Galaxy Recession Speed and Lookback Time
Calculate how fast a galaxy is receding and estimate its lookback time from its distance.
Includes superluminal recession check.
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 ≈ 14.4 Gly (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 — it is space itself expanding. Light from galaxies beyond ~46 billion light-years (the particle horizon) can never reach us.
Why v > c is allowed in cosmology: Special relativity limits motion through space to v < c. But cosmic recession is due to the expansion of space — there is no “motion” through a medium. The recession velocity v = H₀d is a coordinate velocity, not a proper velocity through spacetime.
Key distances:
- Andromeda (M31): 2.537 Mly: blueshifted, approaching!
- Virgo Cluster: 53.8 Mly: recession v ≈ 1,170 km/s
- Coma Cluster: 320 Mly: v ≈ 6,960 km/s
- Most distant galaxy (observed): ~33 Gly comoving distance (z ≈ 13+)
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