Module 05 — Cosmology & Space

Duration: 3–4 weeks | Prereq: Modules 00–04

This is where everything comes together. Cosmology is the study of the universe as a whole — its structure, origin, evolution, and fate. It draws on every branch of physics you've covered: mechanics (gravity, orbital motion), waves (redshift, the cosmic microwave background), electromagnetism (stellar emission, radio telescopes), and quantum physics (nuclear reactions in stars, particle physics in the early universe).

It's also, frankly, the most mind-expanding area of science. The scales involved, the conclusions reached, and the questions still unanswered are extraordinary.

1. Stellar Physics — What Stars Are

The Hertzsprung-Russell (HR) Diagram

Plot stars on a graph of luminosity (brightness) vs surface temperature (or colour). The result isn't random — stars fall into clear groupings:

Main sequence: a diagonal band from hot-bright to cool-dim. This is where stars spend most of their lives, fusing hydrogen to helium. The Sun is a middle-of-the-road main sequence star.
Red giants / supergiants: upper-right. Cool surface, enormous size, high luminosity. Old stars running out of hydrogen fuel.
White dwarfs: lower-left. Hot surface, tiny, very dim. The remnants of dead low-mass stars.

A star's position on the HR diagram is a direct diagnostic of its age, mass, and evolutionary stage.

Stellar classification

Stars are classified by spectral type (surface temperature), from hottest to coolest: O B A F G K M (mnemonic: "Oh Be A Fine Girl/Guy, Kiss Me")

O: >30,000 K — blue-white, very massive, short-lived
G: ~5,500 K — yellow, like our Sun
M: <3,500 K — red dwarfs, most common, very long-lived

How stars work

Stars are held up by the pressure of energy release from nuclear fusion, balanced against the inward pull of gravity. This balance is hydrostatic equilibrium.

In the Sun: hydrogen → helium (proton-proton chain)

4 ¹H → ⁴He + 2e⁺ + 2v_e + energy

Energy released: E = Δm × c² (the helium nucleus weighs 0.7% less than the four protons — that "missing" mass is released as energy)

The Sun fuses ~600 million tonnes of hydrogen per second. It has enough fuel for about 5 billion more years.

Stellar evolution

The story of a star's life depends almost entirely on its initial mass:

Low/medium mass stars (like the Sun):

Main sequence (hydrogen fusion) — billions of years
Red giant (hydrogen shell fusion, then helium core fusion)
Planetary nebula (outer layers expelled)
White dwarf (carbon/oxygen core, no more fusion) → cools slowly over trillions of years

Massive stars (> ~8 solar masses):

Main sequence — millions of years (shorter because they burn so fast)
Red supergiant
Supernova (catastrophic collapse and explosion — briefly outshines entire galaxies)
Remnant: neutron star (for medium-massive stars) or black hole (for very massive stars)

Supernovae are where heavy elements come from. Elements up to iron are forged in stellar cores during normal fusion. Elements heavier than iron — gold, silver, uranium — require the extreme conditions of a supernova or neutron star merger to form (the r-process). The iron in your blood was made in a stellar core; the gold in jewellery was made in a cataclysmic explosion. You are literally made of stardust.

2. Black Holes

A black hole forms when mass is compressed into a small enough volume that the escape velocity exceeds the speed of light. Nothing — not even light — can escape from within the event horizon.

The Schwarzschild radius

The radius within which escape velocity = c:

r_s = 2GM / c²

For the Sun: r_s ≈ 3 km (the Sun would need to be compressed to the size of a small city to become a black hole)

For Earth: r_s ≈ 9 mm

What happens at the event horizon

From a distant observer's perspective, someone falling into a black hole appears to slow down and freeze at the event horizon (due to gravitational time dilation) — never quite crossing it.

From the perspective of the infalling observer: they cross the event horizon normally, feeling nothing special at that moment, and reach the singularity — a point of infinite density — within their own future.

Hawking radiation

Stephen Hawking showed in 1974 that black holes aren't perfectly black. Due to quantum effects near the event horizon, virtual particle pairs can form — one particle escapes, one falls in — resulting in the black hole slowly losing mass. For stellar-mass black holes, this effect is negligible. For tiny black holes, it would be catastrophic.

The temperature of Hawking radiation:

T = ħc³ / (8πGMk_B)

Smaller black hole → higher temperature → faster evaporation.

Hawking radiation remains theoretical — we haven't observed it yet. But it's taken seriously because it follows from applying quantum mechanics to black hole physics.

Types of black hole

Type	Mass	Formation
Stellar	3–100 M☉	Supernova remnant
Intermediate	100–10⁵ M☉	Unknown; possibly globular clusters
Supermassive	10⁶–10¹⁰ M☉	Centre of most galaxies; unknown formation

The supermassive black hole at the centre of the Milky Way (Sgr A*) has mass ~4 × 10⁶ solar masses and has been imaged indirectly (the Event Horizon Telescope, 2019–2022).

3. Special Relativity

Einstein published special relativity in 1905. It starts from two postulates:

The laws of physics are the same for all observers in uniform motion.
The speed of light in a vacuum is the same for all observers, regardless of their motion or the motion of the source.

Postulate 2 is the radical one. It means you cannot "catch up" with light — no matter how fast you go, light still passes you at c. The consequences are deeply counterintuitive.

Time dilation

Moving clocks run slow. A clock moving at speed v relative to an observer ticks more slowly:

t' = t₀ × γ (where γ = 1 / √(1 − v²/c²))

Here t₀ is the proper time — time measured on the moving clock (the one in the frame where the events happen at the same location). t' is the longer time measured by the stationary observer. Since γ ≥ 1, t' ≥ t₀: the moving clock always shows less elapsed time.

γ (the Lorentz factor) is ≥ 1 and increases steeply as v → c.

Example: A muon (unstable particle) created in the upper atmosphere by cosmic ray collision has a half-life of 2.2 μs. At the speeds they travel (~0.99c), they should decay before reaching the ground. But they don't — because from our perspective, their "clock" runs 7× slower. They survive long enough to reach detectors on the ground. This is confirmed experimentally.

GPS satellites must account for both special relativity (their speed makes their clocks run slow) and general relativity (their altitude makes their clocks run fast). Uncorrected, GPS would drift by ~10 km per day.

Length contraction

Moving objects are contracted along the direction of motion:

L' = L / γ

Objects moving at high speed are shorter along the direction of travel from the observer's perspective.

The twin paradox

One twin travels to a distant star at high speed, returns. The travelling twin is younger — they have experienced less time. This is real (tested with atomic clocks on aeroplanes). The "paradox" dissolves when you account for the fact that the travelling twin must decelerate and change direction — they are not in inertial (uniform) motion throughout.

Mass-energy equivalence

E = mc²

Energy and mass are two aspects of the same thing. The full relativistic energy of a moving object:

E² = (mc²)² + (pc)²

For a stationary object (p = 0): E = mc² (rest energy). For a massless photon (m = 0): E = pc.

The "rest energy" stored in mass is enormous. 1 kg of matter contains ~9 × 10¹⁶ J — more than the energy released by a 20-megaton nuclear weapon. Nuclear reactions only convert a fraction of a percent of mass to energy. Matter-antimatter annihilation converts 100%.

What special relativity does NOT cover

Special relativity handles inertial reference frames (constant velocity). Einstein spent the next decade extending it to accelerating frames and gravity — this became General Relativity (1915).

4. General Relativity (Conceptual Overview)

In general relativity, gravity is not a force — it's the curvature of spacetime caused by mass and energy.

The core idea: Mass tells spacetime how to curve; spacetime curvature tells mass how to move.

A massive object like the Sun curves spacetime around it. Earth "falls" through this curved spacetime — what we call its orbit is actually a straight-line path (geodesic) through curved spacetime.

Key predictions of GR, all confirmed

Gravitational time dilation: clocks run slower deeper in a gravitational field. GPS must correct for this.
Gravitational lensing: light follows the curvature of spacetime, so mass bends light beams. The first confirmation came in 1919 (Eddington's eclipse observation).
Gravitational waves: disturbances in spacetime curvature that propagate as waves at speed c. First directly detected by LIGO in 2015 — from two merging black holes 1.3 billion light-years away.
Black hole event horizons: a direct prediction.
Expansion of the universe: GR predicts the universe can't be static; it must be expanding or contracting.

5. The Expanding Universe and Hubble's Law

Edwin Hubble (1929) observed that virtually all distant galaxies are redshifted — their spectral lines are shifted to longer wavelengths, indicating they're moving away from us. The further away a galaxy, the faster it recedes.

Hubble's Law: v = H₀d

Where v is the recession velocity, d is the distance, and H₀ is the Hubble constant (~70 km/s/Mpc — for every megaparsec of distance, recession velocity increases by 70 km/s).

Critical point: The galaxies aren't moving through space. Space itself is expanding — stretching the light as it travels. The redshift is a cosmological redshift, not a Doppler shift (though the maths is similar for nearby galaxies).

Does this mean we're at the centre of the universe? No. Every point in the universe sees every other point moving away from it. There is no centre. Imagine dots on an expanding balloon — every dot sees every other dot receding.

6. The Big Bang

Hubble's observation implies that if you run time backwards, everything was once closer together. Run it back far enough: the entire observable universe was compressed into a point of almost infinite density and temperature — the Big Bang, approximately 13.8 billion years ago.

Timeline of the universe

Time after Big Bang	Event
10⁻⁴³ s	Planck epoch — physics as we know it breaks down
10⁻³⁶ s	Inflation — universe expands exponentially fast
10⁻¹² s	Electroweak symmetry breaking; W and Z bosons acquire mass; electromagnetic and weak forces separate
10⁻⁶ s	Quarks combine into protons and neutrons
3 minutes	Nucleosynthesis — hydrogen and helium nuclei form
380,000 years	Recombination — electrons combine with nuclei; universe becomes transparent
~200 million years	First stars ignite
~1 billion years	First galaxies form
~9.2 billion years	Solar System forms
13.8 billion years	Now

The Cosmic Microwave Background (CMB)

At 380,000 years after the Big Bang, the universe cooled enough for electrons to combine with protons to form neutral hydrogen. Before this, photons couldn't travel freely — the universe was opaque. After this, photons streamed freely — the universe became transparent.

That flash of light is still visible today, cooled to a temperature of just 2.725 K — microwave radiation filling the entire sky uniformly. This is the Cosmic Microwave Background, discovered accidentally by Penzias and Wilson in 1965.

The CMB is our best evidence for the Big Bang. It's essentially a "baby photo" of the universe.

Tiny temperature fluctuations in the CMB (~1 part in 100,000) represent the seeds of all the structure in the universe — the galaxies, clusters, and voids we see today. The pattern of these fluctuations tells cosmologists about the geometry, composition, and age of the universe with remarkable precision.

7. Dark Matter and Dark Energy

Dark matter

Observations of galaxy rotation curves (how stars orbit within galaxies) reveal that galaxies spin faster than they should given their visible mass. Stars at the edges of galaxies orbit as fast as those near the centre — this should be impossible given the visible mass.

Explanation: there's additional invisible mass — dark matter — that doesn't interact with light but does exert gravity.

Dark matter accounts for ~27% of the universe's energy content. Its nature is unknown. Leading candidates: WIMPs (Weakly Interacting Massive Particles), axions, primordial black holes. Direct detection experiments are ongoing.

Dark energy

In 1998, two independent teams measuring distant supernovae discovered that the universe's expansion is accelerating — driven by some form of repulsive energy pervading space, called dark energy.

Dark energy accounts for ~68% of the universe's energy content. Normal matter (everything you can see) is only ~5%.

The universe is ~95% stuff we don't understand. This is a good reminder that physics, for all its extraordinary achievements, is still very far from a complete picture.

8. Gravitational Waves

General relativity predicts that accelerating masses create ripples in spacetime — gravitational waves — that travel at the speed of light.

On 14 September 2015, LIGO detected gravitational waves for the first time, from the merger of two black holes ~1.3 billion light-years away. The signal lasted a fraction of a second. The mirrors in the detector moved by 10⁻¹⁸ m — one-thousandth the diameter of a proton.

This opened gravitational wave astronomy — an entirely new way of observing the universe, sensitive to events invisible to light (black hole mergers, neutron star collisions deep in dusty regions).

The 2017 detection of a neutron star merger was simultaneously observed in gravitational waves, gamma rays, optical light, X-rays, and radio waves — the first multi-messenger astronomy event. It confirmed that neutron star mergers produce gold and other heavy elements.

9. Self-Check Questions

A star has surface temperature 3,500 K. What spectral class is it? Where on the HR diagram?
What is the Schwarzschild radius of an object with mass 3 × 10³⁰ kg? (G = 6.67 × 10⁻¹¹ N m² kg⁻²)
A spaceship travels at 0.8c relative to Earth. Its onboard clock shows a journey took 3 years. How long did the journey take for an Earth observer?
A galaxy at 200 Mpc shows a redshift of z = 0.015. Is this consistent with Hubble's Law? (H₀ = 70 km/s/Mpc)
The CMB has temperature 2.725 K. Using Wien's law (λ_max = b/T, b = 2.898 × 10⁻³ m K), what is the peak wavelength of the CMB?

Answers:

3,500 K → spectral class M (red dwarf). On the HR diagram: lower right — cool, low luminosity main sequence.
r_s = 2GM/c² = 2 × 6.67×10⁻¹¹ × 3×10³⁰ / (9×10¹⁶) = 4.002×10²⁰ / 9×10¹⁶ = 4,447 m ≈ 4.4 km
γ at 0.8c: γ = 1/√(1−0.64) = 1/√0.36 = 1/0.6 = 1.667. Earth time = t₀ × γ = 3 × 1.667 = 5 years
v = H₀d = 70 × 200 = 14,000 km/s. z = v/c = 14,000 / 300,000 = 0.047. This does not match the given z = 0.015 — these values are inconsistent. A galaxy at 200 Mpc should have z ≈ 0.047; a galaxy with z = 0.015 would be at ~64 Mpc. The question tests whether you can apply Hubble's law; spotting the inconsistency is the correct answer.
λ_max = b/T = 2.898×10⁻³ / 2.725 = 1.064 × 10⁻³ m = 1.064 mm — in the microwave range, as expected.

Where to Go From Here

You've now covered the breadth of A Level Physics. More importantly, you should have a sense of which areas genuinely caught your attention. Here are clear paths forward:

If Mechanics & Relativity lights you up

Next: The Feynman Lectures on Physics, Vol. 1 — free at feynmanlectures.caltech.edu
Then: Spacetime Physics by Taylor & Wheeler — the best first course in special relativity
Then: Gravitation by Misner, Thorne & Wheeler — the classic GR text (demanding but magnificent)
Accessible popular science: The Elegant Universe by Brian Greene; Black Holes & Time Warps by Kip Thorne

If Cosmology & Astrophysics is your thing

Next: A Brief History of Time — Hawking (if you haven't read it since 1998, it holds up)
Then: The Whole Shebang by Timothy Ferris — the best popular account of cosmology written
Then: Cosmology by Steven Weinberg (requires some maths but accessible to a motivated reader)
YouTube: PBS Space Time — genuinely rigorous popular cosmology content; episodes on the CMB, dark matter, and inflation are outstanding

If Quantum & Atomic Physics pulls you

Next: QED: The Strange Theory of Light and Matter — Feynman (no maths required)
Then: In Search of Schrödinger's Cat by John Gribbin — still the best popular introduction to QM
Then: The Principles of Quantum Mechanics by Dirac (the original and still a masterpiece — for when you're ready)
YouTube: PBS Space Time, Sixty Symbols, Looking Glass Universe

If Electricity & Electromagnetism excites you

Next: The Feynman Lectures on Physics, Vol. 2 (electromagnetism)
Then: Introduction to Electrodynamics by Griffiths — the standard undergraduate text
Practical path: Electronics, radio, antennas, RF engineering — all directly follow from Maxwell

For structured learning with problems

Isaac Physics (isaacphysics.org) — free, A Level and university level, excellent problem sets
MIT OpenCourseWare — free university-level physics courses with full lecture notes, problem sets, and exams
Khan Academy — strong on worked examples for any A Level topic

You've completed the guide. Now find what lights you up — and go deep.