📚 AS Physics: Cosmology Essentials | AS物理：宇宙学考点精讲
Cosmology is the scientific study of the origin, evolution, and large-scale structure of the universe. At AS level, you will explore the key observational evidence that underpins our modern understanding of an expanding cosmos, from the Doppler shift and Hubble's law to the discovery of the cosmic microwave background radiation. This article will guide you through the essential concepts, equations, and interpretations that frequently appear in examination questions.
宇宙学是关于宇宙起源、演化和大尺度结构的科学研究。在 AS 阶段，你将探索支撑现代宇宙观的关键观测证据，从多普勒频移和哈勃定律到宇宙微波背景辐射的发现。本文将带你梳理常出现在考题中的核心概念、方程式及其解释。
1. The Scale of the Universe | 宇宙的尺度
mind-boggling. Astronomers use special units: one astronomical unit (AU) is the mean Earth– ravels in a year (9.46 × 10¹⁵ m), and one parsec (pc) is the distance from which the Earth–Sun separation subtends an angle of one arcsecond (1 pc ≈ 3.09 × 10¹⁶ m).
宇宙学中涉及的距离令人难以想象。天文学家使用特殊单位：1 天文单位 (AU) 是地日平均距离（约 1.50 × 10¹¹ 米），1 光年 (ly) 是光在一年内传播的距离 (9.46 × 10¹⁵ 米)，1 秒差距 (pc) 是地日距离张角为 1 角秒处的距离 (1 pc ≈ 3.09 × 10¹⁶ 米)。
For even larger scales, kiloparsecs (kpc) and megaparsecs (Mpc) are used to describe galaxies and galaxy clusters. Remember that the Milky Way is roughly 30 kpc across, while the Andromeda galaxy lies about 0.78 Mpc away.
对于更大尺度，千秒差距 (kpc) 和百万秒差距 (Mpc) 被用来描述星系和星系团。记住银河系的直径大约为 30 kpc，而仙女座星系距离我们约 0.78 Mpc。
2. Stars as Black Body Radiators | 作为黑体辐射源的恒星
Stars behave approximately as black bodies, emitting a continuous spectrum whose peak wavelength depends on their surface temperature. Wien's displacement law states:
恒星大致可视为黑体，发出连续光谱，其峰值波长取决于表面温度。维恩位移定律表述为：
λmax T = 2.9 × 10⁻³ m·K
where λmax is the wavelength at which the intensity is greatest. Hotter stars peak in the blue/ultraviolet, while cooler stars peak in the red/infrared.
其中 λmax 是辐射强度最大处的波长。较热的恒星峰值在蓝/紫外区，而较冷的恒星峰值在红/红外区。
o estimate stellar temperatures from observed spectra, without needing to resolve the star's disc. Combined with the Stefan–Boltzmann law (luminosity L ∝ T⁴ × surface area), we can infer a star's radius and classify it.
这一关系使得天文学家能够从观测光谱估算恒星温度，而无需分辨星面。结合斯特藩–玻尔兹曼定律（光度 L ∝ T⁴ × 表面积），我们可以推算恒星的半径并对其分类。
3. Stellar Spectra and Classification | 恒星光谱与分类
When starlight is passed through a diffraction grating, dark absorption lines appear. These lines correspond to elements in the star's outer atmosphere and are used to assign spectral classes: O, B, A, F, G, K, M (from hottest to coolest). An easy mnemonic is 'Oh Be A Fine Girl/Guy, Kiss Me'.
当星光通过衍射光栅时，会出现暗吸收线。这些谱线对应恒星外层大气中的元素，并用于划分光谱型：O, B, A, F, G, K, M（从最热到最冷）。一个简单的记忆口诀是 'Oh Be A Fine Girl/Guy, Kiss Me'。
The strength of hydrogen Balmer lines peaks at class A; cooler stars show strong molecular bands (e.g. TiO in M stars). The spectral class together with luminosity class gives the full MK system classification, but at AS level you mainly need to recognise the temperature sequence.
氢的巴耳末线强度在 A 型星中最强；更冷的恒星显示出强的分子带（如 M 型星中的 TiO）。光谱型与光度型结合构成完整的 MK 分类系统，但在 AS 阶段你主要需要识别温度序列。
4. The Hertzsprung–Russell Diagram | 赫罗图
The H–R diagram is a plot of luminosity (or absolute magnitude) against temperature (or spectral class). Most stars lie on the main sequence, a band running from hot, luminous O stars to cool, dim M stars. In this phase, stars fuse hydrogen into helium in their cores.
赫罗图是一幅描绘光度（或绝对星等）与温度（或光谱型）的关系图。大多数恒星位于主序带上，这是一条从炽热明亮的 O 型星延伸到寒冷暗淡的 M 型星的带域。在此阶段，恒星在其核心将氢聚变为氦。
Evolved stars depart from the main sequence: giants and supergiants are cool but very luminous (large radii), while white dwarfs are hot but faint (small radii). The position on the H–R diagram therefore encodes a star's mass, age, and internal physics.
演化后的恒星离开主序：巨星和超巨星温度低但光度高（半径大），而白矮星温度高但光度低（半径小）。因此，恒星在赫罗图上的位置编码了其质量、年龄及内部物理过程。
5. Doppler Effect and Redshift | 多普勒效应与红移
The Doppler effect describes the change in observed wavelength when a source of waves moves relative to an observer. For light, if a star or galaxy moves away, its spectral lines are shifted to longer (redder) wavelengths — a redshift. If it moves towards us, we see a blueshift.
多普勒效应描述了波源相对于观察者运动时观测波长的变化。对于光，如果恒星或星系远离我们，其光谱线会向长波（红端）移动——即红移。如果朝向我们运动，则会看到蓝移。
For speeds v much smaller than the speed of light c, the redshift z is given by:
对于速度 v 远小于光速 c 的情况，红移 z 由下式给出：
z = (λobs – λrest) / λrest ≈ v / c
Positive z indicates recession. This simple formula underpins the measurement of cosmic expansion.
正的 z 值表示退行。这一简单公式是测量宇宙膨胀的基础。
6. Hubble's Law | 哈勃定律
In 1929, Edwin Hubble discovered that the recession speed v of a galaxy is proportional to its distance d from us:
1929 年，埃德温·哈勃发现星系的退行速度 v 与其距离 d 成正比：
v = H₀ d
where H₀ is the Hubble constant. Its accepted value is approximately 70 km s⁻¹ Mpc⁻¹, though you will often see values around 68–74 depending on the data set.
其中 H₀ 是哈勃常数。目前普遍接受的数值约为 70 km s⁻¹ Mpc⁻¹，尽管根据不同数据集你可能看到 68–74 之间的数值。
Hubble's law is powerful evidence that the universe is expanding uniformly. It implies that the space between galaxies is stretching, not that galaxies are moving through a static space like shrapnel.
哈勃定律是宇宙正在均匀膨胀的有力证据。它表明星系间的空间本身在伸展，而非星系在静态空间里像弹片一样飞离。
7. The Expanding Universe and the Big Bang | 膨胀的宇宙与大爆炸
Extrapolating Hubble's expansion backwards in time leads to the idea that all matter and energy were once concentrated in an extremely hot, dense state. This initial singularity and its subsequent expansion is called the Big Bang. The approximate age of the universe, t0, can be estimated by 1 / H₀, which gives about 13.8 billion years.
将哈勃膨胀沿时间反推，会得出所有物质和能量曾集中于一个极热、致密的状态。这个初始奇点及其随后的膨胀被称为大爆炸。宇宙的大致年龄 t0 可通过 1 / H₀ 估算，结果约为 138 亿年。
Note that the Big Bang was not an explosion into pre-existing space; it was the rapid expansion of space itself. The model is supported by three main pillars: the recession of galaxies, the abundance of light elements (hydrogen and helium), and the cosmic microwave background radiation.
注意，大爆炸并不是物质在既有空间中的爆炸，而是空间本身的急剧膨胀。该模型有三大支柱支持：星系的退行、轻元素（氢和氦）的丰度以及宇宙微波背景辐射。
8. Cosmic Microwave Background Radiation | 宇宙微波背景辐射
The cosmic microwave background (CMB) is a faint glow of microwave radiation that fills the whole sky. It was first detected by Penzias and Wilson in 1965. The CMB has a black body spectrum corresponding to a temperature of about 2.73 K, which is the cooled remnant of the hot, dense early universe.
宇宙微波背景 (CMB) 是充满整个天空的微弱微波辐射辉光。它由彭齐亚斯和威尔逊于 1965 年首次探测到。CMB 具有对应于约 2.73 K 的黑体谱，是早期炙热致密宇宙冷却的遗迹。
The remarkable uniformity of the CMB across the sky (isotropy) supports the cosmological principle: on large scales the universe is homogeneous and isotropic. Tiny fluctuations (anisotropies of about 1 part in 100,000) provide seeds for the formation of galaxies.
CMB 在天空中高度的均匀性（各向同性）支持了宇宙学原理：在大尺度上宇宙是均匀且各向同性的。微小的起伏（大约十万分之一的不均匀性）为星系形成提供了种子。
9. Dark Matter and Dark Energy | 暗物质与暗能量
Rotation curves of galaxies show that visible mass cannot account for the orbital speeds of stars at large radii; there must be additional invisible mass — dark matter. Furthermore, observations of distant Type Ia supernovae reveal that the universe's expansion is accelerating, driven by a mysterious dark energy.
星系旋转曲线显示，可见的质量无法解释外围恒星的轨道速度；必定存在额外的不可见物质——暗物质。此外，对遥远 Ia 型超新星的观测表明宇宙的膨胀正在加速，其驱动力来自神秘的暗能量。
The standard Lambda-CDM model (Λ Cold Dark Matter) estimates that ordinary matter makes up only about 5% of the total energy content of the universe, with dark matter contributing ~27% and dark energy ~68%.
标准 ΛCDM 模型（冷暗物质模型）估算，普通物质仅占宇宙总能量的大约 5%，暗物质约占 27%，暗能量约占 68%。
10. The Fate of the Universe | 宇宙的命运
The future of the universe depends on the balance between its expansion rate and the gravitational pull of its contents. If the average density of the universe exceeds the critical density ρc, the expansion will eventually halt and reverse (a closed universe). If it equals ρc, the universe is flat and will expand forever at a decreasing rate. If it is less, an open universe expands forever.
宇宙的未来取决于其膨胀率与内容物引力之间的平衡。如果宇宙的平均密度超过临界密度 ρc，膨胀最终将停止并逆转（闭合宇宙）。如果等于 ρc，宇宙是平坦的，将以减速率永远膨胀。如果小于 ρc，则为开放宇宙，永远膨胀。
Current evidence, dominated by dark energy, suggests a flat universe that will continue to expand at an accelerating rate, ultimately leading to a cold, dilute 'heat death'. The geometry of the universe appears to be Euclidean on the largest scales.
目前以暗能量为主导的证据表明，宇宙是平坦的，并将持续加速膨胀，最终走向寒冷、稀薄的“热寂”。在最大尺度上，宇宙的几何看似是欧几里得的。
11. Tackling Cosmology Calculations | 宇宙学计算考点
Examination questions often require you to convert between distance units, apply Wien's law to find surface temperatures, use the redshift formula, and calculate recession velocities or ages using Hubble's law. A common pitfall is mismatching units when using H₀ in km s⁻¹ Mpc⁻¹ — always convert distances to Mpc or speeds to km s⁻¹ consistently.
考试题常要求你转换距离单位、应用维恩定律求表面温度、使用红移公式，以及利用哈勃定律计算退行速度或宇宙年龄。一个常见陷阱是使用 H₀ (km s⁻¹ Mpc⁻¹) 时单位不匹配——务必统一将距离转换为 Mpc 或速度转换为 km s⁻¹。
verse in seconds is roughly 1 / H₀ after converting units. Remember that 1 / H₀ is a time, so 1 / (70 km s⁻¹ Mpc⁻¹) must be converted to seconds by expressing Mpc in km.
例如，若测得某星系距离 d = 100 Mpc，使用 H₀ = 70 km s⁻¹ Mpc⁻¹ 可得 v = 7000 km s⁻¹。宇宙年龄（以秒计）为单位转换后的 1 / H₀。记住 1 / H₀ 是时间量纲，因此需通过将以 km 表达的 Mpc 代入来将 1 / (70 km s⁻¹ Mpc⁻¹) 转换为秒。
12. Summary and Exam Tips | 总结与备考提示
Mastering AS cosmology means confidently linking observational evidence to theoretical models. Be prepared to describe the significance of the CMB and its isotropy, explain how Hubble's law implies an expanding universe, and interpret H–R diagrams in terms of stellar evolution. Practise unit conversions and order-of-magnitude estimates to handle numerical questions efficiently.
掌握 AS 宇宙学意味着能够自信地将观测证据与理论模型联系起来。做好准备描述 CMB 及其各向同性的重要性，解释哈勃定律如何暗示宇宙膨胀，并基于恒星演化解读赫罗图。练习单位换算和数量级估算，以高效应对数值推理题。
Always define your symbols, show the formula before substituting numbers, and check that your final answer is physically plausible — a galaxy recession speed should not exceed the speed of light in simple Hubble flow calculations, and stellar temperatures must lie within reasonable ranges.
始终定义符号，先写公式再代入数据，并检查最终答案在物理上是否合理——在简单的哈勃流计算中，星系退行速度不应超过光速，恒星温度必须位于合理范围内。
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