Federica Spoto

Orbit and Bulk Density of the OSIRIS-REx Target Asteroid (101955) Bennu

The target asteroid of the OSIRIS-REx asteroid sample return mission, (101955) Bennu (formerly 1999 RQ 36), is a half-kilometer near-Earth asteroid with an extraordinarily well constrained orbit. An extensive data set of optical astrometry from 1999 to 2013 and high-quality radar delay measurements to Bennu in 1999, 2005, and 2011 reveal the action of the Yarkovsky effect, with a mean semimajor axis drift rate da=dt ¼ð � 19:0 � 0:1 Þ� 10

Asteroid families classification: Exploiting very large datasets

Abstract The number of asteroids with accurately determined orbits increases fast, and this increase is also accelerating. The catalogs of asteroid physical observations have also increased, although the number of objects is still smaller than in the orbital catalogs. Thus it becomes more and more challenging to perform, maintain and update a classification of asteroids into families. To cope with these challenges we developed a new approach to the asteroid family classification by combining the Hierarchical Clustering Method (HCM) with a method to add new members to existing families. This procedure makes use of the much larger amount of information contained in the proper elements catalogs, with respect to classifications using also physical observations for a smaller number of asteroids. Our work is based on a large catalog of high accuracy synthetic proper elements (available from AstDyS), containing data for >330,000 numbered asteroids. By selecting from the catalog a much smaller number of large asteroids, we first identify a number of core families; to these we attribute the next layer of smaller objects. Then, we remove all the family members from the catalog, and reapply the HCM to the rest. This gives both satellite families which extend the core families and new independent families, consisting mainly of small asteroids. These two cases are discriminated by another step of attribution of new members and by merging intersecting families. This leads to a classification with 128 families and currently 87,095 members. The number of members can be increased automatically with each update of the proper elements catalog; changes in the list of families are not automated. By using information from absolute magnitudes, we take advantage of the larger size range in some families to analyze their shape in the proper semimajor axis vs. inverse diameter plane. This leads to a new method to estimate the family age, or ages in cases where we identify internal structures. The analysis of the plot above evidences some open problems but also the possibility of obtaining further information of the geometrical properties of the impact process. The results from the previous steps are then analyzed, using also auxiliary information on physical properties including WISE albedos and SDSS color indexes. This allows to solve some difficult cases of families overlapping in the proper elements space but generated by different collisional events. The families formed by one or more cratering events are found to be more numerous than previously believed because the fragments are smaller. We analyze some examples of cratering families (Massalia, Vesta, Eunomia) which show internal structures, interpreted as multiple collisions. We also discuss why Ceres has no family.

Asteroid family ages

Abstract A new family classification, based on a catalog of proper elements with ∼384,000 numbered asteroids and on new methods is available. For the 45 dynamical families with >250 members identified in this classification, we present an attempt to obtain statistically significant ages: we succeeded in computing ages for 37 collisional families. We used a rigorous method, including a least squares fit of the two sides of a V-shape plot in the proper semimajor axis, inverse diameter plane to determine the corresponding slopes, an advanced error model for the uncertainties of asteroid diameters, an iterative outlier rejection scheme and quality control. The best available Yarkovsky measurement was used to estimate a calibration of the Yarkovsky effect for each family. The results are presented separately for the families originated in fragmentation or cratering events, for the young, compact families and for the truncated, one-sided families. For all the computed ages the corresponding uncertainties are provided, and the results are discussed and compared with the literature. The ages of several families have been estimated for the first time, in other cases the accuracy has been improved. We have been quite successful in computing ages for old families, we have significant results for both young and ancient, while we have little, if any, evidence for primordial families. We found 2 cases where two separate dynamical families form together a single V-shape with compatible slopes, thus indicating a single collisional event. We have also found 3 examples of dynamical families containing multiple collisional families, plus a dubious case: for these we have obtained discordant slopes for the two sides of the V-shape, resulting in distinct ages. We have found 2 cases of families containing a conspicuous subfamily, such that it is possible to measure the slope of a distinct V-shape, thus the age of the secondary collision. We also provide data on the central gaps appearing in some families. The ages computed in this paper are obtained with a single and uniform methodology, thus the ages of different families can be compared, providing a first example of collisional chronology of the asteroid main belt.

Nongravitational perturbations and virtual impactors: the case of asteroid (410777) 2009 FD

Asteroid (410777) 2009 FD could hit Earth between 2185 and 2196. The long term propagation to the possible impacts and the intervening planetary encounters make 2009 FD one of the most challenging asteroids in terms of hazard assessment. To compute accurate impact probabilities we model the Yarkovsky effect by using the available physical characterization of 2009 FD and general properties of the near Earth asteroid population. We perform the hazard assessment with two independent methods: the first method is a generalization of the standard impact monitoring algorithms in use by NEODyS and Sentry, while the second one is based on a Monte Carlo approach. Both methods generate orbital samples in a seven-dimensional space that includes orbital elements and the parameter characterizing the Yarkovsky effect. The highest impact probability is 2.7 × 10 −3 for an impact during the 2185 Earth encounter. Impacts after 2185 corresponding to resonant returns are possible, the most relevant being in 2190 with a probability of 3 × 10 −4 . Both numerical methods can be used in the future to handle similar cases. The structure of resonant returns and the list of the possible keyholes on the target plane of the scattering encounter in 2185 can be predicted by an analytic theory.

Families classification including multiopposition asteroids

In this paper we present the results of our new classification of asteroid families, upgraded by using catalog with ¿ 500,000 asteroids. We discuss the outcome of the most recent update of the family list and of their membership. We found enough evidence to perform 9 mergers of the previously independent families. By introducing an improved method of estimation of the expected family growth in the less populous regions (e.g. at high inclination) we were able to reliably decide on rejection of one tiny group as a probable statistical fluke. Thus we reduced our current list to 115 families. We also present newly determined ages for 6 families, including complex 135 and 221, improving also our understanding of the dynamical vs. collisional families relationship. We conclude with some recommendations for the future work and for the family name problem.

The Effect of Parallax and Cadence on Asteroid Impact Probabilities and Warning Times

We study the time evolution of the impact probability for synthetic, but realistic, impacting and close-approaching asteroids detected in a simulated all-sky survey. We use the impact probability to calculate the impact warning time (tw) as the time interval between when an object reaches a Palermo Scale value of -2 and when it impacts Earth. A simple argument shows that tw ∝ Dx, with the exponent in the range [1.0,1.5], and our derived value was x = 1.3 ± 0.1. The low-precision astrometry from the single simulated all-sky survey could require many days or weeks to establish an imminent impact for asteroids larger than 100 m in diameter that are discovered far from Earth. Most close-approaching asteroids are quickly identified as not being impactors, but a size-dependent percentage, even for those larger than 50 m diameter, have a persistent impact probability of greater than 10-6 on the day of closest approach. Thus, a single all-sky survey can be of tremendous value in identifying Earth-impacting and close-approaching asteroids in advance of their closest approach, but it can not solve the problem on its own: high-precision astrometry from other optical or radar systems is necessary to rapidly establish an object as an impactor or close approacher. We show that the parallax afforded by surveying the sky from two sites is only of benefit for a small fraction of the smallest objects detected within a couple days before impact: probably not enough to justify the increased operating costs of a two-site survey. Finally, the survey cadence within a fixed time span is relatively unimportant to the impact probability calculation. We tested three different reasonable cadences and found that one provided ~10 times higher (better) value for the impact probability on the discovery night for the smallest (10 m diameter) objects, but the consequences on the overall impact probability calculation are negligible.

Detecting the Yarkovsky effect among near-Earth asteroids from astrometric data

We present an updated set of near-Earth asteroids with a Yarkovsky-related semimajor axis drift detected from the orbital fit to the astrometry. We find 87 reliable detections after filtering for the signal-to-noise ratio of the Yarkovsky drift estimate and making sure the estimate is compatible with the physical properties of the analyzed object. Furthermore, we find a list of 24 marginally significant detections, for which future astrometry could result in a Yarkovsky detection. A further outcome of the filtering procedure is a list of detections that we consider spurious because unrealistic or not explicable with the Yarkovsky effect. Among the smallest asteroids of our sample, we determined four detections of solar radiation pressure, in addition to the Yarkovsky effect. As the data volume increases in the near future, our goal is to develop methods to generate very long lists of asteroids with reliably detected Yarkovsky effect, with limited amounts of case by case specific adjustments. Furthermore, we discuss the improvements this work could bring to impact monitoring. In particular, we exhibit two asteroids for which the adoption of a non-gravitational model is needed to make reliable impact predictions.

Shadowing Lemma and chaotic orbit determination

Orbit determination is possible for a chaotic orbit of a dynamical system, given a finite set of observations, provided the initial conditions are at the central time. The Shadowing Lemma (Anosov 1967; Bowen in J Differ Equ 18:333–356, 1975) can be seen as a way to connect the orbit obtained using the observations with a real trajectory. An orbit is a shadowing of the trajectory if it stays close to the real trajectory for some amount of time. In a simple discrete model, the standard map, we tackle the problem of chaotic orbit determination when observations extend beyond the predictability horizon. If the orbit is hyperbolic, a shadowing orbit is computed by the least squares orbit determination. We test both the convergence of the orbit determination iterative procedure and the behaviour of the uncertainties as a function of the maximum number of map iterations observed. When the initial conditions belong to a chaotic orbit, the orbit determination is made impossible by numerical instability beyond a computability horizon, which can be approximately predicted by a simple formula. Moreover, the uncertainty of the results is sharply increased if a dynamical parameter is added to the initial conditions as parameter to be estimated. The Shadowing Lemma does not dictate what the asymptotic behaviour of the uncertainties should be. These phenomena have significant implications, which remain to be studied, in practical problems of orbit determination involving chaos, such as the chaotic rotation state of a celestial body and a chaotic orbit of a planet-crossing asteroid undergoing many close approaches.