**DDA2001, April2001**

*Session 12. Planetary Dynamics*

Wednesday, 1:00-2:30pm
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## [12.02] Very Long-Term Stability of Extrasolar Planets in Binary Star Systems

*D.B. Spencer, H. Yamato (Penn State University)*

This paper identifies the issues and discusses possible
solution methods to analyze the orbital dynamics and assess
the very long-term stability of planets orbiting in binary
star systems. Here, very long-term is defined as at least a
billion years. The implications of the resulting
mathematical and computational analysis are that, should an
extrasolar planet exist in a binary star system for a
billion years or more, it may be possible for life to evolve
on that planet given favorable environmental exposure.
Results from this analysis will give observational
astronomers and astrobiologists a starting point to focus
their observational campaigns on binary systems where stable
orbits could exist long enough for life to evolve.

There are various locations in binary star systems where
stable planetary orbits could exist. These include planets
that orbit one of the binary stars, with the orbital motion
of the planet being perturbed by the gravitational force of
the other star, and can exist for either binary star.
Planets can also orbit both binaries, either around the
outside of the stars or a figure eight or racetrack pattern.
They can also exist in orbits around a Lagrange point. Each
possibility poses unique challenges. Before these
dynamically possible systems can be examined, our
preliminary analysis has been focusing on the issue of
numerical integration techniques.

Classical one-step and multi-step integration methods have
been developed and applied to the orbital dynamics. Further
work is underway evaluating symplectic integrators.
Truncation and round-off errors are the driving forces
affecting the numerical stability, and the effects of these
errors on the periodic motion of various geometries of
restricted three-body problem are being analyzed.

While results are still very preliminary, this paper
provides an overview of the technical problems being
investigated, and demonstrates the process needed to solve
this problem.

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