Astronomy 2e · Galaxies
The Expanding Universe
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In 30 seconds
In 1929, Edwin Hubble announced a result that reshaped astronomy: galaxies are receding from us at speeds proportional to their distances. A galaxy twice as far away recedes twice as fast. This velocity–distance relation, now called Hubble's law v = H₀d: recession velocity proportional to distance Full entry →,
v = H₀ × d
(where v is Recession velocity Speed at which a galaxy moves away due to expansion Full entry →, d is distance, and H₀ is the Hubble constant), is the observational foundation of modern cosmology. It means the universe itself is expanding — not galaxies hurling through space like shrapnel, but space stretching and carrying the galaxies apart with it.
This topic walks through what the law says, the evidence behind it, what it implies about the past (a universe that was once tiny and hot — the Big Bang, Chapter 29), and the limits of the simple version you learn first.
Why this matters
The expanding universe is the bridge between the study of galaxies (this chapter) and the origin of everything (the Big Bang chapter). It gives you:
- A way to measure cosmic distances: redshift → recession velocity → distance, the top rung of the extragalactic distance ladder built in the previous topic.
- A way to measure the age of the universe: if expansion is running backward in time, the rate tells you when everything was together.
- A way to see the past: because distance means Lookback time How far in the past we see an object at distance d Full entry →, deep observations reveal a younger universe — the central idea of Chapter 28.
Exam questions on this topic almost always test the same core moves: compute a recession velocity or distance from Hubble's law, interpret a redshift, and explain why "expansion" is not "motion through space."
The college version
Core Concepts
Redshift as a measure of recession
When a source of light moves away from you, its wavelengths stretch: lines in its spectrum shift toward the red. The redshift z is defined as the fractional change in wavelength:
z = Δλ / λ
For galaxies that are not too far away, the recession velocity is approximately v ≈ c × z (c = speed of light). A galaxy with z = 0.05 is receding at about 5% of the speed of light, or ~15,000 km/s. Astronomers measure z by matching observed spectral lines (hydrogen Balmer lines, calcium H and K lines) to their laboratory wavelengths.
Hubble's law: velocity proportional to distance
The key relationship, confirmed by Hubble and refined ever since:
v = H₀ × d
The Hubble constant H₀ has units of velocity per distance, commonly written km/s per Mpc (1 Mpc ≈ 3.26 million light-years). A commonly taught reference value is H₀ ≈ 70 km/s/Mpc; modern measurements cluster near 67–74 km/s/Mpc, and the gap between different measuring techniques (the "Hubble tension") is an active research topic. At 100 Mpc, a galaxy recedes at about 7,000 km/s; at 200 Mpc, about 14,000 km/s. The plot of velocity versus distance — the Hubble diagram Plot of recession velocity vs. distance Full entry → — is a straight line whose slope is H₀.
Hubble's original value was near 500 km/s/Mpc — far too high, because the Cepheid-based distances he used were badly underestimated. Correcting the distance scale lowered H₀ and raised the implied age of the universe.
Expansion of space, not motion through space
The classic raisin-bread analogy: as dough rises, every raisin moves away from every other raisin, and the farther apart two raisins are, the faster they separate — yet no raisin is the "center." In our universe, galaxies are the raisins and space is the dough. Two consequences worth internalizing:
- There is no center (and no edge) to the expansion. Every galaxy sees the same pattern of recession.
- Expansion is not universal on small scales. Where gravity is strong enough — inside the Local Group, for instance — bound systems resist the stretch. The Andromeda Galaxy, our close neighbor, is approaching us, not receding.
The Hubble time and the age of the universe
Run the expansion backward: if the rate were constant, the time since everything was in one place would be the Hubble time 1/H₀ ≈ 14 billion years; the age if expansion were constant Full entry →, t_H = 1/H₀. With H₀ ≈ 70 km/s/Mpc this works out to roughly 14 billion years (a commonly taught figure; verify against current sources). The actual age of the universe, about 13.8 billion years (also a commonly taught reference value), is close but not identical, because gravity slowed the early expansion and dark energy has since accelerated it. The expansion history is more interesting than a single number — that history is the subject of the Big Bang chapter.
Lookback time: the universe as a time machine
Because light takes time to travel, a galaxy at a distance of 1 billion light-years is seen as it was 1 billion years ago. The deeper we look, the younger the universe we see. This single idea — distance equals time — connects everything in this topic to the galaxy-evolution story of Chapter 28.
Common Confusions
| Do Not Confuse | With | Difference |
|---|---|---|
| Expansion = galaxies moving through space | Space itself stretching | Galaxies are carried by expanding space; no "motion through" an absolute frame |
| We are at the center (everything recedes from us) | The universe expanding everywhere | Every observer sees the same recession pattern — no galaxy is special |
| H₀ is a constant velocity | H₀ is a rate per unit distance | Units are km/s/Mpc, not km/s; velocity grows with distance |
| Any redshift is a Doppler shift from motion | Cosmological redshift from expansion | Light's wavelength stretches while traveling through expanding space |
| The universe expands "into" something | Space expanding with no outside | The balloon/raisin analogies have no edge and no exterior |
| Every galaxy recedes | Bound systems like the Local Group | Where gravity dominates, systems stay put — Andromeda approaches us |
| v = c·z works at any redshift | Only for z ≪ 1 | At high z (Chapter 29) you need relativistic corrections |
Eli explains
The same idea, in plain words
Explain it like I’m 10
Imagine dots painted on a balloon. When you blow the balloon up, every dot moves away from every other dot, and dots that start far apart move apart the fastest — but no dot is the "center." That's our universe: space itself is stretching, carrying galaxies along. By measuring how fast galaxies fly apart, astronomers can run the movie backward and figure out how long ago everything was packed together — about 14 billion years.
Worked example
Suppose a galaxy's spectrum shows the hydrogen-alpha line — rest wavelength 656.3 nm — at an observed wavelength of 672.7 nm.
Step 1 — redshift: z = (672.7 − 656.3) / 656.3 = 16.4 / 656.3 ≈ 0.025.
Step 2 — velocity: v ≈ c × z = 300,000 km/s × 0.025 = 7,500 km/s.
Step 3 — distance: d = v / H₀ = 7,500 / 70 ≈ 107 Mpc, or about 350 million light-years.
Step 4 — age estimate: 1/H₀ = 1 / (70 km/s/Mpc). A quick unit conversion gives ≈ 14 billion years — a first, crude answer to "how old is the universe?" Notice that the same spectrum that told us the distance also told us we are looking 350 million years into the past.
Key takeaways
- Hubble's law: v = H₀ × d. The slope of the Hubble diagram is H₀ ≈ 70 km/s/Mpc (commonly taught reference value).
- Redshift z = Δλ/λ, with v ≈ c·z for small z; z = 0.05 → ~15,000 km/s.
- Expansion = stretching of space, not motion through space: no center, no edge; bound systems (Local Group) do not expand.
- Hubble time t_H = 1/H₀ ≈ 14 billion years; the universe's actual age is ~13.8 billion years (commonly taught values).
- Hubble's original H₀ was far too large because his Cepheid distances were wrong — a classic lesson in distance-scale errors.
- Distant galaxies are seen as they were long ago (lookback time) — the key to galaxy evolution studies.
Check yourself
6 review questions from the chapter. Try each one, then open the answer.
A galaxy is 200 Mpc away. Using H₀ = 70 km/s/Mpc, how fast is it receding?
Show answer
v = H₀d = 70 × 200 = 14,000 km/s.
A spectrum shows z = 0.10. Roughly what is the recession velocity, and why is the simple formula only an approximation here?
Show answer
v ≈ c × z = 30,000 km/s (10% of light speed). The approximation v = cz is valid only for small z; at z = 0.10 it's still roughly usable, but for large redshifts the relativistic form must be used.
Why is the Andromeda Galaxy approaching us instead of receding?
Show answer
Andromeda is part of the Local Group, a gravitationally bound system; expansion is overcome locally by gravity.
What is the Hubble time, and how does it relate to the actual age of the universe?
Show answer
t_H = 1/H₀ ≈ 14 billion years — the age if expansion had always run at today's rate. The actual age (~13.8 billion years, a commonly taught value) differs because gravity decelerated early expansion and dark energy later accelerated it.
Why was Hubble's original value of H₀ so much larger than today's value?
Show answer
His Cepheid-based distances were systematically too small, which made H₀ (velocity/distance) come out far too large.
What does it mean to say a galaxy at z ≈ 1 is seen "as it was" 7+ billion years ago?
Show answer
Light left that galaxy over 7 billion years ago, so we see it as it was then — lookback time means deep observations are snapshots of the young universe.
Study tools & related lessonsKey vocabulary · Related
Key vocabulary
- Hubble's law
- v = H₀d: recession velocity proportional to distance
- Hubble constant (H₀)
- Rate of expansion, ~70 km/s per Mpc (commonly taught)
- Redshift (z)
- Fractional stretch of wavelengths, Δλ/λ
- Recession velocity
- Speed at which a galaxy moves away due to expansion
- Megaparsec (Mpc)
- 1 million parsecs ≈ 3.26 million light-years
- Hubble time
- 1/H₀ ≈ 14 billion years; the age if expansion were constant
- Lookback time
- How far in the past we see an object at distance d
- Hubble diagram
- Plot of recession velocity vs. distance
Sources & references
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