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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.