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On the Calculation of Average Lifetimes for the 3-body Problem

Published online by Cambridge University Press:  01 September 2007

David Urminsky
David Urminsky*
Affiliation:
School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh, UK email: david.urminsky@ed.ac.uk
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Abstract

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Numerical solutions for the 3-body problem can be extremely sensitive to small errors. We consider how small errors in calculations can affect the lifetime of these systems. In particular, we show that numerical errors can shorten the average lifetime of a 3-body system. This is illustrated using the Sitnikov Problem as an example. To give a theoretical explanation, we construct an approximate Poincaré map for this problem and delineate the structure of the escape regions. We show that numerical errors can destroy escape regions and can cause orbits to migrate to a region in which escape is faster.

Keywords

stellar dynamicstime
Type
Contributed Papers
Information
Proceedings of the International Astronomical Union , Volume 3 , Symposium S246: Dynamical Evolution of Dense Stellar Systems , September 2007 , pp. 235 - 236
Copyright
Copyright © International Astronomical Union 2008

References

Moser, J. 1973, Stable and Random Motions in Dynamical Systems, Princeton University Press.Google Scholar
Urminsky, D. J. 2007, PhD thesis, University of Edinburgh. (in preparation)Google Scholar