轨道方程以及运行它们所需的功率
由于今天对 SO IRC 的讨论，我对轨道力学和
- 方程 感到好奇解决轨道问题所需
- 的计算能力解决复杂问题所需的计算
能力特别是计算地球何时撞向太阳（或反之亦然，具体取决于参照系）。
我怀疑太阳系内的所有引力可能都需要计算，这让我想知道需要什么类型的计算机集群，或者这可以在一个盒子上完成吗？
我没有在这里进行餐巾纸背面测试的经验，但也许你有？
另外，非常感谢 Gortok 的原始灵感（见评论）。
-亚当
Due to a discussion on the SO IRC today, I'm curious about orbital mechanics, and
- The equations needed to solve orbital problems
- The computing power required to solve complex problems
The question in particular is calculating when the Earth will plow into the Sun (or vice versa, depending on the frame of reference).
I suspect that all the gravitational pulls within our solar system may need to be calculated, which makes me wonder what type of computer cluster is required, or can this be done on a single box?
I don't have the experience to do a back of the napkin test here, but perhaps you do?
Also, much thx to Gortok for the original inspiration (see comments).
-Adam
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请参阅维基百科上的三体问题。 当引力场中有两个以上的物体并且你无法简化问题时，这是非常困难的:)
See Three Body Problem on Wikipedia. When you have more than two bodies in a gravitational field and you cannot simplify the problem, it is very difficult :)
对于超过三个实体，不存在封闭形式的解决方案。 有多种近似方法（请参阅 N-Body 模拟文章 此处 或 < a href="http://www.scholarpedia.org/article/N-body_simulations" rel="nofollow noreferrer">此处）。 根据您需要的准确度，您将需要七个到数百个尸体。 由于相对规模（与星系模拟相比），您将无法从聚类中获得太多简化。
不过，就具体问题而言，您还必须对太阳直径的变化进行估计。 我认为红巨星阶段会比轨道衰变更早发生，这将使太阳的直径大于当前的地球轨道。
With more than three bodies, there is no closed form solution. There are various methods of approximation (look at the N-Body simulation articles here or here). Depending on how much accuracy you'll require, you'll need anywhere from seven to hundreds of bodies. Because of the relative scale (compared to, say, galaxy simulations), you won't be able to get much simplification from clustering.
As far as the specific question, though, you'd also have to work on estimates for changes in the Sun's diameter. I think the red giant phase would happen sooner than orbital decay, and that will make the Sun's diameter larger than the current Earth orbit.
尽管您提出的问题无疑需要高精度的大量计算（忽略红巨星相位问题，地球轨道是否会衰变为太阳？），但有现成的软件工具可用于执行其他天体路径/轨道计算。 这里只是一些：
最后，虽然 NASA 用于计算航天器未来轨道和轨迹的软件，等，属于 ITAR 限制，它显然确实使一些过去太阳系中各个天体以及过去和当前主要任务的公开轨迹信息。 这是通过导航和辅助信息设施（NAIF）处理的。
NAIF 为上述目的提供软件和数据：
如果您尝试以上所有内容，您可能会了解一些有关轨道方程和所涉及的计算能力的知识。 ;-)
Although the problem you posed undoubtedly requires significant computation with great accuracy (ignoring red giant phase issues, would/will the orbit of the Earth decay into the Sun?), there are software tools readily available to perform other celestial path/orbit calculations. Here are just a few:
Lastly, although the software that NASA uses to calculate future orbits and trajectories for spacecraft, etc, falls under ITAR restrictions, it apparently does make some past trajectory information publicly available for various bodies in our solar system as well as major past and current missions. This is handled through the Navigation and Ancillary Information Facility (NAIF).
NAIF provides software and data for the above purpose:
If you try out all of the above, you might learn something about orbital equations and the computing power involved. ;-)
在费曼的一场演讲中，他谈到了使用 20 世纪 60 年代的计算机进行轨道计算，以及这有多好。 20 世纪 60 年代初期的任何计算机都无法与我的手机或 DS 相比，而且我实际购买用作计算机的东西的功能要强大得多。
你已经有了计算机，朋友。 这些力也很容易计算，因为它都是引力，而且行星可以被视为点质量。 通过分析计算行星轨道，并将引力扰动视为离散的推力可能会更容易。 大胆试试吧。 如果您需要帮助，请查找有关轨道力学的内容或与物理学家或天文学家交谈。
这不会帮助你找到地球何时撞击太阳，因为我们的轨道非常稳定。 然而，在几十亿年之后，太阳将会膨胀很多，并可能到达我们的轨道。 尽管如此，这可能是一个有趣的项目。
In one of the Feynman lectures, he talks about doing orbital calculations with 1960s-era computers, and how good that was. No computer from the early 1960s has anywhere near the power of my phone or DS, and the stuff I actually buy for use as computers is much more powerful.
You've got the computrons, friend. The forces are easy to calculate, too, since it's all gravitational and the planets can be treated as point masses. It might be easier to calculate planetary orbits analytically, and treat gravitational perturbations as discrete pushes. Go for it. If you want help, find something on orbital mechanics or talk to a physicist or astronomer.
This isn't going to help you find when the Earth hits the Sun, since our orbit is extremely stable. However, in a few billion years, the Sun is going to expand a lot, and might reach our orbit. Still, it might be a fun project.