--- title: "星系旋转曲线与质量分解" description: "从球与盘的引力到保存数据拟合，再逐图阅读反馈暗晕与修改动力学的条件比较。" canonical_url: "https://sandboxphysics.com/zh/stories/galaxy-rotation-curves/" language: "zh-CN" page_type: "story" alternate_languages: en: "https://sandboxphysics.com/stories/galaxy-rotation-curves/" last_modified: "2026-11-05" --- 星系旋转曲线 # 星系旋转曲线与质量分解 Sandbox Physics · 2026-11-05 圆周运动告诉我们需要多大的内向引力。先从这个图景出发，分清球与盘，再计算分项引力，研究几何怎样影响保存数据的质量拟合。 1. L1 ## [平坦的旋转曲线怎样衡量引力](https://sandboxphysics.com/zh/stories/galaxy-rotation-curves/what-a-flat-curve-measures/) 星系外圈的气体为何仍转得很快？从圆周运动需要的引力出发，看恒星盘与暗晕为什么难以唯一分开。 2. L1 ## [先分清球体与圆盘的引力](https://sandboxphysics.com/zh/stories/galaxy-rotation-curves/why-a-disk-is-not-a-sphere/) 从圆周加速度推导球对称内部质量，再用同一张指数盘比较球近似与盘面引力，完成有单位的质量例题。 3. L2 ## [把恒星、气体和暗晕的引力加起来](https://sandboxphysics.com/zh/stories/galaxy-rotation-curves/adding-starlight-gas-and-a-halo/) 从有符号径向力到总圆轨速度，推导NFW与平核球晕的质量，并区分理想薄指数盘与原生有限厚度盘。 4. L3 ## [距离与倾角为什么会改变整条曲线](https://sandboxphysics.com/zh/stories/galaxy-rotation-curves/moving-a-whole-rotation-curve/) 推导距离与倾角的共同变换、固定观测坐标中的完整高斯似然与轮廓分析，用例题分清整体误差和独立噪声。 5. L3 ## [从具名SPARC文件重新算质量模型](https://sandboxphysics.com/zh/stories/galaxy-rotation-curves/recomputing-a-named-sparc-galaxy/) 独立运行合成数据与NGC2403的保存、六起点拟合、质量光度比轮廓和共同距离倾角场景，保留真实数据的明显残差。 6. L4 ## [怎样读反馈、暗晕与MOND的条件比较](https://sandboxphysics.com/zh/stories/galaxy-rotation-curves/reading-feedback-and-gravity-comparisons/) 逐图阅读固定2026年Smith等人论文，分清核—尖峰、重子反馈、几何先验和弱透镜平均曲线，并完成一个势场变化的轨道算例。 ## 独立科学复算材料 [下载科学复算ZIP](https://sandboxphysics.com/stories/galaxy-rotation-curves/materials/galaxy-rotation-science-v1.zip) · [阅读安装与计算范围](https://sandboxphysics.com/stories/galaxy-rotation-curves/materials/README.md) 离线计算需要Python、NumPy与SciPy，默认合成数据会完整生成并重新拟合。可选的具名SPARC文件只在自己的电脑取得；ZIP不含原始观测或浏览器交互引擎。 单件脚本、字节与SHA-256 - [README.md](https://sandboxphysics.com/stories/galaxy-rotation-curves/materials/README.md) (6785 B) `5fbf0d29e006fc06f35d2290fd8fee7d5abc2301b601814165495331f9c37a84` - [LICENSE.txt](https://sandboxphysics.com/stories/galaxy-rotation-curves/materials/LICENSE.txt) (1325 B) `4f15facc82fd0218a74907ae83f1716569277d9c40f55b249451dd8d89191b2f` - [requirements.txt](https://sandboxphysics.com/stories/galaxy-rotation-curves/materials/requirements.txt) (185 B) `359f4c650ca6dd5a2705535e32377aa86db27d8d6ebd9b47333070850b9c5980` - [source-identities.json](https://sandboxphysics.com/stories/galaxy-rotation-curves/materials/source-identities.json) (724 B) `409cf4931c19dc97049f943eb005165a59f88d1842a3dd2596eaa1dabcfbd458` - [own-observation.json](https://sandboxphysics.com/stories/galaxy-rotation-curves/materials/own-observation.json) (9009 B) `48cd32150a8eff02b4c3e870cb82f8df008d90c2b5aed3f9bca743506852a5e1` - [analyze.py](https://sandboxphysics.com/stories/galaxy-rotation-curves/materials/analyze.py) (2750 B) `5baed281117d3980af0f0e19e428c4163f79a97a84d1db71955ecbee7993ac3a` - [conditional\_fit.py](https://sandboxphysics.com/stories/galaxy-rotation-curves/materials/conditional_fit.py) (3618 B) `37700d28edc852a10d09f949a7270a652b61f1c9d30cc2d8d0e99d4347e92d70` - [fetch\_named\_source.py](https://sandboxphysics.com/stories/galaxy-rotation-curves/materials/fetch_named_source.py) (5014 B) `240b29a1c6e929895b5ead31269b495b1223be0615da62c703e2962028e6de5a` - [generate\_observation.py](https://sandboxphysics.com/stories/galaxy-rotation-curves/materials/generate_observation.py) (849 B) `c5442424f9cecdcd81022ec31cae0b81bdc21400f06eea6dde4108c7062de743` - [observation\_record.py](https://sandboxphysics.com/stories/galaxy-rotation-curves/materials/observation_record.py) (2693 B) `2d791013b5c8b289e6bfdc5ba9ed408e18b9fc4334d44ba32091546ed297e752` - [physical\_units.py](https://sandboxphysics.com/stories/galaxy-rotation-curves/materials/physical_units.py) (255 B) `2db6448e5f4e657ef48ffd9d2a58c7487c6f7655a8033dc001327fe43192507c` - [plot.py](https://sandboxphysics.com/stories/galaxy-rotation-curves/materials/plot.py) (5734 B) `c30e8e160f1f73f6451ebb903402a316ecba858814e6b1d5059ad31926abb4e1` - [rotation\_model.py](https://sandboxphysics.com/stories/galaxy-rotation-curves/materials/rotation_model.py) (2003 B) `97c2c5ca56373f20996b26ef179267549ad3a341817b29666ce368029cfa96a1` - [save\_native.py](https://sandboxphysics.com/stories/galaxy-rotation-curves/materials/save_native.py) (655 B) `bbf0881e28cf1dd4d13105af656cc4072e3a42a62a5f7013b9f48075b764c082` - [spherical\_halos.py](https://sandboxphysics.com/stories/galaxy-rotation-curves/materials/spherical_halos.py) (1459 B) `4678e06bf172167f3a8a3a5d199447658eb51860507405b80110807165c5ef83` - [synthetic\_record.py](https://sandboxphysics.com/stories/galaxy-rotation-curves/materials/synthetic_record.py) (1538 B) `6285cda07f2b9324806d25ecc89712eb6b94479e3caaa1f24a88c004d449a063` - [thin\_disk\_reference.py](https://sandboxphysics.com/stories/galaxy-rotation-curves/materials/thin_disk_reference.py) (1298 B) `67ba0512e47c10d10c5b8d17f435d808812eec25f0edce296b6c80eaf72e0bc0` - [validate.py](https://sandboxphysics.com/stories/galaxy-rotation-curves/materials/validate.py) (5709 B) `7cfbf116c5e51e9a3e1aa0ecd113a24f7a069706336ae01221de67dbf331cb6d` - [verify\_analytic\_limits.py](https://sandboxphysics.com/stories/galaxy-rotation-curves/materials/verify_analytic_limits.py) (3073 B) `68bca45f2d3d8a1f8cda804bb45c3e165025effa0221c2f45d7c1416009bae6a` - [verify\_nuisance\_mapping.py](https://sandboxphysics.com/stories/galaxy-rotation-curves/materials/verify_nuisance_mapping.py) (4184 B) `04b8587eb21a257b809fe930c33d43ddb2e008e4ebf2026134ee0a1d35b4015e` - [SHA256SUMS.json](https://sandboxphysics.com/stories/galaxy-rotation-curves/materials/SHA256SUMS.json) (3306 B) `2fb52c937f2026d872f053e17343e55595fb3568862c20573d59123f3d897b49` - [galaxy-rotation-science-v1.zip](https://sandboxphysics.com/stories/galaxy-rotation-curves/materials/galaxy-rotation-science-v1.zip) (29081 B) `f389268ed651be3a66ad7d87ee6760ebe39d87f6bd2498b2fb8904c9f10893a3` ## 来源与计算范围 1. [Lelli, McGaugh & Schombert (2016), SPARC, AJ152,157](https://astroweb.cwru.edu/SPARC/) 官方固定Table1与Rotmod\_LTG.zip，只使用具名NGC2403成员。主论文第3.1至3.3及5.1至5.3节、原Table2说明用于核读气体符号、单位恒星质量光度比、有限厚度与误差语义。新取源与缓存复算分别记录；原观测与实测派生图留在本地。 2. [Navarro, Frenk & White (1997), fixed astro-ph/9611107v1](https://arxiv.org/abs/astro-ph/9611107v1) 核读固定原文的密度律、数值分辨率背景、第3.2至3.3节与原式2至3。课程对给定球对称密度作数学积分，没有重跑宇宙学模拟，也不把数学极限当作任意物理尺度的认证。 3. [Li et al., Fitting the radial acceleration relation, arXiv:1803.00022v1](https://arxiv.org/abs/1803.00022v1) 此前核读固定文件的全局参数讨论、式4至5与图1；2018年arXiv水印与2022年内部排版日期分别记录。课程的坐标Jacobian推导和数值检查是自有计算，没有重现175星系MCMC。 4. [Spherical shell theorem foundation Lab](https://sandboxphysics.com/labs/gravity-shell-theorem/) 复用球壳抵消与球外中心力基础。旋转曲线路线增加保存分量、几何与条件拟合。 5. [Smith et al., Dark Matter and MOND successes and degeneracies, arXiv:2610.33157v1](https://arxiv.org/abs/2610.33157v1) 完整核读固定26页预印本，并视觉检查图1/5/6/10/14与表3。水印2026年10月23日；摘要页注MNRAS已接收，PDF仍留接收占位符和2025排版年。指南沿第2至6节，区分固定与可变几何、BIC各自参考与叠加透镜条件。未重现147对象MCMC或私下提供的协方差，不再发布原PDF或原图。 6. [Independent saved-observation rotation-curve calculation](https://sandboxphysics.com/stories/galaxy-rotation-curves/materials/galaxy-rotation-science-v1.zip) 自有MIT Python实际生成合成观测、六起点拟合、轮廓、共同几何场景、正密度/圆环势/Jacobian参照与SVG。可选具名源获取、73点保存转换和拟合均实际执行。默认离线，ZIP不含Lab引擎、原SPARC行、论文或实测派生图。