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To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.icarus.2009.05.029 Byline: Andrea Milani (a), Steven R. Chesley (b), Maria Eugenia Sansaturio (c), Fabrizio Bernardi (a)(d), Giovanni B. Valsecchi (d), Oscar Arratia (c) Keywords: Asteroids; Dynamics; Impact processes; Orbit determination Abstract: The potentially hazardous Asteroid (101955) 1999 RQ.sub.36 has a possibility of colliding with the Earth in the latter half of the 22nd century, well beyond the traditional 100-year time horizon for routine impact monitoring. The probabilities accumulate to a total impact probability of approximately 10.sup.-3, with a pair of closely related routes to impact in 2182 comprising more than half of the total. The analysis of impact possibilities so far in the future is strongly dependent on the action of the Yarkovsky effect, which raises new challenges in the careful assessment of longer term impact hazards. Even for asteroids with very precisely determined orbits, a future close approach to Earth can scatter the possible trajectories to the point that the problem becomes like that of a newly discovered asteroid with a weakly determined orbit. If the scattering takes place late enough so that the target plane uncertainty is dominated by Yarkovsky accelerations then the thermal properties of the asteroid, which are typically unknown, play a major role in the impact assessment. In contrast, if the strong planetary interaction takes place sooner, while the Yarkovsky dispersion is still relatively small compared to that derived from the measurements, then precise modeling of the nongravitational acceleration may be unnecessary. Author Affiliation: (a) Department of Mathematics, University of Pisa, Largo Pontecorvo 5, 56127 Pisa, Italy (b) Jet Propulsion Laboratory, Calif. Inst. of Tech., Pasadena, CA 91109, USA (c) E.T.S. de Ingenieros Industriales, University of Valladolid, Paseo del Cauce 59, 47011 Valladolid, Spain (d) IASF-Roma, INAF, via Fosso del Cavaliere 100, 00133 Roma, Italy Article History: Received 22 January 2009; Revised 4 May 2009; Accepted 18 May 2009

To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.icarus.2005.07.004 Byline: Andrea Milani (a), Giovanni F. Gronchi (a), Zoran KneA3/4eviA (b), Maria Eugenia Sansaturio (c), Oscar Arratia (c) Keywords: Celestial mechanics; Asteroids; dynamics; Orbits Abstract: When the observational data are not enough to compute a meaningful orbit for an asteroid/comet we can represent the data with an attributable, i.e., two angles and their time derivatives. The undetermined variables range and range rate span an admissible region of Solar System orbits, which can be sampled by a set of Virtual Asteroids (VAs) selected by means of an optimal triangulation [Milani, A., Gronchi, G.F., de' Michieli Vitturi, M., KneA3/4eviA, Z., 2004. Celest. Mech. Dyn. Astron. 90, 59-87]. The attributable 4 coordinates are the result of a fit and they have an uncertainty, represented by a covariance matrix. Two short arcs of observations, represented by two attributables, can be linked by considering for each VA (in the admissible region of the first arc) the covariance matrix for the prediction at the time of the second arc, and by comparing it with the attributable of the second arc with its own covariance. By defining an identification penalty we can select the VAs allowing to fit together both arcs and compute a preliminary orbit. Two attributables may not be enough to compute an orbit with convergent differential corrections. Thus the preliminary orbit is used in a constrained differential correction, providing solutions along the Line Of Variation which can be used as second generation VAs to further predict the observations at the time of a third arc. In general the identification with a third arc will ensure a well determined orbit, to which additional sets of observations can be attributed. To test these algorithms we use a large scale simulation and measure the completeness, the reliability and the efficiency of the overall procedure to build up orbits by accumulating identifications. Under the conditions expected for the next generation asteroid surveys, the methods developed in this and in the preceding papers are efficient enough to be used as primary identification methods, with very good results. One important property is that the completeness in finding the possible identifications is as good for comparatively rare orbits, such as the ones of Near-Earth Objects, as for main belt orbits. Author Affiliation: (a) Dipartimento di Matematica, Universita di Pisa, Via Buonarroti 2, 56127 Pisa, Italy (b) Astronomical Observatory, Volgina 7, 11160 Belgrade 74, Serbia and Montenegro (c) E.T.S. de Ingenieros Industriales, University of Valladolid Paseo del Cauce s/n 47011 Valladolid, Spain Article History: Received 28 February 2005; Revised 1 July 2005

When a new near Earth asteroid is discovered, it is important to know whether or not there is the possibility of an impact with the Earth in the near future. In this paper, we describe the technical approaches employed by the two operational second-generation asteroid impact monitoring systems, CLOMON2 and Sentry, paying particular attention to the similarities and differences between these independent systems. The detection and characterization of a potential impact requires the propagation of the orbital probability density function from the time of discovery to the time of hypothetical impact. Since the N-body problem is not integrable, this can be done only by sampling the orbital elements space with a finite number of Virtual Asteroids (VAs), the orbit of each one being propagated numerically. Our methods, illustrated in this paper, use the Line Of Variation (LOV), a unidimensional subspace, to perform this sampling. The primary goal is to detect Virtual Impactors (VIs), which are regions in the initial conditions space leading to dynamically distinct collision solutions; then a probability integral needs to be computed on the volume of the VI. An important issue is how to assure completeness of such a search down to some impact probability threshold. This problem cannot be efficiently solved just by computing more VAs, but requires a geometric description of the behavior of the LOV in order to identify the critical segments of this curve. We have studied these behaviors on the Target Plane (TP) through our analytical theory and the output of many numerical tests. Assuming that the geometry is the simplest compatible with the data available from the sampling, we obtain a classification which allows us to use iterative methods, appropriate for each case, to find the closest approach distance possible along the LOV. After an LOV minimum has been identified, it is possible to use a probability density linearized at this point. However, when the cross section of the Earth is not crossed by the LOV, there is no guarantee that nonlinearity would be negligible in the direction on the TP transversal to the LOV. We describe how to test for such nonlinearity, and thus reduce or eliminate the possibility of spurious VIs. In this way, the performance of our impact monitoring systems has been significantly increased in comparison to the earlier and simpler solitary system. These more advanced systems have identified and then eliminated (through additional observations) more than one hundred cases of asteroids with VIs in the years 2002-2003. Keywords: Celestial mechanics; Asteroids, dynamics; Impacts