AQA A-Level Physics: Astrophysics (7408)

This study guide teaches section 3.9 Astrophysics of the AQA AS and A-level Physics specification (7407/7408, version 1.4, AS and A-level exams June 2016 onwards), sub-sections 3.9.1 to 3.9.3. Astrophysics is one of the five options (sections 3.9 to 3.13): you study one, and it is assessed in Paper 3 Section B (35 of the paper’s 80 marks). Section A of Paper 3 assesses practical skills and data analysis. All of section 3.9 is A-level only.

The course hub lists every topic, the printable checklist tracks outcomes, and the free diagnostics find weak spots. For recall use the revision notes; to test yourself use the practice questions.

What this topic covers (A-level only, option)

Spec ref	Content
3.9.1.1–3.9.1.4	Refracting and Cassegrain telescopes, aberrations, radio/IR/UV/X-ray telescopes, Rayleigh criterion, collecting power, eye vs CCD
3.9.2.1–3.9.2.6	Magnitudes, parsec and light year, black bodies, spectral classes, HR diagram, supernovae, neutron stars, black holes
3.9.3.1–3.9.3.4	Doppler shift, Hubble’s law, Big Bang evidence, quasars, exoplanets

Angles are in radians throughout.

3.9.1 Telescopes

Two-lens refracting telescope

A long-focus objective (fₒ) and a short-focus eyepiece (fₑ). In normal adjustment their principal foci coincide, so the lenses are fₒ + fₑ apart and the final image is at infinity.

Ray diagram: parallel rays from a distant object meet the objective at angle α to the axis. The ray through the objective’s centre is undeviated; all the rays meet at one point in the shared focal plane (a real, inverted intermediate image). Draw a construction line from that point through the eyepiece centre; the rays leave the eyepiece parallel to it, at angle β.

M = (angle subtended by image at eye)/(angle subtended by object at unaided eye) = β/α = fₒ/fₑ. The final image is inverted.

Worked example 1. fₒ = 1.50 m, fₑ = 30 mm; a crater subtends 6.0 × 10⁻⁴ rad.

M = 1.50 / 0.030 = 50
separation = 1.50 + 0.030 = 1.53 m
β = 50 × 6.0 × 10⁻⁴ = 3.0 × 10⁻² rad

Cassegrain reflector

A parabolic concave primary mirror reflects light towards its focus; a convex secondary mirror reflects it back through a hole in the primary to the eyepiece behind. In the ray diagram, parallel rays converge from the primary to the secondary, then converge less steeply through the hole to a focus just behind the primary.

• Spherical aberration: a spherical mirror or lens focuses rays far from the axis at a different point from rays near the axis, blurring the image. A parabolic mirror focuses all rays parallel to the axis at one point.
• Chromatic aberration: a lens refracts blue more than red, so colours focus at different points (coloured fringes). Mirrors have none.

Reflectors win because: no chromatic aberration; a mirror can be supported from behind, so it can be very large; only one surface must be perfect. Refractors suffer because large lenses sag (supported only at the rim), glass must be flawless throughout and absorbs some wavelengths. A reflector’s secondary mirror does block some light and adds diffraction.

Radio, I-R, U-V and X-ray telescopes

A single-dish radio telescope is a parabolic dish reflecting radio waves to an antenna at its focus.

• Structure: both radio and optical use parabolic reflectors; a radio dish can be wire mesh if the gaps are much smaller than λ.
• Positioning and use: the atmosphere is transparent to most radio waves, so radio dishes work on the ground, by day and through cloud, but suffer man-made interference. They are steered to map radio sources.
• Resolving power: much poorer than an optical telescope of the same size, because λ is far longer.
• Collecting power: dishes can be built far larger than mirrors.

Infrared is absorbed by water vapour, so IR telescopes sit on high, dry sites or in space, with cooled detectors. UV and X-ray telescopes must be in space because the atmosphere absorbs these wavelengths; X-ray mirrors work only at grazing incidence.

Advantages of large diameter

Rayleigh criterion: two sources are just resolved when the central maximum of one diffraction pattern falls on the first minimum of the other: θ ≈ λ/D. Collecting power ∝ D² (it depends on area), so larger telescopes see fainter objects.

Worked example 2.

4.0 m mirror at 500 nm:  θ ≈ 500 × 10⁻⁹ / 4.0 = 1.25 × 10⁻⁷ rad
100 m dish at 6.0 cm:    θ ≈ 0.060 / 100 = 6.0 × 10⁻⁴ rad
collecting power ratio = (100/4.0)² = 625

Eye vs CCD: a CCD has much higher quantum efficiency (fraction of photons detected); its resolution depends on pixel spacing, which can be finer than the spacing of the eye’s receptor cells; it is more convenient because it can integrate long exposures and gives a digital image to store and process. The eye gives a real-time view with no equipment.

3.9.2 Classification of stars

Apparent and absolute magnitude

Apparent magnitude m: how bright a star appears from Earth. On the Hipparcos scale the dimmest visible stars have m = 6; brighter objects have lower (even negative) values. Brightness is subjective. A magnitude difference of 1 is an intensity ratio of 2.51, so Δm gives 2.51^Δm.

Light year: distance light travels in one year (≈ 9.46 × 10¹⁵ m). Parsec: distance at which one astronomical unit subtends 1 arcsecond (≈ 3.08 × 10¹⁶ m).

Absolute magnitude M: the apparent magnitude at 10 pc. m − M = 5 log₁₀(d/10), d in parsecs.

Worked example 3. m = 2.0 and m = 6.0 differ by 4: ratio 2.51⁴ = 39.7. A star with m = 9.0, M = 1.5: d = 10 × 10^(7.5/5) = 316 pc = 9.74 × 10¹⁸ m.

Black-body radiation

Treat a star as a black body. Black-body curves rise to one peak; a hotter body is higher at every wavelength and peaks at a shorter wavelength.

• Wien: λₘₐₓT = 2.9 × 10⁻³ m K, used to estimate surface temperature.
• Stefan: P = σAT⁴, A = 4πr². Use it to compare power, temperature and size.
• Inverse square law: I = P/4πd², assuming the star radiates equally in all directions and nothing absorbs radiation on the way.

Worked example 4. Peak at 500 nm: T = 2.9 × 10⁻³/500 × 10⁻⁹ = 5800 K. A 3000 K star with 50 times the radius of a 6000 K star: P ratio = 50² × (0.5)⁴ = 156.

Spectral classes

Class	Colour	T / K	Prominent absorption lines
O	blue	25 000 – 50 000	He⁺, He, H
B	blue	11 000 – 25 000	He, H
A	blue-white	7 500 – 11 000	H (strongest), ionised metals
F	white	6 000 – 7 500	ionised metals
G	yellow-white	5 000 – 6 000	ionised and neutral metals
K	orange	3 500 – 5 000	neutral metals
M	red	< 3 500	neutral atoms, TiO

Balmer lines need hydrogen atoms with electrons in n = 2, which absorb visible photons. Cool stars have few atoms excited to n = 2; in the hottest stars most hydrogen is ionised. So the lines are strongest in A stars. Energy levels are covered in Particles and radiation.

HR diagram

Absolute magnitude (+15 bottom to −10 top) against temperature falling left to right (50 000 K to 2 500 K), or class O to M. The main sequence runs top left to bottom right; giants and supergiants are top right (cool, luminous, large); white dwarfs bottom left (hot, faint, small). The Sun is a G-class main-sequence star, M about +5, about 5800 K.

Sun-like star: protostar → main sequence → expands and cools up and right to a red giant → loses its outer layers; the core moves left and down to a white dwarf.

Supernovae, neutron stars and black holes

• Supernova: rapid increase in absolute magnitude.
• Neutron star: made almost entirely of neutrons, density similar to a nucleus (of order 10¹⁷ kg m⁻³).
• Black hole: escape velocity > c (escape velocity is in Fields and their consequences); event horizon at Rs ≈ 2GM/c².
• Gamma ray bursts: from supergiants collapsing to neutron stars or black holes. Compare energy with the Sun’s lifetime output (power × lifetime in seconds).
• Supermassive black holes sit at galaxy centres.
• Type 1a standard candles: the light curve rises quickly to a peak and declines slowly over months; the peak absolute magnitude is about the same each time (about −19), so m gives d. Distant ones were fainter than expected, suggesting accelerating expansion and dark energy — controversial because dark energy’s nature is unknown and the method assumes identical peaks.

Worked example 5. 6.0 solar masses (1.99 × 10³⁰ kg each): Rs = 2 × 6.67 × 10⁻¹¹ × 1.194 × 10³¹/(3.00 × 10⁸)² = 1.77 × 10⁴ m. A type 1a peaks at m = 14.2 with M = −19.3: d = 10 × 10^(33.5/5) = 5.0 × 10⁷ pc.

3.9.3 Cosmology

Doppler effect

For v ≪ c: Δf/f = v/c and z = Δλ/λ = −v/c (v positive for approach). Recession gives red shift (λ increases); use magnitudes, z = v/c. It applies to optical and radio frequencies, galaxies and quasars.

Binary stars in the plane of orbit: lines shift periodically. Maximum shift → orbital speed v; cycle time → period T; r = vT/2π.

Worked example 6. A 589.0 nm line shifts up to ±0.025 nm every 3.0 days: v = 3.00 × 10⁸ × 0.025/589.0 = 1.27 × 10⁴ m s⁻¹; r = vT/2π = 5.25 × 10⁸ m.

Hubble’s law and the Big Bang

v = Hd: the Universe is expanding. If H is constant, age ≈ 1/H (H in s⁻¹).

Worked example 7. Hα (656.3 nm) observed at 669.4 nm; H = 70 km s⁻¹ Mpc⁻¹.

z = 13.1/656.3 = 0.0200;  v = zc = 5.99 × 10⁶ m s⁻¹
d = 5990 / 70 = 85.5 Mpc
H = 70 × 10³ / 3.08 × 10²² = 2.27 × 10⁻¹⁸ s⁻¹
age ≈ 1/H = 4.40 × 10¹⁷ s = 1.40 × 10¹⁰ years

Big Bang (qualitative): the Universe began hot and dense, and has expanded and cooled. Evidence: the cosmological microwave background radiation, black-body radiation at about 2.7 K arriving almost uniformly from every direction, is stretched radiation from the hot early Universe; the relative abundance of hydrogen and helium (roughly 3 : 1 by mass) matches fusion predicted in the early Universe.

Quasars

The most distant measurable objects, discovered as bright radio sources, with large optical red shifts. Large z → large d by Hubble’s law; with I = P/4πd² this gives enormous power. They form from active supermassive black holes.

Worked example 8. z = 0.10, I = 2.0 × 10⁻¹² W m⁻², H = 70 km s⁻¹ Mpc⁻¹: v = 30 000 km s⁻¹, d = 429 Mpc = 1.32 × 10²⁵ m, P = 4πd²I = 4.4 × 10³⁹ W.

Exoplanets

Direct detection is hard: the planet is faint beside a bright star, and the angular separation is tiny. Radial velocity: the star orbits the common centre of mass, so its lines show a periodic Doppler shift. Transit: the planet crosses the star and intensity dips; the light curve is flat, dips to a flat bottom, recovers, and repeats each orbit. Fractional dip ≈ (r_planet/r_star)².

Common errors

• Using M = fₑ/fₒ, or θ in degrees in θ ≈ λ/D.
• Forgetting a lower magnitude means brighter, or using d in metres in m − M = 5 log(d/10).
• Leaving H in km s⁻¹ Mpc⁻¹ when finding 1/H.

Then try the practice questions. For Paper 3 planning see exam preparation.

Official syllabus

AQA AS and A-level Physics specification (7407/7408), version 1.4, July 2026, AS and A-level exams June 2016 onwards: section 3.9 Astrophysics (A-level only).