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Dynamics and stability of the two body problem with Yukawa correction

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Abstract

We explore the dynamics and stability of the two-body problem by modifying the Newtonian potential with the Yukawa potential. This model may be considered a theory of modified gravity; where the interaction is not simply the Kepler solution for large distance. We investigate stability by deriving the Jacobian of the linearized matrix equation and evaluating the eigenvalues of the various equilibrium points calculated during the analysis. The subcases of a purely Yukawa and purely Newtonian potential are also explored.

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Acknowledgements

The authors would like to thank an anonymous reviewer with help of which this manuscript is improved considerably.

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Authors and Affiliations

  1. Department of Physics and Computer Science, Wilfrid Laurier University, Waterloo, ON, Canada

    Eli Cavan, Ioannis Haranas & Kristin Cobbett

  2. Department of Mathematics, NOVA, 8333 Little River Turnpike, Annandale, VA, 22003, USA

    Ioannis Gkigkitzis

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  1. Eli Cavan
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  2. Ioannis Haranas
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  3. Ioannis Gkigkitzis
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  4. Kristin Cobbett
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Correspondence to Ioannis Haranas.

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Cavan, E., Haranas, I., Gkigkitzis, I. et al. Dynamics and stability of the two body problem with Yukawa correction. Astrophys Space Sci 365, 36 (2020). https://doi.org/10.1007/s10509-020-3749-z

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  • DOI: https://doi.org/10.1007/s10509-020-3749-z

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