Over a thousand new periodic orbits of a planar threebody system with unequal masses
Abstract
The threebody problem is common in astronomy, examples of which are the solar system, exoplanets, and stellar systems. Due to its chaotic characteristic, discovered by Poincaré, only three families of periodic threebody orbits were found in 300 years, until 2013 when Šuvakov and Dmitrašinović (2013, Phys. Rev. Lett., 110, 114301) found 13 new periodic orbits of a Newtonian planar threebody problem with equal mass. Recently, more than 600 new families of periodic orbits of triple systems with equal mass were found by Li and Liao (2017, Sci. ChinaPhys. Mech. Astron., 60, 129511). Here, we report 1349 new families of planar periodic orbits of the triple system where two bodies have the same mass and the other has a different mass. None of the families have ever been reported, except the famous "figureeight" family. In particular, 1223 among these 1349 families are entirely new, i.e., with newly found "free group elements" that have been never reported, even for threebody systems with equal mass. It has been traditionally believed that triple systems are often unstable if they are nonhierarchical. However, all of our new periodic orbits are in nonhierarchical configurations, but many of them are either linearly or marginally stable. This might inspire the longterm astronomical observation of stable nonhierarchical triple systems in practice. In addition, using these new periodic orbits as initial guesses, new periodic orbits of triple systems with three unequal masses can be found by means of the continuation method, which is more general and thus should have practical meaning from an astronomical viewpoint.
 Publication:

Publications of the Astronomical Society of Japan
 Pub Date:
 August 2018
 DOI:
 10.1093/pasj/psy057
 arXiv:
 arXiv:1709.04775
 Bibcode:
 2018PASJ...70...64L
 Keywords:

 celestial mechanics;
 chaos;
 methods: numerical;
 Nonlinear Sciences  Chaotic Dynamics;
 Physics  Classical Physics;
 Physics  Computational Physics
 EPrint:
 84 pages, 3 figures. arXiv admin note: text overlap with arXiv:1705.00527