OCR物理 天体物理 视差 维恩定律 哈勃定律
天体物理在 OCR 物理 A（H556）里是模块 5 牛顿世界与天体物理的最后一节，考纲编号 5.5，目前使用的是 2026 年 3 月发布的第 3.0 版 specification，内容拆成恒星、恒星发出的电磁辐射、宇宙学三小块。这部分的分值不算高，出题却很稳定，几乎每次都在 Component 01 Modelling physics 里出现，那份卷子 100 分、2 小时 15 分，占总成绩 37%。真正的难点不是公式数量，而是判断一道题到底要你用维恩定律、斯特藩定律，还是视差和哈勃定律。下面按考纲顺序把公式、单位和常见失手位置走一遍。
Astrophysics is the final section of Module 5 in OCR Physics A (H556), and it is assessed almost entirely in Component 01, Modelling physics. That paper carries 100 marks in 2 hours 15 minutes and is worth 37 per cent of the A level. Few formulas appear, so marks are usually lost on unit conversion and on choosing the wrong relationship rather than on algebra.
行星 卫星 彗星 太阳系 星系与宇宙的层级
考纲 5.5.1(a) 先要求把这几个词分清，因为题干里换一个词，答案就换一套物理。行星绕恒星转，行星卫星绕行星转，彗星沿很扁的轨道绕恒星转。太阳系是一颗恒星加它的行星系统，星系是上亿颗恒星的集合，宇宙是全部星系与它们之间空间的总和。尺度上从行星到宇宙跨了十几个数量级。很多学生以为星系就是太阳系的放大版，其实太阳系只是银河系里一个很小的成员。答题时写清中心天体是谁，比堆形容词更容易拿分。阅卷时常见的情况是把彗星写成绕行星运动，这一个词就把分丢了。
A planet orbits a star, a planetary satellite orbits a planet, and a comet follows a very elongated orbit around a star; a solar system is one star with its planets, a galaxy is a collection of hundreds of millions of stars, and the universe is everything. Getting the centre of motion right matters more than adding adjectives, and examiners regularly see comets described as orbiting planets. The scale range from a planet to the universe spans more than a dozen orders of magnitude, which is why these terms are tested as definitions rather than as data.
星际尘埃与气体塌缩 氢聚变如何点火
恒星从星际气体与尘埃云开始。云团在自身引力下收缩，引力势能转成内能，中心温度与密度一起升高。温度到达上千万开尔文时，氢核聚变点火，四个氢核合成一个氦核并放出能量。向外的辐射压与气体压顶住向内的引力，恒星进入稳定的主序阶段。这个平衡叫流体静力学平衡，考试常要求用它解释恒星大小为什么能长期不变。常见的错误是只写聚变放能，不写压力平衡，答案就少一半。恒星质量越大，引力压得越紧，核心温度越高，聚变越快，寿命反而越短。
A star begins as a cold cloud of interstellar gas and dust that contracts under its own gravity, converting gravitational potential energy into thermal energy. When the core reaches about ten million kelvin, hydrogen fusion starts, and the outward radiation pressure then balances the inward weight of the outer layers. Many students describe fusion alone and forget that balance, which is exactly what the mark scheme wants when it asks why a main sequence star keeps a steady size.
红巨星 行星状星云与白矮星
类太阳恒星核心的氢烧完后，核心收缩升温，外壳膨胀变冷，恒星变成红巨星。氦在核心聚变成碳和氧，外层气体随后被抛出去，形成行星状星云。剩下的核心不再聚变，靠电子简并压支撑，就是白矮星。电子简并压来自泡利不相容原理，电子被压进很小的体积也不能占有相同状态。白矮星质量不能超过钱德拉塞卡极限，约 1.4 个太阳质量，超过就撑不住。很多学生以为白矮星还在聚变，其实它只是余热在慢慢散掉。这一点在解释白矮星为什么逐渐变暗时特别有用。
After the hydrogen in the core is used up, a Sun-like star swells into a red giant as the core contracts while the outer layers expand and cool. Helium then fuses into carbon and oxygen, the envelope is ejected as a planetary nebula, and the exposed core becomes a white dwarf held up by electron degeneracy pressure. The Chandrasekhar limit of about 1.4 solar masses sets the ceiling, and a white dwarf above it cannot support itself.
红超巨星 超新星 中子星与黑洞
质量超过约八个太阳质量的恒星，演化路径完全不同。核心聚变一路做到铁，铁核聚变不再放能，核心突然失去支撑并坍缩。外层物质被反弹激波抛射出去，形成超新星爆发。核心残骸的质量决定结局，剩下约 1.4 到 3 个太阳质量时形成中子星，更大就塌成黑洞。中子星半径只有十几公里，密度达到每立方厘米上亿吨，快速自转并发出射电束的就是脉冲星。黑洞的逃逸速度超过光速，连光也出不来。常见的错误是把超新星当成恒星烧完了，其实那是核心坍缩引发的爆发现象。
A star above roughly eight solar masses fuses elements all the way to iron, and once the iron core stops releasing energy the core collapses in seconds. The rebounding outer layers produce a supernova, leaving a neutron star if the remnant is between about 1.4 and 3 solar masses, or a black hole if it is heavier. Neutron stars pack a solar mass into a radius of about ten kilometres, while a black hole has an escape velocity above the speed of light.
赫罗图 主序带 红巨星与白矮星的位置
赫罗图把恒星的光度对温度作图，是考纲里唯一要求会读的图。横轴是表面温度，习惯上从左向右递减，纵轴是光度，通常用对数刻度，单位取太阳光度。主序带从左上到右下斜穿全图，质量大的热星在左上，质量小的冷星在右下。红巨星和红超巨星在右上，光度高而温度低，因为半径很大。白矮星在左下，温度不低但光度很小，因为半径只有地球量级。很多学生以为图上位置越靠右越亮，其实横轴方向是反的。读图题先看坐标轴标签和方向，再谈结论。
The Hertzsprung-Russell diagram plots luminosity against surface temperature, with temperature decreasing to the right and luminosity usually on a logarithmic scale. Main sequence stars run diagonally from hot and bright at the top left to cool and dim at the bottom right, red giants sit at the top right, and white dwarfs sit at the bottom left. Reading the axes before reading the stars is the habit that saves marks here.
能级跃迁 光子能量 hf 与发射谱线
孤立气体原子里的电子只能待在分立的能级上，能级取负值，表示电子被束缚在原子核附近。电子从高能级跳到低能级，放出一个光子，能量等于两个能级的差。光子能量写成 E = hf，也可以写成 E = hc/λ，两条式子由普朗克常数串起来。不同元素的能级间隔不同，发出的谱线波长也不同，所以看谱线就能判断恒星里有哪些元素。吸收谱线是反过来发生的，光穿过较冷的气体时，正好对应能级差的光子被吸收。学生最常把发射线和吸收线记反，答题时先想光是发出还是被吃掉。这一节的计算几乎都在考 hf 与 hc/λ 的互换，单位用焦耳或电子伏都行。
Electrons in an isolated gas atom occupy discrete energy levels whose negative values show that the electron is bound to the nucleus. A transition downwards emits a photon of energy E = hf = hc/λ, and because every element has its own level spacing, its line wavelengths identify it inside a star. Absorption lines form the other way round, when photons of exactly the right energy are removed from a continuous spectrum by cooler gas.
连续谱 发射谱 吸收谱与衍射光栅 nλ 等于 d sinθ
连续谱由炽热的固体或高压气体发出，各波长都有，看起来没有暗线。发射谱是低压热气体发出的若干条亮线，位置由元素决定。吸收谱是连续谱穿过冷气体后留下的暗线，暗线位置与同一元素的亮线一一对应。考纲要求会用透射衍射光栅测波长，公式是 nλ = d sinθ，d 是相邻缝的间距。实验中量出某一级亮纹的角度 θ，就能算出 λ。常见的错误是把 d 当成缝宽，其实它是缝间距，等于 1 除以每米刻线数。考纲还专门写明，光学光谱仪的结构与使用不作要求，答题时不必花篇幅描述仪器。
A continuous spectrum comes from a hot dense source, an emission spectrum from a low pressure hot gas, and an absorption spectrum from a continuous source seen through cooler gas. A transmission diffraction grating gives nλ = d sinθ, where d is the spacing between adjacent slits rather than the slit width. The specification states that the structure and use of an optical spectrometer are not required, so a description of the instrument earns nothing.
维恩位移定律 峰值波长与表面温度
维恩位移定律说，恒星辐射最强的波长与表面温度成反比，λmax T = 2.9 × 10⁻³ m K。温度越高，峰值波长越短，所以蓝色星比红色星热。用它可以由测到的峰值波长估出表面温度，太阳的峰值波长约 500 nm，代入得 T 约 5800 K。代入前要把 nm 换成 m，500 nm 是 5.0 × 10⁻⁷ m。学生最常把 500 直接代进公式，得到 5.8 × 10⁻⁶ K 这种明显不合理的答案。反过来给温度求峰值波长时，结果通常以 m 为单位，写成 nm 更直观。阅卷时单位写错一样扣分，公式对但数量级离谱的答案拿不到分。
Wien's displacement law states that the peak wavelength of a star's radiation is inversely proportional to its surface temperature, λmax T = 2.9 x 10^-3 m K. For the Sun, a peak near 500 nm gives about 5800 K once the wavelength is converted to 5.0 x 10^-7 m. Substituting 500 without converting produces an answer several orders of magnitude out, which is the most common error on this calculation.
斯特藩定律 光度 半径与温度的四次方
斯特藩定律把恒星的光度、半径和表面温度连在一起，L = 4πr²σT⁴，σ 是斯特藩常数 5.67 × 10⁻⁸ W m⁻² K⁻⁴。温度翻倍，光度变成十六倍，这个四次方关系是考试最爱考的地方。已知光度和温度就可以反解半径，太阳光度约 3.8 × 10²⁶ W，温度约 5800 K，代入得半径约 6.9 × 10⁸ m。这个结果与太阳的实际半径同一量级，可以用来检验答案是否合理。很多学生以为光度只由温度决定，忘了半径的平方也在里面。红巨星光度高而温度低，正是因为半径大。把维恩定律和斯特藩定律连用，就能从光谱同时估出温度和半径。
Stefan's law links luminosity, radius and surface temperature through L = 4πr²σT⁴ with σ = 5.67 x 10^-8 W m^-2 K^-4. Doubling the surface temperature multiplies the luminosity by sixteen, so a cool red giant can still outshine a hot main sequence star. Rearranging for the Sun gives a radius near 6.9 x 10^8 m, a useful check that a calculated radius is sensible.
天文单位 光年 秒差距与恒星视差
天文距离用天文单位、光年和秒差距表示，考纲要求三种单位都会换算。天文单位是地球到太阳的平均距离，光年是光走一年的距离，OCR 数据表给出 1 光年约 9.5 × 10¹⁵ m，1 秒差距约 3.1 × 10¹⁶ m。恒星视差是地球绕太阳运动造成的近星相对背景的位移，视差角 p 用角秒表示，距离用秒差距表示时 d = 1/p，这条式子在考纲里直接给出。很多学生以为 p 是地球半年内走过的总角度，其实它是总位移的一半。视差只对较近的恒星有效，越远的星位移越小，测量误差很快吞掉信号。换算时先统一到米或秒差距再代公式，能避免数量级错误。
Astronomical distances are quoted in astronomical units, light years and parsecs, and the OCR data sheet gives 1 light year ≈ 9.5 x 10^15 m and 1 parsec ≈ 3.1 x 10^16 m. Stellar parallax uses the apparent shift of a nearby star against background stars, and with the parallax angle p in seconds of arc the distance in parsecs is d = 1/p. The angle measured is half of the total shift over six months, and the method fails once that shift becomes smaller than the measurement uncertainty.
多普勒效应 红移与谱线位移
光源相对观察者运动时，观测到的频率会改变，这叫多普勒效应。远离时频率变低、波长变长，靠近时反过来。对电磁辐射，考纲给出的关系是 Δf/f = v/c，v 是退行速度，c 是光速。星系光谱的谱线普遍向长波方向移动，称为红移，这说明星系在远离我们。算速度时先把频率变化写成比值，再乘光速，能少一步换算错误。常见的错误是把红移当成恒星颜色变红，其实那是观测到的谱线位置移动。红移量通常很小，谱线位移要与实验室波长仔细比对才能测出来。
The Doppler effect changes the observed frequency of radiation from a source moving relative to the observer, with Δf/f = v/c for electromagnetic radiation. Galaxies show redshifts, meaning their lines sit at longer wavelengths than in the laboratory, and that is the evidence for recession. Redshift is a shift of spectral lines rather than a change in a star's own colour, which is where answers often go wrong.
哈勃定律 宇宙年龄与大爆炸
哈勃定律写成 v ≈ H0 d，H0 叫哈勃常数，考纲要求会用它出现在两种单位里，一种是 km s⁻¹ Mpc⁻¹，另一种是 s⁻¹。用 Mpc 时距离要先换成米，不然速度会算成天文数字。哈勃常数近似为 2.2 × 10⁻¹⁸ s⁻¹ 时，取倒数得到宇宙年龄约 4.4 × 10¹⁷ s，也就是一百多亿年。宇宙学原理说宇宙在大尺度上均匀、各向同性，物理定律处处适用。大爆炸模型正是由星系红移和这个均匀性推出来的，宇宙早期温度极高、密度极大。很多学生以为哈勃定律说的是星系自己在空间里飞，其实空间本身在膨胀。这条定律的不确定度主要来自 H0 的测量差异，答论述题时要写清这一点。
Hubble's law is written v ≈ H0 d, and the specification requires H0 in both km s^-1 Mpc^-1 and s^-1. With H0 near 2.2 x 10^-18 s^-1, the reciprocal gives an age of about 4.4 x 10^17 s, roughly fourteen billion years. The cosmological principle, that the universe is homogeneous and isotropic on large scales, underpins the Big Bang model, and the spread in measured H0 values is the main uncertainty quoted for that age.
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