**DPS Meeting, Madison, October 1998**

*Session 10. Asteroid Dynamics I*

Contributed Oral Parallel Session, Monday, October 12, 1998, 2:15-3:35pm, Madison Ballroom D
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## [10.08] Upper Bounds for the Earth-XF_{11} Collision Probability

*K. Muinonen (Univ. Helsinki)*

For a given time interval, upper bounds for the collision
probability of two planetary bodies can be established using
maximum likelihood collision orbits, i.e., orbital elements
that minimize the observational residuals with the condition
of collision some time within the given interval. The
maximum likelihood collision orbit lies on a certain
confidence boundary---assigning all the probability outside
the boundary to collision provides a robust upper bound for
the collision probability. Using the collision orbits and
other newly-developed statistical methods, the asteroid 1997
XF_{11} close approach to the Earth (time interval 2028
October 24.0-31.0 TDT) is analyzed in detail starting from
1997 December 6. Three days after discovery, in December 9,
the orbit is still highly indeterminate, the collision
probability being smaller than 0.007. The December 19 and 21
observations bring the upper bound below ~10^{-42}.
In 1998 February 4, formally at ~10^{-966}, the upper
bound is negligibly small and, in March 4, the number
further diminishes to ~10^{-1117}. Archive
observations from 1990 put the final upper bound at
~10^{-9772}. In conclusion, the upper bound for the
collision probability decreases steadily when more and more
observations are incorporated into orbit determination. By
1998 December 21, the collision probability has decreased to
a negligible level---assuming that all relevant factors
affecting the orbit determination have been correctly
accounted for.

The author(s) of this abstract have provided an email address
for comments about the abstract: Karri.Muinonen@Helsinki.Fi

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