Dipartimento di Matematica, Università di Pisa
Via Buonarroti 2
56127 PISA, ITALY
Giovanni B. Valsecchi
Area di ricerca CNR
Via Fosso del Cavaliere
00133 ROMA, ITALY
Revised version, February 23, 1999
Manuscript pages: 25; Figures: 10.
Running title: Target Plane Confidence Boundaries
Keywords: Asteroids, Dynamics; Comets, Dynamics; Impact Processes
These arguments can be applied to whatever small body approaching any planet, but in the case of a Potentially Hazardous Object (PHO), either an asteroid or a comet whose orbit comes very close to that of the Earth, the application is most important. We apply this technique to discuss the recent case of asteroid 1997 XF11, which, on the basis of the observations available up to March 11, 1998, appeared to be on an orbit with a near miss of the Earth in 2028. Although the least squares solution had a close approach at 1/8 of the lunar distance, the linear confidence regions corresponding to acceptable size of the residuals are very elongated ellipses which do not include collision; this computation was reported by Chodas and Yeomans. In this paper, we compute the semilinear confidence boundaries, and find that they agree with the results of the Monte Carlo method, but differ in a significant way from the linear ellipses, although the differences occur only far from the Earth. The use of the 1990 pre-discovery observations has confirmed the impossibility of an impact in 2028 and reduces the semilinear confidence regions to subsets of the regions computed with less data, as expected. The confidence regions computed using the linear approximation, on the other hand, do not reduce to subsets of the regions computed with less data. We also discuss a simulated example [Bowell and Muinonen 1992] of an Earth impacting asteroid. In this hypothetical case the semilinear confidence boundary has a completely different shape from the linear ellipse, and indeed for orbits determined with only few weeks of observational data the semilinear confidence boundary correctly includes possible collisions, while the linear one does not. Free software is available now, allowing everyone to compute target plane confidence boundaries as in this paper; in case a new asteroid with worrisome close approaches is discovered, our method allows to quickly perform an accurate risk assessment.