科学与数学nowykurier.com
重力模拟器
Gravity Simulator
2010 — 2014，它一次次回到首页
黑点是上首页（≥ 50 分）的那次投稿，空心点是没冲上去的投稿，点越大分数越高。
导读
这是一个网页引力模拟玩具：放置有质量的粒子，观察它们相互吸引、绕行甚至合并，还可以开启轨迹来查看运动路径。评论里既有人用它画出 8 字形轨道、玩双体振荡，也有人批评其质量设定和数值积分不够符合真实物理。
为什么经久不衰：它用简单直观的方式把多体引力、轨道与混沌呈现出来，既能玩出漂亮图案，也能引发关于物理准确性的讨论，因此多年后仍值得点开。
HN 评论精选
开启轨迹后能观察到三体相互作用导致合并和重新捕获的稳定循环。
很不错。一定要打开路径（paths），我用它画酷东西玩得很开心。图里是我尝试让一个小粒子围绕两个较大粒子走 8 字形，两者距离足够远，不会强烈相互作用。当然，小粒子从两个大粒子之间穿过时，会轻微推动它们，足以让两者慢慢相向移动；小粒子则朝右上方向直飞。当两个大粒子终于靠近并合并成一个巨大粒子时，它把小粒子吸引回来，此后小粒子慢慢回到大粒子处，只稍微推动它一下又被“重新发射”进行新一圈。系统似乎完全稳定。
p4bl0查看英文原文
It's really nice. Be sure to activate paths, I'm having a lot of fun using that to draw cool stuff :). https://i.imgur.com/j3YwI5y.png That was me trying to have a small particle making an 8-shaped path around two bigger ones that would be sufficiently far apart to not interact too strongly with each other. Of course, when the small particle went between the two bigger ones, it shifted their position a tiny bit, but sufficiently for those two to start very slowly moving towards each other, while the small particle was headed straight to the up-right direction. But when the two bigger particles became close enough to finally meet and become one single huge particle, it attracted back the small one, which since then goes back slowly to the huge particle only to shift it a bit and be "relaunched" by it for a new lap. The system seems to be totally stable that way. Update: https://i.imgur.com/heHekdc.png
批评质量模型不物理，认为质量应正比于半径立方。
原文说“粒子质量是半径的对数”。为什么不用真实物理，让质量正比于半径的立方？那样也更容易计算。事实上取对数方向错了——行星质量确实随半径立方增长，变化方向与 log 相反。
lutusp查看英文原文
Quote: "Particle mass is log of radius". Why not use real physics and make the mass proportional to the cube of the radius? It's also easier to compute. In fact, taking the log of the radius goes in the wrong direction -- the mass of a planet really does increase as the cube of its radius, which changes in a way opposite to log(). Oh, well. Here's my gravity simulator -- it uses JavaScript, no flash required: http://arachnoid.com/orbital_dynamics
模拟存在数值误差，会出现动量不守恒的问题。
这个模拟在数值上相当差。如果我从一个原行星盘开始，然后在它左边紧挨着放一个不动的 OMFG 粒子，初始静止的整个系统最终会获得明显的向左动量，尽管几乎没有粒子带向右动量。这不仅不符合物理尺度，凭空产生动量也完全违背物理。
fhars查看英文原文
The simulation is quite bad numerically. If I start with a proto disk and then put an non-moving OMFG particle immediately to the left of it, the whole system that is initially at rest will end a with a considerable momentum to the left, even though no or almost no particles carry any momentum to the right. That is not only not to physical scale, generating momentum out of nothing is completely unphysical.
双体可以形成长期互相振荡的轨道，并询问这种平衡的名称。
很酷！我让两个质量以有趣的方式互相振荡，它们似乎会永远这样下去。这种平衡叫什么？
zaptheimpaler查看英文原文
Very cool! I was able to get 2 masses to oscillate around each other in a funny way[1]. Seems they keep going like that forever. What is this kind of equilibrium called? [1]http://imgur.com/FQYpo9V
历次讨论
同类还值得读
如果月球只有 1 像素：一个极其精确的太阳系模型（2014）
If the moon were only 1 pixel: A tediously accurate solar system model (2014)
一个网页版太阳系模型，以“如果月亮只有 1 像素”的真实比例呈现：你必须一路横向滚动，才能体会行星之间空旷到何等程度。
科学与数学上首页 7 次 · 2014–2025joshworth.com编辑精选沉浸式线性代数（2016）
Immersive Linear Algebra (2016)
《Immersive Linear Algebra》是一本完全免费、开放在线的线性代数“超文本教科书”，其最大特色是大量可交互的图形：读者可以直接拖动、操作图中的向量、矩阵和变换…
科学与数学上首页 5 次 · 2015–2024immersivemath.com编辑精选如何将贝果切成两个相连的半环（2009）
How to Slice a Bagel into Two Linked Halves (2009)
数学家 George Hart 的经典教程，演示如何用一刀把贝果切成两个相互扣住的环，并附上切割步骤与数学原理。
科学与数学上首页 5 次 · 2009–2022georgehart.com“犹太问题”：一组用于歧视的数学题
Jewish problems
一篇 arXiv 论文，整理并讨论苏联时期犹太学生在申请大学数学系时被问到的特殊数学难题：这些题往往有简单解法却极难想到，被用作面试中拒绝犹太考生的手段。
科学与数学上首页 5 次 · 2011–2021arxiv.org你的身体并非为长久而造：人类死亡率数据的一课
Your body wasn’t built to last: a lesson from human mortality rates
文章从人类死亡率随年龄变化的统计规律出发，解释身体并非为长久使用而设计：年轻时死亡风险较低，之后随年龄近似指数上升，像复杂系统在不断累积损伤。
科学与数学上首页 5 次 · 2009–2018gravityandlevity.wordpress.com