Other
Scientific paper
Sep 2006
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006aca....56..283s&link_type=abstract
Acta Astronomica, Vol. 56, pp.283-292
Other
2
Minor Planets, Asteroids, Celestial Mechanics
Scientific paper
If we find an impact orbit of the Earth-crossing asteroid we can determine the impact point location on the Earth surface. If we want to find other orbits, very similar to the impact one, we have to select randomly a number of such ``clones'' and to integrate equations of motion many times from the osculation epoch to the collision date. Then we can determine a path of hypothetical impact points on a map of the Earth.
We elaborated a method allowing us to avoid the repeating of long-term integration. The method is based on a special feature of the cracovian least squares correction applied to the random orbit selection. After finding the impact orbit we randomly select an arbitrary number of ``clones'', perform only one time-consuming integration, and find quickly many similar impact orbits for the collision date.
We applied our method for four chosen asteroids: 2004 VD_17, 1950 DA, Apophis (2004 MN_4), and Hathor. We show that we are able to ``clone'' the impact orbit in a very difficult case and when it is impossible to do this in another way.
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