Galaxy Recession Velocities vs Distance

What does this graph show? Every dot is a galaxy. Its position along the x-axis tells you how far away it is; its height on the y-axis tells you how fast it is moving away from us. The further away a galaxy is, the faster it recedes — that relationship is Hubble's Law.

The orange dots (Hubble 1929) are the 24 galaxies Edwin Hubble measured in his original 1929 paper. They only reach about 2 Mpc — roughly the edge of our Local Group. Slide the x-clip right to see how tiny his sample was compared to the modern dataset.

Why was Hubble's H₀ so wrong? Hubble measured distances using Cepheid variable stars as "standard candles". His calibration was off by a factor of roughly 7 — the period–luminosity relationship he used had a systematic error. This made all his distances too small, pushing his H₀ up to ~500 km/s/Mpc. Modern measurements give H₀ ≈ 67–73 km/s/Mpc.

What are the blue-shifted galaxies? A small number of points sit below the zero line (v < 0) — they are moving towards us. These are gravitationally bound members of the Local Group (e.g. the Andromeda galaxy, M31). At short distances, random peculiar velocities swamp the Hubble flow.

Specification link: Cambridge A-level Physics 9702, topic 20 (cosmology) — Hubble's Law, v = H₀d, recession of galaxies, evidence for the Big Bang.

Suggested classroom sequence. Start with the slider fully left (Hubble 1929 only, x-clip at ~2.5 Mpc). Ask students what they notice. Then reveal the H₀ line — they should see Hubble's steep slope. Drag x-clip out to 150 Mpc, then slowly reveal modern data with the reveal slider. The H₀ readout in the header updates live as the slope flattens toward the modern value.

Key misconception to address. Students often assume that because Hubble's conclusion (the universe is expanding) was correct, his H₀ value must also be roughly right. This is a good opportunity to discuss how systematic calibration errors can preserve a qualitative result while corrupting a quantitative one — and why scientific constants get revised over decades rather than converging immediately.

The scatter at low distances is worth dwelling on. Below ~30 Mpc, peculiar velocities (galaxies' own gravitational motions within clusters) are comparable to the Hubble flow velocity. This is why Hubble's sample, confined to the Local Group, gave such a noisy and misleading slope. The Hubble Law only reliably emerges at larger distances — a nice illustration of why sample size and range matter in data collection.

The "Hubble tension" is a live research problem. H₀ measured from the early universe (CMB, Planck: ~67 km/s/Mpc) disagrees with H₀ measured from local distance ladders (Cepheids + Type Ia supernovae: ~73 km/s/Mpc) at ~5σ significance. This dataset gives H₀ ≈ 64 km/s/Mpc, consistent with the CMB value. Worth mentioning as an example of an unresolved tension at the frontier of physics.

Extension question. Why does the scatter decrease as you zoom out (increase x-clip)? What does this tell us about the relationship between peculiar velocity and Hubble flow at large distances?