The error ellipsoid in phase space of stellar encounters and its evolution in time

Details The error ellipsoid in phase space of stellar encounters and its evolution in time The error ellipsoid in phase space of stellar encounters and its evolution in time

Oct 2011

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2011an....332..831s&link_type=abstract

Astronomische Nachrichten, Vol.332, Issue 8, p.831

Mathematics

Probability

Scientific paper

We systematically investigate stellar encounters in their six-dimensional phase space, including also the error ellipsoid and its evolution in time. It allows to give not only a mathematical model of stellar encounters but also an error model for this process. On that occasion we derive fundamental formulae for the positional error in \mathbb{R}n: the probability of a position X falling into the error ellipsoid, the standard deviation in an arbitrary direction, and we briefly discuss the mean positional error in \mathbb{R}n. The case of the close encounter of the star GL 710 (HIP 89825) is an illuminating example of applying the derived results. Moreover, we show that the error ellipsoid can also be successfully applied to approximate the confidence region.

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