant (may be due to our uncertain or incomplete knowledge of the three pairs), but 4 are high mass ratio pairs that were unpredicted by the theory of asteroid pair formation by rotational fission. We discuss a (remotely) possible way that they could be created by rotational fission of flattened parent bodies followed by re-shaping of the formed components. The 13 asteroid pairs with binary primaries are particularly interesting systems that place important constraints on formation and evolution of asteroid pairs. We present two hypotheses for their formation: The asteroid pairs having both bound and unbound secondaries could be “failed asteroid clusters”, or they could be formed by a cascade primary spin fission process. Further studies are needed to reveal which of these two hypotheses for formation of the paired binary systems is real.

Geodetic Evidence That Mercury Has A Solid Inner Core

Geodetic analysis of radio tracking measurements of the MESSENGER spacecraft while in orbit about Mercury has yielded new estimates for the planet's gravity field, tidal Love number, and pole coordinates. The derived right ascension (α = 281.0082° ± 0.0009°; all uncertainties are 3 standard deviations) and declination (δ =61.4164° ± 0.0003°) of the spin pole place Mercury in the Cassini state. Confirmation of the equilibrium state with an estimated mean (whole-planet) obliquity ϵ of 1.968 ± 0.027 arcmin enables the confident determination of the planet's normalized polar moment of inertia (0.333 ± 0.005), which indicates a high degree of internal differentiation. Internal structure models generated by a Markov-Chain Monte Carlo process and consistent with the geodetic constraints possess a solid inner core with a radius (r ic ) between 0.3 and 0.7 that of the outer core (r oc ).

Small body shapes and spins reveal a prevailing state of maximum topographic stability

Over the past thirty years, spacecraft missions, Earth-based radar experiments, and telescopic observations have revolutionized our knowledge of Main Belt asteroids, near-Earth asteroids, and comet nuclei. As a result of this effort, we now possess high resolution shape models and well-constrained spin rates, pole orientations, and basic surface properties for a few dozen such small bodies. Here we present the results of a geomorphological examination of 32 such small body shape models along with their associated spin properties, and show that small body shape, gravity, and spin combine to gradually drive the surface towards a condition of maximum topographic stability; that is, a state of low topographic variation, low slopes, and low surface erosion (mass-wasting) rates. Of the 32 bodies investigated, 15 (47%) reside within this ‘zone of maximum topographic stability’, and when asteroid lightcurve-derived rotation rate and body elongation estimates are included, 1941 (70%) of 2791 well-observed asteroids reside within this zone. This finding indicates that given a mobile surface layer and sufficient time, small body surfaces naturally tend to erode, and their spin states gradually evolve, towards a state of maximum topographic stability, which also corresponds to a state of lowest internal stress. This erosional effect is most prominent on bodies several kilometers and larger in diameter, where YORP induced spin-state changes are small.

Systematic Structure and Sinks in the YORP Effect

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