Ch 1 · 25 Astronomy and Cosmology · A Level Physics 9702
Topic 1 of 1 in Astronomy and Cosmology — A Level Physics 9702 — 77 lessons.
Introduction
We can never visit the stars, yet we know how far away they are, how hot, how big, and that the Universe is expanding. All of it comes from measuring the light that reaches us: its brightness, its colour and its spectral lines. (Syllabus topic 25: sections 25.1–25.3.)
Key ideas — 25.1 (a) Luminosity and radiant flux intensity
The luminosity L of a star is the total power of radiation it emits (W).
🧑🏫 Teacher's explanation
Imagine you are standing in the middle of a dark field holding a single, powerful lightbulb. The total energy the bulb produces every second is its luminosity. If you were to wrap that light in a giant, invisible spherical balloon, the luminosity is the total energy passing through the entire surface of that balloon. As you move further away, that same amount of energy has to spread out over a much larger surface area. Because the area of a sphere increases with the square of the radius, the intensity of light you actually feel on your skin drops off very quickly—this is the inverse square law.
📖 Definitions
🔍 Worked example — Easy
A star has a luminosity of 3.8 imes 10^26 W. Calculate the radiant flux intensity F received at a distance of 4.0 imes 10^16 m.
🔍 Worked example — Exam-style
A star's luminosity is 100 times that of the Sun (L_odot = 3.8 imes 10^26 W). If the star is 10 light-years away, calculate its flux. (Use 1 ly = 9.46 × 10^15 m).
⚠️ Common errors
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🎯 Exam question
Key ideas — 25.1 (b) Standard candles
A standard candle is an astronomical object of known luminosity. Examples: Cepheid variable stars (whose luminosity is linked to their period of pulsation) and type Ia supernovae (which all reach about the same peak luminosity).
🧑🏫 Teacher's explanation
Imagine you are standing in a dark field at night and see a light bulb in the distance. If you know for a fact that the bulb is a 60 W bulb (its luminosity), you can calculate exactly how far away it is just by measuring how bright it looks to your eyes (the flux). If the light looks very dim, it must be far away; if it looks very bright, it must be close. This is the core concept of a 'standard candle'.
📖 Definitions
⚠️ Common errors
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🎯 Exam question
(a) Calculate the distance to the star in meters. [2] (b) Explain how the use of standard candles allows astronomers to determine the distance to galaxies. [2] [4 marks]
Key ideas — 25.2 (a) Wien's displacement law
A star emits a continuous spectrum, like a black body. The wavelength at which the emission is greatest, λ_max, is inversely proportional to the surface temperature:
🧑🏫 Teacher's explanation
Imagine a piece of metal being heated in a forge. At first, it just gets redder and redder. As it gets much hotter, it starts to glow orange, then yellow, and eventually it turns a brilliant blue-white. This happens because as the temperature increases, the energy is released at shorter, more energetic wavelengths.
📖 Definitions
🔍 Worked example — Easy
A star has a peak emission wavelength of 600\ nm. Calculate its surface temperature using λ_maxT = 2.9 × 10^-3\ m K.
🔍 Worked example — Standard
A cool red star has a peak wavelength of 1.2\ mum. Calculate its surface temperature.
🔍 Worked example — Exam-style
A hot blue star peaks at 400\ nm. Calculate its temperature. Then, determine the ratio of its temperature to a red star peaking at 1200\ nm.
⚠️ Common errors
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🎯 Exam question
(a) Calculate the surface temperature of the star. [2] (b) The star's luminosity is 3.0 × 10^26\ W and its radius is 7.0 × 10^8\ m. Calculate the surface temperature using the Stefan-Boltzmann law, L = 4πσ r^2 T^4, where σ = 5.67 × 10^-8\ W m^-2\ K^-4. [3] [5 marks]
Key ideas — 25.2 (b) The Stefan–Boltzmann law
The luminosity of a star of radius r and surface temperature T:
🧑🏫 Teacher's explanation
Imagine a star as a glowing sphere. The total energy it spits out every second is its luminosity, L. This depends on two things: how big the surface area is and how 'hotly' it glows. If you make the star bigger, there is more surface area to radiate energy. If you make it hotter, it glows much more intensely.
📖 Definitions
🔍 Worked example — Standard
A star's temperature increases from 4000 K to 8000 K, while its radius remains constant. By what factor does the luminosity change?
⚠️ Common errors
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🎯 Exam question
Key ideas — 25.2 (c) Estimating a star's radius
🧑🏫 Teacher's explanation
Imagine a star as a glowing lightbulb in a dark, vast room. The 'luminosity' is simply the total power (in Watts) that the bulb emits. If you stand far away, the light spreads out over a huge sphere, making it look dim. This 'dimness' is the flux, or intensity, which decreases with the square of your distance.
📖 Definitions
🔍 Worked example — Easy
A star has a peak wavelength λ_max = 500 nm and a luminosity L = 3.0 × 10^26 W. Calculate the radius of the star. (Use σ = 5.67 × 10^-8 W m^-2 K^-4 and Wien's constant b = 2.90 × 10^-3 m K)
⚠️ Common errors
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🎯 Exam question
Key ideas — 25.3 (a) Redshift
The emission and absorption lines in the spectra of distant galaxies appear at longer wavelengths than the known values measured in the laboratory. This is redshift, caused by the source moving away from us.
🧑🏫 Teacher's explanation
Imagine you are standing on a platform as a train passes you. If the train is moving towards you, the pitch of the whistle sounds higher; if it is moving away, the pitch sounds lower. Light behaves similarly. When a galaxy moves away from us, the light waves it emits are 'stretched' out. Since longer wavelengths correspond to the red end of the visible spectrum, we call this 'redshift'.
📖 Definitions
🔍 Worked example — Easy
A distant galaxy shows a spectral line that is normally observed at 650 nm in a laboratory. In the galaxy's spectrum, this line is observed at 650.5 nm. Calculate the recession speed v of the galaxy. (Take c = 3.00 × 10^8 m/s)
🔍 Worked example — Standard
A galaxy is receding from Earth at a speed of 1.5 × 10^5 m/s. A known hydrogen emission line has a wavelength of 486.1 nm. Calculate the observed wavelength of this line in the galaxy's spectrum.
🔍 Worked example — Exam-style
The light from a distant star is redshifted such that the wavelength of a specific spectral line increases by a factor of 1.0002. Calculate the recession speed of the star.
⚠️ Common errors
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🎯 Exam question
(a) Calculate the recession speed of the galaxy. [2] (b) State what this observation implies about the state of the Universe. [1] [3 marks]
Key ideas — 25.3 (b) The expanding Universe
Light from almost all distant galaxies is redshifted, so they are all moving away from us, and from each other. This suggests that the Universe is expanding.
🧑🏫 Teacher's explanation
Imagine you are standing in a large hall and someone shouts a word to you. If they are walking toward you, the sound waves are compressed and the pitch sounds higher. If they are walking away, the sound waves are stretched out and the pitch sounds lower. Light behaves similarly. When a galaxy moves away from us, the light waves it emits are 'stretched' to longer wavelengths. In the visible spectrum, longer wavelengths are red, which is why we call this 'redshift'.
📖 Definitions
🔍 Worked example — Easy
A distant galaxy shows a redshift of Δλ = 50 nm for a spectral line originally at λ = 500 nm. Calculate the recessional velocity v of the galaxy. (Take c = 3.00 × 10^8 m s^-1)
🔍 Worked example — Standard
A galaxy is at a distance of 4.5 × 10^8 light-years from Earth. Using Hubble's Law v = H_0 d with H_0 = 70 km s^-1 Mpc^-1, calculate the recessional velocity. (Note: 1 Mpc = 3.26 × 10^6 light-years)
⚠️ Common errors
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🎯 Exam question
Key ideas — 25.3 (c) Hubble's law and the Big Bang
Plotting the recession speed v of galaxies against their distance d gives a straight line:
🧑🏫 Teacher's explanation
Imagine you are standing in a large hall filled with balloons, each with a dot drawn on it. If you start inflating all the balloons simultaneously, the dots on the balloons that are further away from you will appear to move away faster than the dots on balloons closer to you. This is because the space between you and the far balloon is expanding more than the space between you and a near balloon.
📖 Definitions
🔍 Worked example — Easy
A galaxy is at a distance of 5.0 × 10^6 parsecs. Using Hubble's law with H_0 = 70 km s^-1 Mpc^-1, calculate its recession speed v.
🔍 Worked example — Standard
A galaxy shows a redshift such that its recession speed is 1.2 × 10^5 km s^-1. If the Hubble constant H_0 is 2.3 × 10^-18 s^-1, calculate the distance d to the galaxy in meters.
⚠️ Common errors
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🎯 Exam question
(a) Calculate the distance to the galaxy in Megaparsecs (Mpc). (b) Explain how the observation of redshift in distant galaxies supports the Big Bang theory. [4 marks]
Worked example
Example 1: distance from a standard candle. A Cepheid has luminosity 3.8 × 10^30 W and its measured flux intensity is 1.0 × 10^-12 W m⁻².
🔍 Worked example — Easy
A Cepheid variable star is used as a standard candle. It has a luminosity L = 3.8 × 10^30 W. If the measured flux intensity F at Earth is 1.0 × 10^-12 W m^-2, calculate the distance d to the star.
⚠️ Common errors
Common mistakes
Practice
Answers: (1) Luminosity: total power of radiation emitted by a star; standard candle: an object of known luminosity. (2) It doubled (F ∝ 1/d^2). (3) L ∝ T^4: A is 16 times as luminous. (4) v = 0.020 × 3.00 × 10^8 = 6.0 × 10^6 m s⁻¹; d = 2.6 × 10^24 m. (5) Galaxies recede at speeds proportional to their distance, so the Universe is expanding uniformly; tracing back, everything was at one point at a finite time in the past: the Big Bang.