One family of 13315 stable periodic orbits of non-hierarchical unequal-mass triple systems
One family of 13315 stable periodic orbits of non-hierarchical unequal-mass triple systems
复制标题
非分级不等质量三重系统的一族 13315 个稳定周期轨道
DOI：
10.1007/s11433-020-1624-7
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Shijun Liao
中科院分区：
文献类型：
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作者：
Xiaoming Li;Xiaochen Li;Shijun Liao
三体问题可以追溯到1687年的牛顿，但今天它仍然是一个悬而未决的问题。请注意，在牛顿提出这个著名问题后的300年里，只有少数几个三体系统的周期轨道被发现。虽然三元系统在天文学中很常见，但实际上所有观测到的周期三元系统都是分层的（类似于太阳，地球和月球）。传统上人们认为，非等级三元系是不稳定的，因此应该分裂成一个稳定的双星系统和一颗星星，因此非等级三元系的稳定周期轨道预计是相当稀缺的。然而，我们在这里报告一个家庭的135445个周期轨道的非分级三重系统不等的质量，其中13315是稳定的。与三体系统稳定的“8”型周期轨道存在的狭窄质量范围（仅10−5）相比，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，许多这些数值发现稳定的非层次周期轨道的质量比接近的层次三重系统，已与天文观测测量。这意味着，这些稳定的周期轨道的非分级三重系统具有明显不等的质量，很可能在实践中可以观察到。我们的研究还表明，应该存在无穷多个稳定的周期轨道的非分级三重系统具有明显不等的质量。注意，我们的方法具有一般意义：以类似的方式，具有两个或三个相等质量的三体系统的每个已知周期轨道族都可以用作起点，以产生具有明显不等质量的三重系统的数千个新周期轨道。
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.