Physics › 🌌 Astrophysics & Space

The Expanding Universe

Every galaxy in the night sky is fleeing from us — and the pattern in that flight reveals the universe's birth, size, and age.

High school
💡
The big idea: In the 1920s, Edwin Hubble noticed that almost every galaxy's light is shifted toward the red end of the spectrum, and the farther away a galaxy is, the more its light is stretched. That single pattern — redshift growing with distance — is the observational backbone of the Big Bang picture: run the expansion backward in time and everything converges toward a single hot, dense beginning roughly 13.8 billion years ago.
🎯 By the end, you'll be able to
  • explain Hubble's law and use it to calculate a galaxy's recession velocity from its distance
  • describe what redshift is and how it's measured from shifted spectral lines
  • estimate the age of the universe from the Hubble constant and explain why that estimate is only approximate
  • explain why cosmic expansion has no center — it's space itself stretching, not galaxies flying through a fixed space
📎 You should already know
  • Waves: wavelength, frequency, and the wave speed equation
  • Basic rates (distance = speed × time) and unit conversion
  • Reading and rearranging simple algebraic formulas

Every Galaxy Is Running Away From Us

In 1929, astronomer Edwin Hubble compared two things for a set of distant galaxies: how far away each one was, and how fast its light suggested it was moving. Almost every galaxy he checked was moving away from us — and that was strange enough on its own. But the deeper pattern was even stranger: the farther a galaxy sat, the faster it appeared to recede. A galaxy twice as distant was moving away roughly twice as fast. That simple, repeatable relationship turned out to be one of the most important discoveries in the history of science.

🔑 Hubble's Law: distance sets the pace of recession

Hubble's observation is now a law: recession velocity is proportional to distance. This isn't galaxies flying like cannonballs through empty, unchanging space. It's space itself stretching — and every galaxy is carried along for the ride, the way two dots drawn on a balloon drift apart as you inflate it. Nothing is moving through space in the usual sense; the space between things is growing.

\[ v = H_0 d \]
v is a galaxy's recession velocity, d is its distance, and \(H_0\) is the Hubble constant — currently measured at roughly 70 km/s per megaparsec (1 megaparsec ≈ 3.26 million light-years).

What Redshift Actually Measures

You've heard how an ambulance siren drops in pitch as it speeds away — the sound waves get stretched out behind it. Light does something similar. When a galaxy recedes, the wavelengths of light it emits get stretched longer as they travel to us, shifting toward the red end of the spectrum. Astronomers spot this by comparing where a familiar spectral line (say, a specific hydrogen line) should sit in the lab versus where it actually shows up in a galaxy's spectrum.

At the cosmic scale, it isn't quite the ordinary Doppler effect of something moving through space — it's the stretching of space itself carrying the light's wavelength along with it. But for nearby galaxies, the math works out the same way, which makes it a useful and intuitive first approximation.

\[ z = \dfrac{\Delta \lambda}{\lambda} \approx \dfrac{v}{c} \]
z is the redshift, \(\Delta \lambda\) is how much the wavelength shifted, \(\lambda\) is the original (lab) wavelength, and c is the speed of light. This approximation holds well when \(z\) is small (nearby galaxies, slow recession).
\[ t \approx \dfrac{1}{H_0} \]
Flip Hubble's law around and you get a rough age for the universe. With \(H_0 \approx 70\) km/s/Mpc, \(1/H_0 \approx 14\) billion years — strikingly close to the universe's measured age of about 13.8 billion years, found independently from the cosmic microwave background.
🎮 Interactive: Doppler Shift and Cosmic Redshift LIVE
Adjust the source's velocity and watch the wavelength stretch or compress. This is the same underlying physics — waves stretching when their source recedes — that lets astronomers turn a shifted spectral line into a recession velocity.

Winding the Clock Backward: The Big Bang

If every galaxy is moving apart from every other galaxy today, then rewinding the film means everything was closer together in the past — and closer still before that. Run it all the way back, and matter, energy, space, and time appear to converge toward an extremely hot, dense state roughly 13.8 billion years ago. That beginning is what we call the Big Bang: not an explosion happening at one point within space, but the start of space and time expanding everywhere at once.

The scale involved is hard to picture: due to that ongoing expansion, the region of universe we can observe today spans roughly 93 billion light-years across, even though light has only had 13.8 billion years to travel — space itself stretched out while the light was in transit.

📝 Worked example: A galaxy is measured to be 100 megaparsecs (Mpc) away. Using a Hubble constant of \(H_0 = 70\) km/s/Mpc, find its recession velocity.
  1. Start with Hubble's law: \( v = H_0 d \)
  2. Substitute the values: \( v = (70 \text{ km/s/Mpc}) \times (100 \text{ Mpc}) \)
  3. The Mpc units cancel, leaving: \( v = 7000 \) km/s
✓ v ≈ 7,000 km/s — about 4,350 miles every second.
📝 Worked example: A distant galaxy's hydrogen spectral line, normally at 656.3 nm in the lab, is observed at 661.2 nm. Find (a) the redshift z, (b) the recession velocity, and (c) the approximate distance, using \(H_0 = 70\) km/s/Mpc.
  1. Find the wavelength shift: \( \Delta\lambda = 661.2 - 656.3 = 4.9 \) nm
  2. Calculate the redshift: \( z = \dfrac{\Delta\lambda}{\lambda} = \dfrac{4.9}{656.3} \approx 0.00747 \)
  3. Since \(z\) is small, estimate velocity with \( v \approx cz \): \( v \approx (3\times10^5 \text{ km/s})(0.00747) \approx 2240 \) km/s
  4. Use Hubble's law to solve for distance: \( d = \dfrac{v}{H_0} = \dfrac{2240}{70} \approx 32 \) Mpc
✓ z ≈ 0.00747, v ≈ 2,240 km/s, and the galaxy is roughly 32 Mpc away — about 104 million light-years.
⚠️ Two traps worth avoiding

Trap 1: Cosmological redshift isn't quite the same as an object physically speeding away through fixed space — it's the stretching of space itself carrying the light along with it. The \(v \approx cz\) shortcut is a good approximation for nearby galaxies, but it breaks down at very large distances and redshifts, where the full picture needs general relativity.

Trap 2: It's tempting to think Earth sits at the center of the expansion, since everything seems to move away from us specifically. It doesn't. Expansion happens everywhere at once — an observer in any other galaxy would see exactly the same pattern, with every other galaxy receding from them. There is no center.

Check your understanding

1. According to Hubble's Law, a distant galaxy's recession velocity is proportional to what?
Hubble's law is \( v = H_0 d \): recession velocity scales directly with distance, not mass, temperature, or spin.
2. Using Hubble's law with \(H_0 = 70\) km/s/Mpc, what is the recession velocity of a galaxy 150 Mpc away?
\( v = H_0 d = (70 \text{ km/s/Mpc})(150 \text{ Mpc}) = 10{,}500 \) km/s.
3. A galaxy's spectral lines are shifted toward longer (redder) wavelengths. What does this redshift most directly indicate?
A shift toward longer wavelengths — redshift — is the signature of recession: the space the light travels through is stretching, stretching the light's wavelength along with it.
4. Why do astronomers say cosmic expansion has no 'center,' even though every distant galaxy appears to be moving away from Earth?
Expansion happens everywhere in space simultaneously, like dots on an inflating balloon spreading apart. Every location sees the same pattern, so no point is a special 'center.'
✅ Key takeaways
  • Hubble's Law (v = H₀d) says recession velocity grows linearly with distance, with H₀ ≈ 70 km/s per megaparsec.
  • Redshift (z = Δλ/λ ≈ v/c) is how astronomers measure recession: a galaxy's light stretches toward longer wavelengths as the space it travels through expands.
  • Running the expansion backward in time points to a hot, dense beginning — the Big Bang — roughly 13.8 billion years ago; 1/H₀ gives a rough, matching age estimate.
  • Expansion has no center: every location in the universe would see the same pattern of galaxies receding, because space itself is stretching everywhere at once.