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Numerical Solutions

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Three Body Dynamics and Its Applications to Exoplanets

Part of the book series: SpringerBriefs in Astronomy ((BRIEFSASTRON))

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Abstract

All attempts to solve the three-body problem described in the previous chapters have greatly enriched celestial and classical mechanics. However, the ubiquity of fast computers with modes of operation that allow for parallel computations, numerical solutions have been the driving force in finding and studying possible solutions to the three-body problem. In this chapter, we provide a brief overview of common numerical schemes in terms of the mathematics of the algorithms used, as well as short examples written in the open-source programming language Python. The topics included in our discussion deal with numerical integration of the three-body problem, Fourier analysis, determination of mean motion resonances, and chaos indicators.

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Notes

  1. 1.

    See http://rebound.readthedocs.io/en/latest/ipython/PoincareMap.html for a working example using REBOUND.

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Authors and Affiliations

  1. University of Texas at Arlington, Arlington, TX, USA

    Zdzislaw Musielak

  2. University Oklahoma, Norman, Oklahoma, USA

    Billy Quarles

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  1. Zdzislaw Musielak
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  2. Billy Quarles
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Musielak, Z., Quarles, B. (2017). Numerical Solutions. In: Three Body Dynamics and Its Applications to Exoplanets. SpringerBriefs in Astronomy. Springer, Cham. https://doi.org/10.1007/978-3-319-58226-9_4

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