A commend on "Three Classes of Newtonian Three-Body Planar Periodic Orbits" by Šuvakov and Dmitrašinović (PRL, 2013)

Abstract

Currently, the fifteen new periodic solutions of Newtonian three-body problem with equal mass were reported by Šuvakov and Dmitrašinović (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 Šuvakov and Dmitrašinović [1] are not accurate enough to predict periodic orbits. Besides, it is found that these seven orbits are unstable.

5 pages, 5 figures

References in corpus (1)

• Three Classes of Newtonian Three-Body Planar Periodic Orbits

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