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We Just Got 12,000 New Solutions to The Infamous Three-Body Problem
In 1687, Isaac Newton formulated his laws of motion and universal gravity, bringing the movement of distant stars, moons, and planets into focus.
With the stroke of his quill, Newton's pioneering work also triggered a centuries-long search for mathematical solutions to rein in chaotic triple systems, such as the Sun, Moon, and Earth, which researchers are still scratching their heads over to this day.
Ivan Hristov of Sofia University in Bulgaria and colleagues are the latest investigators in a long line of astronomers and mathematicians, who, since Newton's day, have been trying to find solutions to explain how three celestial bodies remain locked in a stable dance, slinging each other about under their reciprocal forces of gravity without colliding or careering off into space.
The quandary is called the three-body problem, and it extends to any trio of gravitationally entwined objects. A solution would allow astronomers to plot the predicted motions of these objects given their initial positions and velocities.
It sounds simple, but throwing a third object into a two-body system makes predicting those movements much harder to do. Supercomputers and neural networks have certainly helped.
Now, Hristov and colleagues have reported a whopping 12,409 orbital patterns for three-body systems that work within the bounds of Newton's laws, and have three equal masses. It's a dizzying number of solutions that have not yet been peer-reviewed, but should nonetheless generate some healthy discussion.
No overarching, universal solution has ever been found to the three-body problem; most systems give rise to chaotic movement that is beyond hard to predict.
But, like this latest study, a host of solutions have been discovered for special cases, when the system operates under certain conditions. However, some are more relevant to practical astronomy than others.
This latest batch of solutions is for systems where the three bodies are stationary to begin with, before 'falling' into the clutches of one another's gravity. So while the solutions might satisfy curious mathematicians, they probably have few real-world applications.
"Most, if not all, require such precise initial conditions that they are probably never realized in nature," Louisiana State University physicist Juhan Frank told journalist Matthew Sparkes for New Scientist.
Nevertheless, Hristov and colleagues used a supercomputer to build on earlier work, published in 2019, that found more than 300 new families of periodic orbits of the free-fall three-body problem, specifically.
According to Hristov and colleagues, "that work left a lot to be desired" and so they sought to resolve the points of mathematical disagreement, namely, that objects in free-fall systems don't fall into closed, looping orbits but swing through open-ended tracks. Hristov and colleagues' work differs though, in that it considers three objects of equal, not random, mass.
Free-fall orbits "may yet prove to be of astronomical relevance," Hristov and colleagues write. Although that depends on how stable the new solutions are when the influence of distant bodies or solar winds is factored in.
Three-body systems have a tendency to collapse, says Frank, with two objects uniting in a binary system and ejecting the third mass.
For now, at least Hristov is just reveling in the beauty of the predicted orbits. "Stable or unstable – they are of great theoretical interest," he told Sparkes. "They have a very beautiful spatial and temporal structure."
注释：
quill: n; v
1. n表示"大翎毛；鹅毛笔；"，means "pen made from a bird's feather"，如：The duke wrote a letter with a quill pen. 公爵用一根羽毛笔写信。
2. v表示" 用刺刺;绕在纬管上；打褶皱"，means ""，如：Through analysis of the quill, the stamping process flow has been determined.通过煤矿用托板加工工艺的分析,确定了冲压工艺流程。
rein: v; n
表示" 驾驭"，means "control and direct with or as if by reins"，如：You must learn to rein in your temper. 你必须学会控制你的脾气.This horse reins well.
这匹马易于驾驭。
reciprocal: adj
表示" 互惠的；相互的；互补的"，means " given and received in return;mutual"，如：Thus there is an important reciprocal relationship between honesty and trust. 基于此,诚实与信任成为重要的互惠关系。
Quandary: n
表示" 困惑；迷惑；为难"，means "a situation from which extrication is difficult especially an unpleasant or trying one;"，如：He's caught in a little bit of a quandary. 海德处于一个困惑的境地。in a quandary 左右为难
whopping: adj
表示" 巨大的；非常大的；异常的"，means " very large"，如：The company made a whopping 75 million dollar loss.公司遭受了7500万美元的巨额损失。
overarching: adj
表示"支配一切的；包罗万象的；首要的"，means "form an arch over"，如：This is your overarching message. 这是你总的要传达的信息。Energy security and supply is an overarching theme of Russia's G8 presidency. 能源安全和供应问题是G8主席俄国所拟定的首要议题。
revel: v
表示" 狂欢作乐"，means "take delight in;"，如：Those that are ready embrace the love that is offered and revel in the joy that it brings as the love dances in their hearts.那些已准备好的人们会拥抱这被提供的爱并陶醉在它所带来的欢乐之中，因为道之爱在他们的心中舞蹈。
中文简要说明：
曾经吹起大陆科幻热潮的小说《三体》，设想在太阳附近的三合星，那里的智慧物种一直面临难以预测潮汐与气候异常，几千代都难以破解。这个情节是借用天体物理学著名的「三体问题」(Three-Body Problem)而来。不过现在科学家靠着超级计算机与人工智能的运动，找到12000个可能解。
1687 年，艾萨克•牛顿(Sir Isaac Newton)提出了运动定律和万有引力定律，使太阳、地球、行星、卫星的位署都变得可以计算。然而我们太阳系这种「一个太阳」的友善情况并不多见，在宇宙中，反而是双星系统与三合星系统更常见。双星系统是大小恒星相互环绕，还算是有规律；要是出现3个互相引力牵引的恒星，那又当如何?
自牛顿时代以来，天体数学家们一直在试图找到解决方案，来解释三个天体如何保持在相互影响的重力作用下，不会发生碰撞或飞入太空。但是数学家很很快就发现，「三体问题」的变数太多，至今仍在摸不着头脑。
既然人类算不出来，那就交给工具去计算，保加利亚的伊凡•赫里斯托夫（Ivan Hristov），利用超级计算机和人工智能系统来协助，结果计算机给了出多达 12,409 个轨道模式，可论是眼花缭乱，目前这些解决方案尚未经过同行评审，但已经引起一些有趣的的讨论。
一些科学家认为，这12409年的可能解，在现实宇宙中恐怕不一定有用，因为交给超级计算机计算的初始条件，是3个星体都是静止的，而现实宇宙的3个星体会有初始速度。
美国路易斯安那州立大学物理学家法兰克 (Juhan Frank)说：「我们需要精确的初始条件才能预测，以至于它们在自然界中可能永远无法实现。」
赫里斯托夫也承认这项工作还有很多不足之处，但是「可能仍具有天文学意义」，他还沉浸在预测轨道的美妙之中。他说：「稳定或不稳定无所谓，至少它们具有很大的理论意义，也有非常美丽的时空结构。」
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