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arXiv · 1312.6796

A commend on "Three Classes of Newtonian Three-Body Planar Periodic Orbits" by \v{S}uvakov and Dmitra\v{s}inovi\'{c} (PRL, 2013)

Xiaoming Li·Shijun Liao
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Abstract

Currently, the fifteen new periodic solutions of Newtonian three-body problem with equal mass were reported by \v{S}uvakov and Dmitra\v{s}inovi\'{c} (PRL, 2013) [1]. However, using a reliable numerical approach (namely the Clean Numerical Simulation, CNS) that is based on the arbitrary-order Taylor series method and data in arbitrary-digit precision, it is found that at least seven of them greatly depart from the periodic orbits after a long enough interval of time. Therefore, the reported initial conditions of at least seven of the fifteen orbits reported by \v{S}uvakov and Dmitra\v{s}inovi\'{c} [1] are not accurate enough to predict periodic orbits. Besides, it is found that these seven orbits are unstable.

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Xiaoming Li, Shijun Liao. 2013-12-24. A commend on "Three Classes of Newtonian Three-Body Planar Periodic Orbits" by \v{S}uvakov and Dmitra\v{s}inovi\'{c} (PRL, 2013). https://doi.org/10.1007/s11433-014-5563-5

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