Mathematics – Probability
Scientific paper
Sep 1999
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999dda....31.0702m&link_type=abstract
American Astronomical Society, DDA meeting #31, #07.02
Mathematics
Probability
1
Scientific paper
Early in 1998, the 2-km asteroid 1997 XF11 became of interest as a possible danger to the earth because it would clearly pass within--possibly well within--the earth's sphere of influence on 2028 Oct. 26 (IAUC 6837). Given the usual model of the solar system, the 2028 passage was entirely predictable in that there was then no possibility of collision with the earth (IAUC 6879). Nevertheless, despite this predictability, several colleagues insisted on estimating impact probabilities, with results ranging from 10(-3) to 10(-1117) ; although this latter figure by Muinonen may be technically correct, it surely invites the imagination of bizarre scenarios that would increase it. Surprisingly, despite a stated desire for ``peer review'' of pronouncements of an asteroid hazard, there was no consideration that 1997 XF11 might have posed a danger to the earth a few years after 2028. Given the 88-day arc of observations, the uncertainty in the 2028 miss distance meant that the object's revolution period, currently 1.73 years, could subsequently have been anything from 1.53 to 1.99 years. Furthermore, the essentially linear annual change of 4000 km in the minimum distance between the earth's orbit and the object's descending node would reduce this distance to zero during the late 2030s. Given the possibility of a post-2028 earth-resonant period such as 5/3, 7/4, 9/5 or 12/7 years, it was also predictable that there existed trajectories for 1997 XF11, entirely consistent with the available observations, that would yield an earth impact during this timeframe. A possible deep impact in 2040, a grazing impact in 2037 and other passages within 2 or 3 earth radii were in fact found. Although the chaos induced in 2028 renders the calculation of impact probabilities rather difficult, a simplistic argument gives a value of about 10(-5) in at least one of the relevant years (albeit at a very specific time). This is larger than the estimated annual 10(-6) impact probability for unknown 2-km asteroids. The discovery and incorporation of observations from 1990 (IAUC 6839) immediately eliminated the possibility of an impact by 1997 XF11 for several millennia. An object in a short-period orbit destined to strike the earth is likely to make other close approaches beforehand. Important lessons to learn from the 1997 XF11 ``fiasco'' are that considerations of simple dynamics and geometry are at least as important as probabilistic estimates, and that there is a need to ensure that searches are made for prediscovery images and that an aggressive observational follow-up program is carried out for new NEO discoveries that may seem only an indirect threat.
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