Stars and the Universe

Star. A massive ball of hot gas (mostly hydrogen) where, at the core, nuclear fusion converts hydrogen into helium, releasing enormous energy.

Sun. Our nearest star. About $1.5 \times 10^{8}\,\text{km}$ away (= $8\,\text{light-minutes}$). Lifespan $\sim 10$ billion years.

Galaxy. A collection of BILLIONS of stars, plus interstellar gas and dust, all gravitationally bound and orbiting a common centre.

The Milky Way. Our home galaxy. About $100{,}000\,\text{light-years}$ across. Contains the Sun, $\sim 200$ billion stars, plus dark matter.

The Universe. Contains hundreds of billions of galaxies. Each galaxy contains hundreds of billions of stars. The numbers are vast.

Hierarchy from small to large:

• Planet → Star (with planets) → Star system → Galaxy → Galaxy cluster → Universe.

Cambridge tip. Cambridge often asks students to estimate or compare. The Sun is one star in $\sim 200$ billion in the Milky Way. The Milky Way is one galaxy in hundreds of billions in the universe.

Light-year (ly). The distance LIGHT travels in one year, in vacuum.

$1\,\text{ly} = 3 \times 10^{8}\,\text{m/s} \times 365.25 \times 24 \times 3600\,\text{s} \approx 9.46 \times 10^{15}\,\text{m}.$

Some distances.

• Sun to Earth: $\sim 8\,\text{light-minutes}$.
• Nearest star (Proxima Centauri): $\sim 4.2\,\text{ly}$.
• Across the Milky Way: $\sim 100{,}000\,\text{ly}$.
• To the nearest galaxy (Andromeda): $\sim 2.5\,\text{million ly}$.
• Edge of the observable universe: $\sim 13.8\,\text{billion ly}$ (limited by the age of the universe).

Looking back in time. Because light takes time to reach us, looking at distant objects is looking BACK in time. The light from Andromeda we see TODAY left it $2.5$ million years ago. That's why telescopes are time machines.

Redshift. Light from a galaxy moving AWAY from us is observed at a longer wavelength than emitted (shifted toward the red end of the spectrum).

Doppler effect for light. Source approaches → wavelength compressed (blue-shifted). Source recedes → wavelength stretched (red-shifted). Same idea as the pitch change in a passing siren.

Hubble's discovery. Light from almost ALL distant galaxies is redshifted, AND the further away a galaxy, the BIGGER the redshift. Conclusion: galaxies are moving away — and farther ones move FASTER.

$v \propto d$ (Hubble's law qualitative). This is exactly the pattern you'd see if the entire universe were expanding uniformly.

Expansion is of SPACE itself. Not galaxies flying through static space, but space stretching between them.

Worked qualitative. Why isn't the Andromeda galaxy redshifted? It's actually BLUESHIFTED — falling toward us. Local gravitational attraction overcomes the cosmic expansion at short distances.

The Big Bang theory. The universe started in an extremely hot, dense state $\sim 13.8\,\text{billion years}$ ago. Since then, space has been expanding and cooling, with matter clumping into stars and galaxies.

Evidence for the Big Bang.

1. Galactic redshift / Hubble's law. Galaxies are moving apart — and faster the further away. Run the expansion BACKWARDS: everything was once together.

2. Cosmic Microwave Background (CMB) radiation. A faint, almost uniform microwave glow filling the entire sky. Predicted by Big Bang theory: as the early hot universe expanded and cooled, the energetic photons were redshifted into microwaves we still detect today. Discovered 1964; near-perfect match to predictions.

3. Hydrogen and helium ratios. The Big Bang predicts about $75\%$ hydrogen and $25\%$ helium by mass, with traces of lithium. Observations match.

Order of evidence (strongest first). CMB, then redshift, then element ratios.

What's NOT explained. The Big Bang theory describes the universe's evolution but not what (if anything) caused it or what happened in the first $10^{-43}\,\text{s}$.

Cambridge tip. When asked about evidence, students often only give redshift. CMB is the more compelling piece — mention both for full marks.