One family of 13315 stable periodic orbits of non-hierarchical unequal-mass triple systems

The three-body problem can be traced back to Newton in 1687, but it is still an open question today. Note that only a few periodic orbits of three-body systems were found in 300 years after Newton mentioned this famous problem. Although triple systems are common in astronomy, practically all observed periodic triple systems are hierarchical (similar to the Sun, Earth and Moon). It has traditionally been believed that non-hierarchical triple systems would be unstable and thus should disintegrate into a stable binary system and a single star, and consequently stable periodic orbits of non-hierarchical triple systems have been expected to be rather scarce. However, we report here one family of 135445 periodic orbits of non-hierarchical triple systems with unequal masses; 13315 among them are stable. Compared with the narrow mass range (only 10−5) in which stable “Figure-eight” periodic orbits of three-body systems exist, our newly found stable periodic orbits have fairly large mass region. We find that many of these numerically found stable non-hierarchical periodic orbits have mass ratios close to those of hierarchical triple systems that have been measured with astronomical observations. This implies that these stable periodic orbits of non-hierarchical triple systems with distinctly unequal masses quite possibly can be observed in practice. Our investigation also suggests that there should exist an infinite number of stable periodic orbits of non-hierarchical triple systems with distinctly unequal masses. Note that our approach has general meaning: in a similar way, every known family of periodic orbits of three-body systems with two or three equal masses can be used as a starting point to generate thousands of new periodic orbits of triple systems with distinctly unequal masses.