Redshift Lab

Every element absorbs and emits light only at its own wavelengths. The game uses the laboratory (rest) wavelengths of hydrogen, helium, calcium, magnesium and sodium from the NIST Atomic Spectra Database, in air, as astronomers use them. When a galaxy moves away, every wavelength is stretched by the same factor, 1 + z, so a line at 656.3 nm moves farther in nanometers than one at 393.4 nm. The redshift is z = (observed − rest) / rest, and for small z the speed is v = cz, with c = 299,792.458 km/s. The spectra you match are drawn by the game at each galaxy's catalog redshift from the NASA/IPAC Extragalactic Database; the line depths and noise are illustrative, not real observations.

v = cz is an approximation that only works for nearby galaxies, below z of about 0.1. At larger distances the redshift measures how much the universe has expanded while the light traveled (1 + z is the ratio of its size now to its size then), and v = cz would give speeds above the speed of light for the galaxies the James Webb Space Telescope sees at z above 10. Andromeda's 300 km/s approach, first measured by Vesto Slipher in 1913, is relative to the Sun; most of it comes from the Sun's own orbit around the Milky Way, and Andromeda approaches the Milky Way's center at about 110 km/s (more on the coming collision).

The Hubble diagram uses the six galaxies of the Megamaser Cosmology Project (Pesce et al. 2020). Their distances are pure geometry, from water masers orbiting each galaxy's central black hole, with no Cepheid stars or supernovae, and their velocities are corrected for our motion through the cosmic microwave background. A plain least-squares line through the origin gives about 75.6 km/s per megaparsec; the team's full analysis, which weighs each distance by its uncertainty and adds 250 km/s of uncertainty to every velocity for the galaxies' own random motions, gives 73.9 ± 3.0. Lemaître in 1927 and Hubble in 1929 found about 500 to 625 with the poor distances of their day.

Running the expansion backward at constant speed gives the Hubble time, 1/H₀ (977.8 divided by H₀ in km/s per megaparsec, in billions of years). The real age is a little different because gravity slowed the expansion for billions of years and dark energy now speeds it up: the Planck 2018 model gives 13.787 ± 0.020 billion years with H₀ = 67.4 ± 0.5, while the SH0ES distance ladder measures 73.04 ± 1.04. That 5-sigma gap is the Hubble tension, and nobody yet knows its cause.