Yarkovsky Force Research Articles

A perturbative treatment of the Yarkovsky-driven drifts in the 2:1 mean motion resonance

Aims. Our aim is to gain a qualitative understanding as well as to perform a quantitative analysis of the interplay between the Yarkovsky effect and the Jovian 2:1 mean motion resonance under the planar elliptic restricted three-body problem. Methods. We adopted the semi-analytical perturbation method valid for arbitrary eccentricity to obtain the resonance structures inside the Jovian 2:1 resonance. We averaged the Yarkovsky force so it could be applied to the integrable approximations for the 2:1 resonance and the ν5 secular resonance. The rates of Yarkovsky-driven drifts in the action space were derived from the quasi-integrable approximations perturbed by the averaged Yarkovsky force. Pseudo-proper elements of test particles inside the 2:1 resonance were computed using N-body simulations incorporated with the Yarkovsky effect to verify the semi-analytical results. Results. In the planar elliptic restricted model, we identified two main types of systematic drifts in the action space: (Type I) for orbits not trapped in the ν5 resonance, the footprints are parallel to the resonance curve of the stable center of the 2:1 resonance; (Type II) for orbits trapped in the ν5 resonance, the footprints are parallel to the resonance curve of the stable center of the ν5 resonance. Using the semi-analytical perturbation method, a vector field in the action space corresponding to the two types of systematic drifts was derived. The Type I drift with small eccentricities and small libration amplitudes of 2:1 resonance can be modeled by a harmonic oscillator with a slowly varying parameter, for which an analytical treatment using the adiabatic invariant theory was carried out.

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.

Dynamical feasibility of (3) Juno as a parent body of the H chondrites

We test the hypothesis that (3) Juno is a parent body of the H chondrites with dynamical modeling of an asteroid-family-forming impact and comparison to current observational data. Using a dynamical model that includes the Yarkovsky force on a simulated Juno family and a simplified cosmic ray exposure age model we examine the expected distribution of Juno family members in both the main belt and near-Earth orbits over 300 Myrs and the cosmic ray exposure distribution for fragments exiting the main belt, via the 3:1J, 5:2J, and 8:3J mean motion resonances. We find that the smallest modeled (D<10 m) family members of (3) Juno cannot be directly responsible for the observed H chondrite flux and that the breakup of larger family members creates an CRE distribution that resembles the measured H chondrite CRE distribution but is still unable to adequately explain the significant number of H chondrites with CRE ages of 6–8 Myrs. A similar model was performed for the asteroid (6) Hebe, another parent body candidate, and produced a CRE age distribution that is inconsistent with the measured H chondrite CRE ages. We also find from our dynamical models that we can expect <7 km-scale Juno family members in near-Earth orbits in the present day, consistent with the recent discovery of the shock-darkened H chondrite-like asteroid (52768) 1998 OR2.

The orbital evolution of Atira asteroids

ABSTRACT Asteroids having perihelion distance q &amp;lt; 1.3 AU are classified as near-Earth objects (NEOs), which are divided into different sub-groups: Vatira-class, Atira-class, Aten-class, Apollo-class, and Amor-class. 2020 AV2, the first Vatira (Orbiting totally inside Venus’ orbit) was discovered by the Twilight project of the Zwicky Transient Facility (ZTF) on 2020 January 4. Upon the discovery of 2020 AV2, a couple of orbital studies of the short-term orbital evolution of 2020 AV2 have been performed and published (e.g. de la Fuente Marcos &amp; de la Fuente Marcos 2020; Greenstreet 2020). In this work, we performed an assessment of the long-term orbital evolution of known near-Earth objects and known Atiras under the Yarkovsky effect by using the Mercury6 N-body code. We considered not only planetary gravitational perturbation but also the non-gravitational Yarkovsky effect. Our calculation shows that the NEOs have generally two dynamical populations, one short-lived and the other long-lived. From our calculation, the transfer probabilities of Atira-class asteroids to Vatira-class asteroids for the first transition are ∼13.1 ± 0.400, ∼13.05 ± 0.005, and ∼13.25 ± 0.450 ${{\ \rm per\ cent}}$ for different values of the Yarkovsky force (i.e. obliquity of 0, 90, and 180 deg), respectively. It suggests that the radiation force may play some role in the long-term evolution of this asteroid population. Finally, our statistical study implicates that there should be 8.14 ± 0.133 Atira-class asteroids and 1.05 ± 0.075 Vatira-asteroids of the S-type taxonomy.

The diurnal Yarkovsky effect of irregularly shaped asteroids

The Yarkovsky effect plays an important role in the motions of small celestial bodies. Increasingly detailed observations bring the need for high-accuracy modelling of the effect. We used the multiphysics software COMSOL to model the diurnal Yarkovsky effect in three dimensions and compare the results with those derived from the widely adopted theoretical linear model. We find that the linear model shows high accuracy for spherical asteroids in most cases. We explored the range of parameters for which the relative error of the linear model is over 10%. For biaxial ellipsoidal asteroids (particularly oblate ones), the linear model systematically overestimates the transverse Yarkovsky force by ~10%. The diurnal effect on triaxial ellipsoids is periodic, and no linear model is available for this phenomenon. Our numerical calculations show that the average effects on triaxial ellipsoids are stronger than those on biaxial ellipsoids. We also investigated the diurnal effect on asteroids of real shapes and find it be overestimated by the linear model by 16% on average, with a maximum of up to 35%. To estimate the strength of the Yarkovsky effect directly from the shape, we introduced the quantity of ‘effective area’ for asteroids of any shape, and find a significant linear relationship between the Yarkovsky migration rate and the effective area. This brings great convenience to the estimation in practice.

Chaotic diffusion of asteroids in the exterior 1:2 mean motion resonance with Mars

ABSTRACT The inner asteroid belt between 2.1 and 2.5 au is of particular dynamical significance because it is the dominant source of both chondritic meteorites and near-Earth asteroids. This inner belt is bounded by an eccentricity-type secular resonance and by the 1:3 mean motion resonance with Jupiter. Unless asteroid perihelia are low enough to allow scattering by Mars, escape requires transport to one of the bounding resonances. In addition Yarkovsky forces are generally ineffective in changing either the eccentricity and/or inclination for asteroids with diameter ≳30 km. Thus, large asteroids with pericentres far from Mars may only escape from the inner belt through large changes in their eccentricities. In this paper, we study chaotic diffusion of orbits near the 1:2 mean motion resonance with Mars in a systematic way. We show that, while chaotic orbital evolution in both resonant and non-resonant orbits increase the dispersion of the inclinations and eccentricities, it does not significantly change their mean values. We show further that, while the dispersive growth is greatest for resonant orbits, at high e the resonance acts to mitigate asteroid scattering by Mars - making the asteroid lifetime in the belt longer than it would have been for a non-resonant orbit. For asteroids of all sizes in both resonant and non-resonant orbits, the changes in eccentricity needed to account for the observations cannot be achieved by gravitational forces alone. The role of resonant trapping in protecting asteroids from encounters with Mars is also analysed.

Preimpact Mutual Orbit of the DART Target Binary Asteroid (65803) Didymos Derived from Observations of Mutual Events in 2003–2021

We modeled photometric observations of mutual events (eclipses and occultations) between the components of the binary near-Earth asteroid (65803) Didymos, the target of the Double Asteroid Redirection Test (DART) space mission, which were taken from 2003 to 2021. We derived parameters of the modified Keplerian mutual orbit (allowing for a quadratic drift in the mean anomaly, which is presumably caused by an interplay between the BYORP effect and mutual tides, or by differential Yarkovsky force) of the secondary, called Dimorphos, around the Didymos primary and estimated its diameter. The J2000 ecliptic longitude and latitude of the orbital pole are 320.°6 ± 13.°7 and −78.°6 ± 1.°8, respectively, and the orbital period is 11.921624 ± 0.000018 hr at epoch JD 2,455,873.0 (asterocentric UTC; all quoted uncertainties correspond to 3σ, except the density estimate below). We obtained the quadratic drift of the mean anomaly of 0.15 ± 0.14 deg yr−2. The orbital eccentricity is ≤0.03. We determined the ecliptic longitude and latitude of the radius vector of Dimorphos with respect to Didymos at the nominal time of the DART impact to Dimorphos (JD 2,459,849.46875 geocentric UTC) to be 222.°8 ± 7.°0 and −1.°6 ± 4.°2, respectively. We also estimated the bulk density of the system to be 2.37 ± 0.30 g cm−3 (1σ uncertainty).

Predicting Orbital Resonance of 2867 Šteins Using the Yarkovsky Effect

While gravitational forces have the largest impact on asteroid orbit determination, thermal forces such as the Yarkovsky and YORP effects also perturb asteroid orbits. We analyzed the impact of these thermal effects on the orbit of asteroid 2867 Šteins, an E-type asteroid measuring five kilometers in diameter. The orbit of Šteins lies within the range of a Kirkwood Gap, a region devoid of asteroids because of Jupiter’s gravitational pull. Given that thermal effects can perturb asteroids of similar properties, we sought to determine whether the Yarkovsky effect would push Šteins into a Kirkwood Gap within 50,000 years. Based on Šteins’ location and size, we hypothesized that the Yarkovsky effect will push Šteins into a Kirkwood gap. We computationally generated a thermal map of Šteins to approximate the Yarkovsky force and YORP torque. Analysis of the thermal map yielded an average Yarkovsky force parallel to velocity of -0.714 N and acceleration of -5.22 x 10-15 m/s2. The torque parallel to the angular velocity due to the YORP effect was 4.680 N m, with an angular acceleration of 1.217 x 10-20 rad/s2. We inputted the calculated Yarkovsky force into NASA’s GMAT to model the resulting change to Šteins’ orbit and found that the Yarkovsky force decays the semi-major axis of Šteins by 16.4 km in 242.2 years, and up to 5,365 km in 50,000 years within 95% confidence. This perturbation is unlikely to transfer Šteins into a Kirkwood Gap.

Asteroid control through surface restructuring

A novel concept for asteroid orbit control by restructuring asteroid surfaces to manipulate albedo and respective radiation pressure effects is introduced. The method itself is propellant-less allowing for prolonged operation and permitting the adaption and even reversing reflection changes. Microscopic restructuring of asteroid surface material allows further for asymmetric manipulation of reflective properties, which can be exploited for influencing orbit and attitude parameters. Asymmetric radiation pressures are well known for their ability to change the orbit of an asteroid through the Yarkovsky effect or rotational parameters by the YORP effect. It is shown that in the simplest form albedo manipulation of a solid surface asteroid can be achieved with a single spacecraft mission. A spacecraft will locally focus energy from a very low (pseudo-)orbit onto the asteroids surface. One technology candidate are CO2 laser systems, while other options exist. First, CO2 laser are used as conventional laser engravers to brighten mineralic and metallic surfaces. Second, CO2 laser cleaning systems are often used to remove silicate residue of industrial processes.It is calculated that an asteroid with a high albedo will experience significantly less Yarkovsky forces, resulting in reduced orbit drift and improved future predictability.Laser technology can further be exploited to create surface structures that represent an asymmetric saw tooth pattern (i.e. repeating sharp right triangles) by using femto second laser pulses or by an angled focal point. This asymmetric surface pattern leads to an angular dependent reflectivity, which can be exploited to create radiation pressure differences. When properly applied, countering spin-rate changes and rotation axis drift of the YORP effect is possible. A preliminary analysis indicates feasibility for a medium size probe equipped for laser treatment of Near Earth Object surfaces.

The functional relation between mean motion resonances and Yarkovsky force on small eccentricities

ABSTRACT This work examines asteroid’s motion with orbital eccentricity in the range (0.1, 0.2) across the two-body mean motion resonance (MMR) with Jupiter due to the Yarkovsky effect. We calculated time delays dtr caused by the resonance on the mobility of an asteroid with the Yarkovsky drift speed. Our final results considered only asteroids that successfully cross over the resonance without close encounters with planets. We found a functional relation that accurately describes dependence between the average time lead/lag 〈dtr〉, the strength of the resonance SR, and the semimajor axis drift speed da/dt with asteroids’ orbital eccentricities in the range (0.1, 0.2). We analysed average values of 〈dtr〉 using this functional relation comparing with obtained values of 〈dtr〉 from the numerical integrations, which were performed in an ORBIT9 integrator with a very large number of test asteroids. We checked the validity of our previous functional relation, derived for asteroids’ orbital eccentricities in the range (0, 0.1), on the present results for eccentricities in the range (0.1, 0.2). Also, we tried to find a unique functional relation for the whole interested interval of asteroids’ orbital eccentricities (0, 0.2) and discussed it.

Evolution of an Asteroid Family under YORP, Yarkovsky, and Collisions

Abstract Any population of asteroids, like asteroid families, will disperse in semimajor axis due to the Yarkovsky effect. The amount of drift is modulated by the asteroid spin state evolution, which determines the balance between the diurnal and seasonal Yarkovsky forces. The asteroid’s spin state is, in turn, controlled in part by the Yarkovsky–O’Keefe–Radzievskii–Paddack (YORP) effect. The otherwise smooth evolution of an asteroid can be abruptly altered by collisions, which can cause impulsive changes in the spin state and can move the asteroid onto a different YORP track. In addition, collisions may also alter the YORP parameters by changing the superficial features and overall shape of the asteroid. Thus, the coupling between YORP and Yarkovsky is also strongly affected by the impact history of each body. To investigate this coupling, we developed a statistical code modeling the time evolution of semimajor axis under YORP–Yarkovsky coupling. It includes the contributions of NYORP (normal YORP), TYORP (tangential YORP), and collisions whose effects are deterministically calculated and not added in a statistical way. We find that both collisions and TYORP increase the dispersion of a family in semimajor axis by making the spin axis evolution less smooth and regular. We show that the evolution of a family’s structure with time is complex and collisions randomize the YORP evolution. In our test families, we do not observe the formation of a “YORP-eye” in the semimajor axis versus diameter distribution, even after a long period of time. If present, the “YORP-eye” might be a relic of an initial ejection velocity pattern of the collisional fragments.

Influence of the Yarkovsky force on Jupiter Trojan asteroids

Aims.We investigate the influence of the Yarkovsky force on the long-term orbital evolution of Jupiter Trojan asteroids.Methods.Clones of the observed population with different sizes and different thermal properties were numerically integrated for 1 Gyr with and without the Yarkovsky effect. The escape rate of these objects from the Trojan region as well as changes in the libration amplitude, eccentricity, and inclination were used as a metric of the strength of the Yarkovsky effect on the Trojan orbits.Results.Objects with radiiR≤ 1 km are significantly influenced by the Yarkovsky force. The effect causes a depletion of these objects over timescales of a few hundred million years. As a consequence, we expect the size-frequency distribution of small Trojans to show a shallower slope than that of the currently observable population (R≳ 1 km), with a turning point betweenR= 100 m andR= 1 km. The effect of the Yarkovsky acceleration on the orbits of Trojans depends on the sense of rotation in a complex way. The libration amplitude of prograde rotators decreases with time while the eccentricity increases. Retrograde rotators experience the opposite effect, which results in retrograde rotators being ejected faster from the 1:1 resonance region. Furthermore, for objects affected by the Yarkovsky force, we find indications that the effect tends to smooth out the differences in the orbital distribution between the two clouds.

Dynamical constraints on the evolution of the inner asteroid belt and the sources of meteorites

AbstractWe have shown that in the inner belt the loss of asteroids from the ν6 secular resonance and the 3:1 Jovian mean motion resonance accounts for the observation that the mean size of the asteroids increases with increasing orbital inclination. We have used that observation to constrain the Yarkovsky loss timescale and to show that the family asteroids are embedded in a background population of old ghost families. We argue that all the asteroids in the inner belt originated from a small number of asteroids and that the initial mass of the belt was similar to that of the present belt. We also show that the observed size frequency distribution of the Vesta asteroid family was determined by the action of Yarkovsky forces, and that the age of this family is comparable to the age of the solar system.

Mechanisms accounting for variations in the proportions of carbonaceous and ordinary chondrites in different mass ranges

AbstractThe number ratio of carbonaceous to ordinary chondrites (the CC/OC ratio) varies with mass. It is very high (≳90) in small mass ranges (10−8 to 10−12 kg) among interplanetary dust particles and micrometeorites; it is moderately high (~5 to 30) for 1 to 10 m size fireball meteoroids (with estimated masses between ~103 and ~106 kg). In the range of most normal‐sized meteorite falls (0.01–20 kg), the ratio is low (0.04–0.05); the ratio increases at greater mass ranges: at ≥200 kg, the ratio is 0.09; at ≥500 kg, the ratio is 0.20. The CC/OC ratio also increases from 0.05 to 0.16 for small meteorite finds (10−3 to 10−4 kg). High CC/OC ratios at low and high mass ranges are due to the predominance of CC material in the outer solar system. Small particles from this region spiral into the inner solar system typically in ≤106 years due to Poynting–Robertson drag. Meter‐sized meteoroids in this region are affected by Yarkovsky forces, pushing them into resonances where they are efficiently transferred to the inner solar system. Normal‐sized meteorites are derived from centimeter‐to‐decimeter‐sized meteoroids that have sluggish drift rates (i.e., they are less affected by the seasonal Yarkovsky effect) compared to larger bodies. Consequently, the centimeter‐to‐decimeter‐sized meteoroids spend more time in interplanetary space (where they are subject to collisions) than larger objects. The greater friability of carbonaceous chondrites relative to ordinary chondrites tends to winnow the carbonaceous chondrites out in this size/mass range during their long interplanetary sojourn, thereby decreasing the CC/OC ratio.

Size-dependent modification of asteroid family Yarkovsky V-shapes

Context.The thermal properties of the surfaces of asteroids determine the magnitude of the drift rate cause by the Yarkovsky force. In the general case of Main Belt asteroids, the Yarkovsky force is indirectly proportional to the thermal inertia, Γ.Aims.Following the proposed relationship between Γ and asteroid diameterD, we find that asteroids’ Yarkovsky drift rates might have a more complex size dependence than previous thought, leading to a curved familyV-shape boundary in semi-major axis, a, vs. 1/Dspace. This implies that asteroids are drifting faster at larger sizes than previously considered decreasing on average the known ages of asteroid families.Methods.The V-Shape curvature is determined for &gt;25 families located throughout the Main Belt to quantify the Yarkovsky size-dependent drift rate.Results.We find that there is no correlation between family age andV-shape curvature. In addition, theV-shape curvature decreases for asteroid families with larger heliocentric distances suggesting that the relationship between Γ andDis weaker in the outer MB possibly due to homogenous surface roughness among family members.

Yarkovsky effect and solar radiation pressure on the orbital dynamics of the asteroid (101955) Bennu

Abstract In this paper, the orbital perturbation of near-Earth asteroid Bennu due to Yarkovsky effect and solar radiation pressure (SRP) is studied. The physical model of the astroid Bennu is used to compute Yarkovsky acceleration. The basic equation of motion is written in perturbed two body problem to show the variations in orbital elements and change in position of Bennu. The change in semi-major axis due to perturbation of Yarkovsky effect is obtained. In the presence of Yarkovsky effect, the semi-major axis decreases by 348 m over one period. The magnitude of Yarkovsky force and solar radiation pressure force is computed. We find that the maximum magnitude of Yarkovsky force and solar radiation pressure force as 0.09 N and 1.16 N, respectively, at the perihelion. It is found that Yarkovsky effect shifts the position of Bennu up to 185.2 km over 12 years of period. The position change of Bennu due to combined effect of Yarkovsky force and solar radiation pressure is 172.35 km. This study shows that the solar radiation pressure has a much smaller effect on the orbit of Bennu than Yarkovsky effect.

Dynamical lifetimes of asteroids in retrograde orbits

The population of known minor bodies in retrograde orbits ($i > 90 ^{\circ}$) that are classified as asteroids is still growing. The aim of our study was to estimate the dynamical lifetimes of these bodies by use of the latest observational data, including astrometry and physical properties. We selected 25 asteroids with the best determined orbital elements. We studied their dynamical evolution in the past and future for $\pm$ 100 My ($\pm$ 1 Gy for three particular cases). We first used orbit determination and cloning to produce swarms of test particles. These swarms were then input into long-term numerical integrations and orbital elements were averaged. Next, we collected the available thermal properties of our objects and used them in an enhanced dynamical model with Yarkovsky forces. We also used a gravitational model for comparison. Finally, we estimated the median lifetimes of 25 asteroids. We found three objects whose retrograde orbits were stable with a dynamical lifetime $\tau \sim 10 \div 100$ My. A large portion of the objects studied displayed smaller values of $\tau$ ($\tau \sim 1$ My). In addition, we studied the possible influence of the Yarkovsky effect on our results. We found that the Yarkovsky effect can have a significant influence on the lifetimes of asteroids in retrograde orbits. Due to the presence of this effect, it is possible that the median lifetimes of these objects are extended. Additionally, the changes in orbital elements, caused by Yarkovsky forces, appear to depend on the integration direction. To explain this more precisely, the same model based on new physical parameters, determined from future observations, will be required.

Non-Vestoid candidate asteroids in the inner main belt

Most Howardite-Eucrite-Diogenite (HED) meteorites (analogs to V-type asteroids) are thought to originate from asteroid (4) Vesta. However, some HEDs show distinct oxygen isotope ratios and therefore are thought to originate from other asteroids. In this study, we try to identify asteroids that may represent parent bodies of those mismatching HEDs. In particular, the origin of the anomalous Bunburra Rockhole meteorite was traced back to the inner main asteroid belt, showing that there might be asteroids that are not genetically linked to the asteroid (4) Vesta (the main source of V-type asteroids and HED meteorites) in the inner main belt. In this work we identify V-type asteroids outside the dynamical Vesta family whose rotational properties (retrograde vs prograde rotation) suggest the direction of Yarkovsky drift that sets them apart from typical Vestoids and Vesta fugitives. Specifically Nesvorny et al. 2008 simulated escapes paths from the Vesta family and showed that typical Vesta fugitives in the inner main asteroid belt at semi-major axis a < 2.3 AU have to have retrograde rotations and physical and thermal parameters that maximize the Yarkovsky force in order to evolve to scattered orbits within 1-2 Gyrs (age of the Vesta collisional family). Therefore large asteroids outside the Vesta family and with a < 2.3 AU and having thermal and rotational properties minimizing the Yarkovsky drift or showing Yarkovsky drift direction towards (4) Vesta are the best candidates for non-Vestoids V-type asteroids and therefore parent bodies of anomalous HED. In this study, we have performed accurate photometric observations and determined sense of rotation for several asteroids testing their links to Vesta and anomalous HED. We have found several potential non-Vestoid candidates. Those objects have to be studied in more detail to fully confirm their link to anomalous HEDs.

Yarkovsky V-shape identification of asteroid families

There are only a few known main belt (MB) asteroid families with ages greater than 2 Gyr (Brož et al., 2013; Spoto et al., 2015). Estimates based on the family producing collision rate suggest that the lack of > 2 Gyr-old families may be due to a selection bias in current techniques used to identify families. Family fragments disperse in their orbital elements, semi-major axis, a, eccentricity, e, and inclination, i, due to secular resonances, close encounters with massive asteroids and the non-gravitational Yarkovsky force. This causes the family fragments to be indistinguishable from the background of the main belt making them more difficult to identify with the hierarchical clustering method (HCM) with increasing family age. The discovery of the Eulalia and new Polana families in the inner belt relied on new techniques because Yarkovsky spreading made them too disperse to be identified using the classical HCM. The techniques used to discover the new Polana and Eulalia families are modified here to identify asteroid families by searching for correlations between a and asteroid diameter, D, or absolute magnitude, H. A group of asteroids is identified as a collisional family if its boundary in the a vs. 1D or a vs. H planes has a characteristic V-shape which is due to the size dependent Yarkovsky spreading. The V-shape boundary is identified with two separate techniques. The first technique identifies a border by measuring a steep drop between the number of objects inside and outside of the border. The second technique identifies the V-shape border by measuring a peak in the number density of objects in a vs. 1D,H space. Families are identified with just one or both V-shape identifying techniques. The V-shape techniques are demonstrated on the known families of Erigone, Vesta, Koronis, and families difficult to identify by HCM such as Flora, Baptistina, new Polana, Eulalia and Karin. Future applications of the technique, such as in a large scale search for > 2 Gyr-old families throughout the MB, are discussed.

On the Astrid asteroid family

Among asteroid families, the Astrid family is peculiar because of its unusual inclination distribution. Objects at $a\simeq$~2.764 au are quite dispersed in this orbital element, giving the family a "crab-like" appearance. Recent works showed that this feature is caused by the interaction of the family with the $s-s_C$ nodal secular resonance with Ceres, that spreads the inclination of asteroids near its separatrix. As a consequence, the currently observed distribution of the $v_W$ component of terminal ejection velocities obtained from inverting Gauss equation is quite leptokurtic, since this parameter mostly depends on the asteroids inclination. The peculiar orbital configuration of the Astrid family can be used to set constraints on key parameters describing the strength of the Yarkovsky force, such as the bulk and surface density and the thermal conductivity of surface material. By simulating various fictitious families with different values of these parameters, and by demanding that the current value of the kurtosis of the distribution in $v_W$ be reached over the estimated lifetime of the family, we obtained that the thermal conductivity of Astrid family members should be $\simeq$ 0.001 W/m/K, and that the surface and bulk density should be higher than 1000 kg/m$^{3}$. Monte Carlo methods simulating Yarkovsky and stochastic YORP evolution of the Astrid family show its age to be $T$ = 140$\pm$30 Myr old, in good agreement with estimates from other groups. Its terminal ejection velocity parameter is in the range $V_{EJ}= 5^{+17}_{-5}$~m/s.] Values of $V_{EJ}$ larger than 25 m/s are excluded from constraints from the current inclination distribution.