Galaxy Recession Speed and Lookback Time

Hubble’s Law gives the recession velocity of a galaxy:

v = H₀ × d

For nearby galaxies (d « Hubble radius), this is a good approximation. For very distant galaxies, the full ΛCDM cosmological model is needed for accuracy.

Lookback time (simplified):

t_lookback ≈ d / c (for nearby galaxies, d « c/H₀)

For distant galaxies, the actual lookback time is shorter than d/c because the universe was expanding faster in the past, so the light had to travel “uphill” against expansion.

The Hubble radius (Hubble sphere):

d_Hubble = c / H₀ ≈ 14.5 Gly (gigalight-years, for H₀ = 67.4 km/s/Mpc)

Galaxies beyond this distance recede faster than the speed of light. This is not a violation of special relativity. Space itself is expanding, and nothing is moving through it faster than c. Two horizons get mixed up here, so it is worth separating them. The particle horizon, about 46.5 billion light-years out in comoving distance, is the edge of everything whose light has already had time to reach us. That is the observable universe, and it grows as time passes. The boundary past which light emitted today will never reach us is the cosmic event horizon, much closer at roughly 16 billion light-years comoving. Galaxies between the two are still visible, but the photons they are emitting right now will never arrive.

Why v > c is allowed in cosmology: Special relativity limits motion through space to v < c. Cosmic recession is not motion through space at all, it is the space between two points getting longer. The recession velocity v = H₀d is a coordinate velocity, not a proper velocity through spacetime.

Key distances:

• Andromeda (M31): 2.537 Mly, and blueshifted rather than receding. It is approaching us at about 110 km/s, because inside the Local Group gravity beats expansion
• Virgo Cluster: 53.8 Mly (megalight-years): recession v ≈ 1,155 km/s at H₀ = 70
• Coma Cluster: 320 Mly: v ≈ 6,868 km/s at H₀ = 70
• Most distant galaxy confirmed so far: JADES-GS-z14-0 at z ≈ 14.3, roughly 33 Gly comoving. We see it as it was about 290 million years after the Big Bang

That Andromeda line is the honest caveat on this whole page. Hubble’s law describes the average behaviour of the universe on scales where gravity has given up, which starts somewhere around 10 to 20 Mpc. Below that, a galaxy’s own motion through its cluster swamps the expansion signal. Virgo’s members scatter over roughly 1,500 km/s of peculiar velocity, which is more than the recession speed the law predicts for Virgo itself, so plugging a nearby galaxy in here gives you a number the sky will not confirm.