Yarkovsky Force Research Articles

Physical models for the normal YORP and diurnal Yarkovsky effects

We propose an analytic model for the normal YORP and diurnal Yarkovsky effects experienced by a convex asteroid. Both the YORP torque and the Yarkovsky force are expressed as integrals of a universal function over the surface of an asteroid. Although in general this function can only be calculated numerically from the solution of the heat conductivity equation, approximate solutions can be obtained in quadratures for important limiting cases. We consider 3 such simplified models: Rubincam's approximation (zero heat conductivity), low thermal inertia limit (including the next order correction and thus valid for small heat conductivity), and high thermal inertia limit (valid for large heat conductivity). All three simplified models are compared with the exact solution.

On the oldest asteroid families in the main belt

Asteroid families are groups of minor bodies produced by high-velocity collisions. After the initial dispersions of the parent bodies fragments, their orbits evolve because of several gravitational and non-gravitational effects,such as diffusion in mean-motion resonances, Yarkovsky and YORP effects, close encounters of collisions, etc. The subsequent dynamical evolution of asteroid family members may cause some of the original fragments to travel beyond the conventional limits of the asteroid family. Eventually, the whole family will dynamically disperse and no longer be recognizable. A natural question that may arise concerns the timescales for dispersion of large families. In particular, what is the oldest still recognizable family in the main belt? Are there any families that may date from the late stages of the Late Heavy Bombardment and that could provide clues on our understanding of the primitive Solar System? In this work, we investigate the dynamical stability of seven of the allegedly oldest families in the asteroid main belt. Our results show that none of the seven studied families has a nominally mean estimated age older than 2.7 Gyr, assuming standard values for the parameters describing the strength of the Yarkovsky force. Most "paleo-families" that formed between 2.7 and 3.8 Gyr would be characterized by a very shallow size-frequency distribution, and could be recognizable only if located in a dynamically less active region (such as that of the Koronis family). V-type asteroids in the central main belt could be compatible with a formation from a paleo-Eunomia family.

Interaction between Yarkovsky force and mean-motion resonances: Some specific properties

Recently, we analyzed the role of mean-motion resonances in semi-major axis mobility of asteroids, and established a functional relationship that describes the dependence of the average time spent inside the resonance on the strength of this resonance and the semi-major axis drift speed. Here we extend this analyzis in two directions. First, we study the distribution of time delays inside the resonance and found that it could be described by the modified Laplace asymmetric distribution. Second, we analyze how the time spent inside the resonance depends on orbital eccentricity, and propose a relation that allows to take into account this parameter as well.

COUPLED SPIN AND SHAPE EVOLUTION OF SMALL RUBBLE-PILE ASTEROIDS: SELF-LIMITATION OF THE YORP EFFECT

We present the first self-consistent simulations of the coupled spin-shape evolution of small gravitational aggregates under the influence of the YORP effect. Because of YORP's sensitivity to surface topography, even small centrifugally driven reconfigurations of aggregates can alter the YORP torque dramatically, resulting in spin evolution that can differ qualitatively from the rigid-body prediction. One third of our simulations follow a simple evolution described as a modified YORP cycle. Two-thirds exhibit one or more of three distinct behaviors---stochastic YORP, self-governed YORP, and stagnating YORP---which together result in YORP self-limitation. Self-limitation confines rotation rates of evolving aggregates to far narrower ranges than those expected in the classical YORP cycle, greatly prolonging the times over which objects can preserve their sense of rotation. Simulated objects are initially randomly packed, disordered aggregates of identical spheres in rotating equilibrium, with low internal angles of friction. Their shape evolution is characterized by rearrangement of the entire body, including the deep interior. They do not evolve to axisymmetric top shapes with equatorial ridges. Mass loss occurs in one-third of the simulations, typically in small amounts from the ends of a prolate-triaxial body. We conjecture that YORP self-limitation may inhibit formation of top-shapes, binaries, or both, by restricting the amount of angular momentum that can be imparted to a deformable body. Stochastic YORP, in particular, will affect the evolution of collisional families whose orbits drift apart under the influence of Yarkovsky forces, in observable ways.

Dynamical evolution and chronology of the Hygiea asteroid family

The asteroid (10) Hygiea is the fourth largest asteroid of the Main Belt, by volume and mass, and it is the largest member of its own family. Previous works investigated the long-term effects of close encounters with (10) Hygiea of asteroids in the orbital region of the family, and analyzed the taxonomical and dynamical properties of members of this family. In this paper we apply the high-quality SDSS-MOC4 taxonomic scheme of DeMeo and Carry (2013) to members of the Hygiea family core and halo, we obtain an estimate of the minimum time and number of encounter necessary to obtain a $3\sigma$ (or 99.7%) compatible frequency distribution function of changes in proper $a$ caused by close encounters with (10) Hygiea, we study the behavior of asteroids near secular resonance configurations, in the presence and absence of the Yarkovsky force, and obtain a first estimate of the age of the family based on orbital diffusion by the Yarkovsky and YORP effects with two methods. The Hygiea family is at least 2 Byr old, with an estimated age of $T = 3200^{+380}_{-120}$ Myr and a relatively large initial ejection velocity field, according to the approach of Vokrouhlick\'{y} et al. (2006a, b). Surprisingly, we found that the family age can be shortened by $\simeq$ 25% if the dynamical mobility caused by close encounters with (10) Hygiea is also accounted for, which opens interesting new research lines for the dynamical evolution of families associated with massive bodies. In our taxonomical analysis of the Hygiea asteroid family, we also identified a new V-type candidate: the asteroid (177904) (2005 SV5). If confirmed, this could be the fourth V-type object ever to be identified in the outer main belt.

Long term stability of Earth Trojans

We explore the long-term stability of Earth Trojans by using a chaos indicator, the Frequency Map Analysis. We find that there is an extended stability region at low eccentricity and for inclinations lower than about $$50^{\circ }$$ even if the most stable orbits are found at $$i \le 40^{\circ }$$ . This region is not limited in libration amplitude, contrary to what found for Trojan orbits around outer planets. We also investigate how the stability properties are affected by the tidal force of the Earth–Moon system and by the Yarkovsky force. The tidal field of the Earth–Moon system reduces the stability of the Earth Trojans at high inclinations while the Yarkovsky force, at least for bodies larger than 10 m in diameter, does not seem to strongly influence the long-term stability. Earth Trojan orbits with the lowest diffusion rate survive on timescales of the order of $$10^9$$ years but their evolution is chaotic. Their behaviour is similar to that of Mars Trojans even if Earth Trojans appear to have shorter lifetimes.

Physical and dynamical characterisation of the unbound asteroid pair 7343-154634

Context. Models have shown that asteroids can undergo fission if their rate of rotation is steadily increased. The forces acting to pull the asteroid apart exceed the material strength and gravitational force holding the asteroid together and material can escape from the surface of the asteroid. Initially forming a binary asteroid system, the components are capable of decoupling at low relative velocity from their mutual orbit if their mass ratio is less than 0.2. A number of asteroids with very similar orbital elements have been shown to have had very recent (<1 Myr) encounters at distances smaller than the Hill sphere radius of the larger of the asteroids. The mass ratio of the asteroids in each pair is estimated to be less than 0.2, suggesting that these unbound pairs are the result of rotational fission. Aims. We determine whether the asteroids in one such unbound pair, (7343) Ockeghem and (154 634) 2003 XX28, share a common composition, indicative of asteroids formed from a common parent and further constrain a likely formation age for this pair. Methods. We have obtained spectroscopic observations of each asteroid covering the wavelength range 0.45 to 1.0 microns. Using thermal observations we have measured the size and albedo of (7343) Ockeghem. Combined with optical lightcurve data of both asteroids, we have constrained the size and density of the asteroids and estimated the strength of the Yarkovsky force experienced by both. This improved physical information has been used in new dynamical simulations of the asteroids’ orbits to better constrain a formation time of this pair. Results. We find that the asteroids have very similar spectra consistent with an S-type taxonomy. The geometric albedo of (7343) Ockeghem, 0.20 ± 0.06 is consistent with this classification. The mass ratio range of the asteroids assuming an equal density, 0.007 to 0.065, is consistent with models of unbound asteroid pair formation. A new dynamical analysis has indicated that an absolute lower limit for the age of this pair is 400 kyr with a more likely age around 560 kyr, lower than a previous estimate of 800 kyr.

On the Emmenthal distribution of highly inclined asteroids

Highly inclined asteroids are objects with sin (i) > 0.3. Among highly inclined asteroids, we can distinguish between objects with inclinations smaller than that of the centre of the ν6= g − g6 secular resonance and objects at higher inclinations. Using the current mechanisms of dynamical mobility, it is not easy to increase the values of an asteroid with an initial small inclination to values higher than that of the centre of the ν6 resonance. The presence of highly inclined objects might therefore be related to the early phases of the Solar system. It has been observed that several dynamically stable regions are characterized by a very low number density of objects, unlike low-inclined bodies that tend to occupy all the dynamically viable regions. The distribution of asteroids at a high inclination in the domain of proper elements in dynamically stable regions resembles an Emmenthal cheese, with regions of low number density close to highly populated areas. While this phenomenon has been observed qualitatively in the past, no quantitative study has yet been carried out on the extent and long-term stability of these regions. In this paper, we identify two dynamically stable regions characterized by very low values of number density and permanence times of 100 Myr or more when the Yarkovsky force is considered. We show that the low number density of objects in these areas cannot be produced as a statistical fluctuation of any simple one-dimensional statistical distribution, such as the Poissonian, uniform and Gaussian distributions, or of a tri-dimensional distribution, such as the tri-variate normal distribution. The presence of unoccupied dynamically stable regions could indicate that the primordial asteroidal population might not have reached all available zones at high-i. This sets constraints on the scenarios for the early phases of the history of our Solar system.

COLLISIONALLY BORN FAMILY ABOUT 87 SYLVIA

There are currently more than 1000 multi-opposition objects known in the Cybele population, adjacent and exterior to the asteroid main belt, allowing a more detailed analysis than was previously possible. Searching for collisionally born clusters in this population, we find only one statistically robust case: a family of objects about (87) Sylvia. We use a numerical model to simulate the Sylvia family long-term evolution due to gravitational attraction from planets and thermal (Yarkovsky) effects and to explain its perturbed structure in the orbital element space. This allows us to conclude that the Sylvia family must be at least several hundreds of million years old, in agreement with evolutionary timescales of Sylvia's satellite system. We find it interesting that other large Cybele-zone asteroids with known satellites—(107) Camilla and (121) Hermione—do not have detectable families of collisional fragments about them (this is because we assume that binaries with large primary and small secondary components are necessarily impact generated). Our numerical simulations of synthetic clusters about these asteroids show they would suffer a substantial dynamical depletion by a combined effect of diffusion in numerous weak mean-motion resonances and Yarkovsky forces provided their age is close to ∼4 billion years. However, we also believe that a complete effacement of these two families requires an additional component, very likely due to resonance sweeping or other perturbing effects associated with the late Jupiter's inward migration. We thus propose that both Camilla and Hermione originally had their collisional families, as in the Sylvia case, but they lost them in an evolution that lasted a billion years. Their satellites are the only witnesses of these effaced families.

ORBITAL IDENTIFICATION FOR ASTEROID 152563 (1992 BF) THROUGH THE YARKOVSKY EFFECT

Often a newly discovered near-Earth asteroid is linked to old observations of a formerly lost object. This orbital identification is done using a standard dynamical model that accounts for gravitational perturbations from planets and relativistic effects. Here we report the first case where such an identification requires consideration of the Yarkovsky effect, a tiny non-gravitational perturbation due to the recoil of thermal radiation from the body. Moreover, this implies that the Yarkovsky force is revealed in the orbital motion of the body, asteroid 152563 (1992 BF), only the second case so far. Orbital fits indicate a drift in the orbital semi-major axis of –(10.7 ± 0.7) × 10–4 AU Myr–1, which we ascribe to Yarkovsky forces. This yields a correlated constraint of physical parameters such as the obliquity, rotation rate, surface thermal inertial, and bulk density. The magnitude and direction of drift point to an obliquity in excess of 120°. Observations taken during 2011 and subsequent close encounters with the Earth might help establish rotation parameters and thereby constrain thermal inertia of 1992 BF, thus making the Yarkovsky strength a measure of this asteroid's bulk density.

Yarkovsky detection opportunities: II. Binary systems

We consider the possibility of detecting the Yarkovsky orbital perturbation acting on binary systems among the near-Earth asteroids. This task is significantly more difficult than for solitary asteroids because the Yarkovsky force affects both the heliocentric orbit of the system's center of mass and the relative orbit of the two components. Nevertheless, we argue these are sufficiently well decoupled so that the major Yarkovsky perturbation is in the simpler heliocentric motion and is observable with the current means of radar astrometry. Over the long term, the Yarkovsky perturbation in the relative motion of the two components is also detectable for the best observed systems. However, here we consider a simplified version of the problem by ignoring mutual non-spherical gravitational perturbations between the two asteroids. With the orbital plane constant in space and the components' rotation poles fixed (and assumed perpendicular to the orbital plane), we do not examine the coupling between Yarkovsky and gravitational effects. While radar observations remain an essential element of Yarkovsky detections, lightcurve observations, with their ability to track occultation and eclipse phenomena, are also very important in the case of binaries. The nearest possible future detection of the Yarkovsky effect for a binary system occurs for (66063) 1998 RO 1 in September 2006. Farther out, even more statistically significant detections are possible for several other systems including 2000 DP 107, (66391) 1999 KW 4 and 1996 FG 3.

Effects of thermal radiation on the dynamics of binary NEAs

The Yarkovsky force, produced when thermal radiation is re-emitted asymmetrically, causes significant orbital evolution of asteroids in the 10 m–10 km size range. When acting on a non-spherical body, the momentum carried by this radiation generally produces a torque, called the YORP effect, which may be important in re-orienting asteroidal spins. Here we explore a related effect, the “binary YORP” (BYORP), that can modify the orbit of a synchronously rotating secondary in a binary system. It arises because a locked secondary is effectively an asymmetric appendage of the primary. It should be particularly important for Near-Earth Asteroids (NEAs) owing to their small sizes, proximity to the Sun, and benign collisional environment. To estimate BYORP's strength, we subjected 100 random Gaussian spheroids to the thermal radiation model of Rubincam (2000, Radiative spin-up and spin-down of small asteroids, Icarus, 148, 2–11). For most shapes, a significant torque arose on the secondary's orbit, typically modifying the orbit's size, eccentricity and inclination in less than 10 5 years, for components of 1 and 0.3 km radii, separated by 2 km, at 1 AU, each of density 1750 kg m −3. Together YORP and BYORP are capable of synchronizing secondaries and circularizing orbits, making tidal dissipation unnecessary to explain the evolved state of observed NEA pairs. However, BYORP's rapid timescale poses a problem for the abundance of observed NEA binaries, since their formation rate is thought to be much slower. We consider and reject the following resolutions of this quandary: (i) the approximation using Gaussian spheroids inadequately models YORP; (ii) most secondaries are not synchronous, but inhabit other spin-orbit resonances (very unlikely); (iii) tidal dissipation is much more efficient than previously estimated, and thus capable of stabilizing observed systems; and (iv) moderately close encounters with planets can re-orient secondaries, turning BYORP into a slower, random-walk process. Finally, we speculate that most observed binary NEAs are in a stable state in which the obliquity-changing torques of YORP (acting on the primary) and BYORP cancel out, and that those systems must be close to 55° inclination, where the momentum-changing torques of both YORP and BYORP tend to be very small. Some retrograde systems might develop such that the nodes precess at a Sun-synchronous rate, while some prograde ones might move into the “evection” resonance. All three of these hypotheses can be tested directly by comparison with the i, Ω and ϖ observed for NEA binaries.

Dynamics of Mars Trojans

In this paper we explore the dynamical stability of the Mars Trojan region applying mainly Laskar's Frequency Map Analysis. This method yields the chaotic diffusion rate of orbits and allows to determine the most stable regions. It also gives the frequencies which are responsible for the instability of orbits. The most stable regions are found for inclinations between about 15° and 30°. For inclinations smaller than 15°, we confirm, by applying a synthetic secular theory, that the secular resonances ν 3 , ν 4 , ν 13 , ν 14 rapidly excite asteroid orbits within a few Myrs, or even faster. The asteroids are removed from the Trojan region after a close encounter with Mars. For large inclinations, the secular resonance ν 5 clears a small region around 30° while the Kozai resonance rapidly removes bodies for inclinations larger than 35°. The dynamical lifetimes of the three L5 Trojans, (5261) Eureka, 1998 VF31, 2001 DH47, and the only L4 Trojan 1999 UJ7 are determined by numerically integrating clouds of corresponding clones over the age of the Solar System. All four Trojans reside in the most stable region with smallest diffusion coefficients. Their dynamical half-lifetime is of the order of the age of the Solar System. The Yarkovsky force has little effect on the known Trojans but for bodies smaller than about 1–5 m the drag is strong enough to destabilize Trojans on a timescale shorter than 4.5 Gyr.

Detection of the Yarkovsky effect for main-belt asteroids

The Yarkovsky effect, a non-gravitational acceleration produced by the anisotropic emission of thermal energy (Öpik, 1951, Proc. Roy. Irish Acad. 54, 165–199), plays an important role in the dynamical evolution of asteroids. Current theoretical models of the Yarkovsky effect, however, rely on a number of poorly known parameters that can only approximate how real asteroids respond to solar heating. To improve this situation, we investigated whether the orbital distribution of the Karin cluster, a 5.8±0.2 Myr old S-type asteroid family (Nesvorný et al., 2002a, Nature 417, 720–722), could be used to determine the rate at which multikilometer main-belt asteroids spread in semimajor axis due to the Yarkovsky effect. Our results indicate that the orbital histories of individual Karin cluster members bear clear signatures of having drifted in semimajor axis drift since their formation. Using numerical methods, we determined the drift speed of ≈70 Karin cluster members (asteroids 1–6 km in diameter). This is the first time the speed that main-belt asteroids evolve in the semimajor axis due to the non-gravitational effects have been measured. The magnitude of measured speeds is similar to those predicted by theoretical models of the Yarkovsky force. Taken together, our results represent the first direct detection of the Yarkovsky effect for main-belt asteroids, and they validate in significant ways the asteroid thermal models described in the recent literature (e.g., Vokrouhlický, 1999, Astron. Astrophys. 344, 362–366). By comparing the measured drift speeds to those calculated from theoretical models of the Yarkovsky effect, we determined that Karin cluster members do not have surface thermal conductivities K in excess of ∼0.1 W m −1 K −1 . Instead, their derived K values are consistent with the presence of regolith over most/all of their ∼5.8 Myr lifetimes. This low-conductive regolith layer may be thin because the penetration depth of the diurnal thermal wave is ≲5 cm. The regolith material may have been deposited in the immediate aftermath of the Karin cluster formation event or was produced over time by impacts. Our method also allows us to estimate spin obliquity values for Karin cluster members. We find that members with diameters ≳3.5-km are predominantly retrograde rotators, while those <3.5-km have obliquities more equally distributed between 0° and 180°. These data may be used to study the spin states of asteroids produced by catastrophic disruption events. Interestingly, we find that a few Karin members have drifted further than predicted by our standard Yarkovsky model. We hypothesize these objects may have: (i) faster drift speeds than predicted by theoretical models, (ii) high albedos (≳0.3), and/or (iii) densities ≲2 g cm −3 .

The influence on the spin vectors of asteroids from the Yarkovsky effect

The spin vector evolution of a solar system object is connected to the orbital evolution of the body. The orbital and spin elements of the asteroids are affected by gravitational as well as thermal forces. When the spin rate, shape and orbital evolution of an object are known. the secular spin vector evolution may be determined. In this study, the orbital and spin vector evolutions of a number of artificial objects are numerically integrated, with special consideration taken to the seasonal and diurnal variants of the Yarkovsky force. The thermal force known as the Yarkovsky effect may perturb the orbital elements of an asteroid and thereby also affect the direction of the spin vector. Concentrating on spherical bodies, the spin axis evolution of bare and regolith covered main belt objects with radii larger than 50 m is examined, especially considering the seasonal and diurnal Yarkovsky forces. The combined effects on the spin vector evolution from these forces and induced periodical perturbations on the orbital elements are also studied. It is found that the effects on the spin vector evolution from the Yarkovsky force always are small or negligible for kilometer sized objects over lime periods of ∼100 Myr or more. The effects are doubled when the object radius is halved. During a given time period, the influences from the seasonal Yarkovsky force on the spin vector evolution of hare basaltic bodies are about 2-3 times as large as those on iron-rich ones. However, since the expected time, t r o , before the spin axis direction is changed by a collisional event is about half as long for a bare basaltic object as for an equal sized iron-rich one, the seasonal Yarkovsky force may be of approximately the same importance for both classes of objects. The effects on regolith covered objects from this force are considerably smaller. On the other hand, the influences from the diurnal Yarkovsky effect are much stronger on regolith covered objects than on bare ones. The effect on the spin vector evolution from both variants of the Yarkovsky force seems to he small for all the objects studied unless very long time periods are considered. The size of t r o t is dependent on several factors, hut the influences from the Yarkovsky force on the psin axis evolution over the present age of the solar system are always negligible when the object radius is larger than ∼10 km. Note that the effects studied in this paper should not be confused with the Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effect.

Dynamical Evolution of Main Belt Meteoroids: Numerical Simulations Incorporating Planetary Perturbations and Yarkovsky Thermal Forces

In the Yarkovsky effect, the recoil from asymmetric, reradiated thermal energy causes objects to undergo semimajor axis drift as a function of their spin, orbit, and material properties. We consider the role played by this mechanism in delivering meteoroids from parent bodies in the main belt to chaotic resonance zones where they can be transported to Earth-crossing orbits. Previous work has approximated the dynamical evolution of meteoroids via Yarkovsky forces, mostly through the use of the perturbations equation and simplified dynamics (e.g., Monte Carlo codes). In this paper, we calculate more precise solutions by formulating the seasonal and diurnal variants of this radiation force and incorporating them into an efficient N-body integrator capable of tracking test bodies for tens of millions of years with all relevant planetary perturbations included. Tests of our code against published benchmarks and the perturbation equations verify its accuracy. Results from long-term numerical integration of meter-sized bodies started from likely meteoroid parent bodies (e.g., 4 Vesta) indicate that dynamical evolution in the inner main belt can be complex. Chaotic effects produced by weaker planetary resonances allow many meteoroids to reach Mars-crossing orbits well before entering the 3:1 mean-motion resonance with Jupiter or the ν 6 secular resonance. Outward-evolving meteoroids sometimes become captured in these weaker resonances, increasing e and/or i while a stays constant. Conversely, inward-evolving meteoroids frequently jump across mean-motion resonances with Jupiter, bypassing potential “escape hatches” from the main belt. Despite these effects, our simulations indicate that most stony meteoroids reach Earth-crossing orbits via the 3:1 or ν 6 resonance after tens of Myr of evolution in the main belt. These time scales correspond well to the measured cosmic ray exposure ages of chondrites and achondrites. The source of these meteorites, however, is less clear, since Yarkovsky drift allows nearly any body in the main belt to add to the cumulate meteoroid flux. Our results suggest that small parent bodies dominate the meteoroid flux if the main belt size distribution at sub-km sizes is in collisional equilibrium, while big parent bodies dominate if observed population trends for km-sized bodies persist to smaller sizes.

The Yarkovsky Seasonal Effect on Asteroidal Fragments: A Nonlinearized Theory for Spherical Bodies

The long-term orbital evolution of meteoroids and small asteroids in the size range up to several kilo- meters is aUected by the ii seasonal ˇˇ Yarkovsky force, caused by radiation pressure recoil on spinning bodies heated by solar radiation to diUerent temperatures at diUerent latitudes on their surfaces. This eUect leads to a draglike, secular semimajor-axis decay, which may inject the bodies into chaotic zones associated with mean motion and secular resonances and eventually deliver them to near-Earth space. To model the Yarkovsky force, two kinds of simplifying assumptions have been frequently made: (1) a linearization in the ratio between temperature variation and average temperature and in the orbital eccentricity and (2) a plane-parallel geometry, that is, body sizes larger than the penetration depth of the seasonal thermal wave (typically, several meters). In a previous paper, we developed a new nonlinearized theory, and here we also remove the assumption of plane-parallel geometry and extend our theory to the more general spherical case, valid for all body sizes, by means of a new numerical approach. We also revise the linear theory, obtaining a fully analytical literal solution, which is well suited to develop ana- lytical and semianalytical secular perturbation theories and allows us to perform a detailed comparison with the results of the more accurate numerical model. We —nd that the accuracy of the linear theory is relatively good (20% or better) for near-circular orbits. Although the temperature variations grow with the orbital eccentricity, we show that the linear theory can still predict the averaged drift rates of the mean orbital elements up to eccentricities of 0.4¨0.5.

The Yarkovsky Seasonal Effect on Asteroidal Fragments: A Nonlinearized Theory for the Plane-parallel Case

The "seasonal" Yarkovsky force is due to radiation pressure recoil, which acts on anisotropically emitting rotating bodies, heated by sunlight to different temperatures at different latitudes on their surfaces. This force gives rise to a significant draglike effect on rapidly spinning asteroid fragments ≈1–100 m in size. Here we present a new treatment of this effect, based on the numerical solution of the heat transfer equation with no linearization in the ratio between the peak temperature difference and the average temperature on the body's surface. Our treatment is restricted to the large-body (plane-parallel) case, valid for radii larger than the penetration depth of the seasonal thermal wave (≈1–20 m depending on the conductivity of the surface layer). Also, we solve numerically the Gaussian perturbation equations for the evolution of the orbital eccentricity, as well of the semimajor axis under the seasonal Yarkovsky force. We find the results to be in broad agreement with the linearized model of D. P. Rubincam, with two main discrepancies: (i) for the same thermal and optical parameters and near-circular orbits, the semimajor axis decay rate predicted by the improved, nonlinearized theory is some 15% lower, and (ii) for some directions of the spin axis relative to the perihelion direction, the Yarkovsky force can cause a secular growth of the eccentricity. When gravitationally induced perihelion precession, spin axis precession, and collisional reorientations are accounted for, however, the eccentricity on average is found to decrease. We also show that the theory can be easily generalized to bodies of spheroidal shapes, with typical discrepancies of a factor of 2 in the semimajor axis decay rate with respect to the spherical case.

Asteroid fragments in Earth-crossing orbits

The dynamics of small bodies in the Solar System are ruled not only by gravitational forces but also by non-gravitational forces such as the Poynting Robertson effect and the Yarkovsky effect. Poynting-Robertson is a dissipative effect, thus making a particle subject to it spiral towards the Sun. For meter-sized bodies, Poynting-Robertson is too weak to cause any observable effect. Another transverse force, also induced by radiation pressure, is dominant for this size range: the Yarkovsky effect. The idea behind the Yarkovsky effect is that re-emission of radiation from a rotating body is higher in the dusk hemisphere than it is in the dawn hemisphere, thus creating a force in the opposite direction to the hotter hemisphere. The Yarkovsky force can be dissipative or antidissipative making the body spiral, either converging to or diverging from the Sun, respectively. The purpose of this work is to better understand the dynamics of meter-sized bodies (for instance asteroid fragments) subject to the Yarkovsky effect. We first solve the time-dependent heat conduction equation to offer a new deduction of the Yarkovsky effect. Then we present some examples of the dynamical evolution of meter-sized bodies suffering dissipative and antidissipative forces. The dissipative force may confirm that many meteorites found on the surface of the Earth have their origin in the combined effect of the Yarkovsky force and resonances with Jupiter. With the antidissipative force some good examples of trappings in resonances with Jupiter can be found, because in these cases the orbits are converging and capture is more natural.