2026-07-06 | A-Level Physics | Astrophysics
Astrophysics is one of the most rewarding optional modules in OCR A-Level Physics. 天体物理是OCR A-Level物理中最值得投入的选修模块之一。Today we cover every key topic from stellar evolution to cosmological redshift.
1. Astronomical Units & Parallax 天文单位与视差
Key units: 1 AU = 1.50 x 10^11 m (Earth-Sun distance). 1 ly = 9.46 x 10^15 m. 1 pc = 3.09 x 10^16 m = 3.26 ly. A parsec is the distance at which 1 AU subtends an angle of 1 arcsecond. 秒差距是1天文单位张角为1角秒时的距离。
Stellar parallax is the most fundamental distance-measurement technique. The parallax angle p (in arcseconds) relates to distance d (in parsecs) by: d = 1/p. This is the single most important formula in the module. 这是模块中最重要的公式。
Ground-based telescopes are limited to ~0.01 arcsecond resolution, so reliable parallax distances max out at ~100 pc. The Gaia space telescope extends this to ~100,000 pc. 地面望远镜受大气限制，盖亚太空望远镜将测距范围大幅扩展。
2. Radiation Laws 辐射定律
Wien's Displacement Law: lambda_max x T = 2.898 x 10^-3 m K. Hotter stars peak at shorter wavelengths (blue); cooler stars peak at longer wavelengths (red). 更热的恒星偏蓝，更冷的偏红。
Stefan-Boltzmann Law: L = 4pi R^2 sigma T^4, where sigma = 5.67 x 10^-8 W m^-2 K^-4. L is total power output, R is stellar radius, T is surface temperature. 光度L是恒星总功率输出。
Exam tip: OCR often combines these two laws. Use Wien to find T from lambda_max, then Stefan-Boltzmann to find L or R. Set up ratios when comparing two stars to simplify calculations. 考试中常结合出题，使用比值法可简化计算。
3. The HR Diagram 赫罗图
The HR diagram plots luminosity against surface temperature (decreasing left to right). Key regions: 赫罗图纵轴为光度，横轴为表面温度（从左到右递减）。关键区域：
Main Sequence - diagonal band where ~90% of stars fuse hydrogen to helium. More massive = hotter, brighter, bluer (upper left). 主序带，约90%恒星在此聚变氢为氦。
Red Giants - cool but luminous (upper right), stars with exhausted core hydrogen. 红巨星，核心氢耗尽。
White Dwarfs - hot but dim (lower left), exposed cores of dead low-mass stars. 白矮星，死亡低质量恒星的核心。
4. Stellar Evolution 恒星演化
Low-mass stars (<8 solar masses): Nebula collapse -> Main Sequence (H fusion) -> Red Giant (shell burning) -> Planetary Nebula -> White Dwarf. Chandrasekhar limit: 1.4 solar masses maximum for stable white dwarfs. 低质量恒星：星云坍缩到主序到红巨星到行星状星云到白矮星。钱德拉塞卡极限为1.4倍太阳质量。
High-mass stars (>8 solar masses): Nebula -> Main Sequence -> fusion chain through heavier elements up to iron -> Type II Supernova -> Neutron Star or Black Hole. Iron fusion is endothermic, triggering core collapse. 大质量恒星聚变到铁后发生II型超新星爆炸，遗迹为中子星或黑洞。铁聚变吸热导致核心坍缩。
5. Magnitude System 星等系统
Apparent magnitude (m) - brightness as seen from Earth. Absolute magnitude (M) - brightness at 10 pc distance. 视星等m与绝对星等M。
Distance modulus: m - M = 5 log10(d/10), where d is in parsecs. Pogson's ratio: a 1-magnitude difference = brightness ratio of 2.512. A 5-magnitude difference = exactly 100x brightness ratio. 距离模数公式，5个星等差异对应100倍亮度比。
6. Spectroscopy & Doppler Effect 光谱与多普勒效应
Spectral classes (hottest to coolest): O B A F G K M. Our Sun is G2. Absorption spectra: dark lines when light passes through cooler gas. Emission spectra: bright lines from hot low-density gas. 光谱型从热到冷：OBAFGKM。太阳为G2型。吸收光谱和发射光谱的区别。
Doppler formula: Delta_lambda / lambda_0 = v / c. Redshift (Delta_lambda > 0): object receding. Blueshift (Delta_lambda < 0): object approaching. Used to detect binary stars and exoplanets. 多普勒频移用于探测双星和系外行星。
7. Cosmology: Hubble's Law 宇宙学：哈勃定律
Hubble's Law: v = H0 x d, where v is recessional velocity, H0 ~ 70 km s^-1 Mpc^-1. Almost all galaxies show redshift, meaning the Universe is expanding. More distant galaxies recede faster. 几乎所有星系呈红移，宇宙在膨胀，更远的星系退行更快。
Age of the Universe: t = 1/H0 (assuming constant expansion), giving approximately 13.8 billion years. Cosmic Microwave Background (CMB): isotropic 2.7 K radiation, discovered by Penzias and Wilson (1965), the redshifted remnant of the early Universe ~380,000 years after the Big Bang. 宇宙年龄约138亿年。CMB是2.7K的各向同性辐射。
8. Telescopes 望远镜
Reflecting telescopes use concave mirrors: no chromatic aberration, large apertures possible. Refracting telescopes use convex lenses: suffer chromatic aberration, lenses sag under weight. Collecting power is proportional to (aperture diameter)^2. Space telescopes avoid atmospheric absorption and turbulence. 反射望远镜无色差，集光本领正比于口径平方。太空望远镜避免大气干扰。
Exam Strategy 考试策略
Always define symbols before using formulas. OCR awards marks for this. 使用公式前先定义符号。Master unit conversions: AU to m, ly to m, pc to m, Mpc to m. Use ratios for Stefan-Boltzmann comparisons between stars. The HR diagram is virtually guaranteed; practice labelling it and drawing evolutionary tracks. Prepare a clear, sequential 6-mark stellar evolution answer for both low-mass and high-mass stars. 掌握单位转换，熟练赫罗图，练习6分恒星演化描述题。
Astrophysics rewards formula fluency and systematic study. Master the core equations and understand the physics behind them, and the exam will reward you. 天体物理奖励公式熟练度和系统性学习，掌握核心方程并理解背后的物理原理。
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