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.

三体问题可以追溯到1687年的牛顿，但今天仍然是一个悬而未决的问题。请注意，在牛顿提到这个著名问题之后的300年中，仅发现了三体系统的几个周期轨道。尽管三重系统在天文学中很常见，但实际上所有观测到的周期三重系统都是分层的（类似于太阳，地球和月球）。传统上，人们认为非三重系统是不稳定的，因此应该分解成一个稳定的双星系统和一个单星，因此，非三重系统的稳定周期轨道被认为是非常稀缺的。但是，我们在这里报告了一个质量不相等的非分层三重系统的135445个周期轨道的一个族。其中13315是稳定的。与较窄的质量范围相比（仅10⁻⁵），当三体系统存在稳定的“八字形”周期轨道时，我们新发现的稳定周期轨道具有相当大的质量区域。我们发现，许多在数值上找到的稳定的非分层周期轨道，其质量比与已经通过天文观测测量的分层三重系统的质量比接近。这意味着，在实践中很可能会观察到质量明显不相等的非分层三重系统的这些稳定周期轨道。我们的研究还表明，应存在无限数量的质量明显不相等的非分层三重系统的稳定周期轨道。请注意，我们的方法具有一般含义：以类似的方式，