Hubble's Law
Hubble's law (v=H0*d) relates a galaxy's recession velocity to its distance.
The foundation of the expanding universe model and Big Bang cosmology.
The Formula
v = H₀ × d
Hubble's law states that distant galaxies move away from us at speeds proportional to their distance. The farther away a galaxy is, the faster it recedes. This is key evidence for the expanding universe.
Variables
| Symbol | Meaning |
|---|---|
| v | Recession velocity of the galaxy (km/s) |
| H₀ | Hubble constant (approximately 70 km/s per Megaparsec) |
| d | Distance to the galaxy (Megaparsecs, where 1 Mpc ≈ 3.26 million light-years) |
Example 1
A galaxy is 100 Mpc away. How fast is it receding?
v = 70 km/s/Mpc × 100 Mpc
v = 7,000 km/s
Example 2
A galaxy has a recession velocity of 21,000 km/s. How far away is it?
d = v / H₀ = 21,000 / 70
d = 300 Mpc ≈ 978 million light-years
When to Use It
Use Hubble's law when:
- Estimating distances to faraway galaxies using their redshift
- Calculating the recession speed of distant objects
- Estimating the age of the universe (1/H₀)
- Studying the rate of expansion of the universe
Limitations
- The Hubble constant H₀ is not precisely known — current measurements range from ~67 to ~73 km/s/Mpc depending on the method used, a discrepancy known as the "Hubble tension"
- Recession velocities derived from Hubble's law can exceed the speed of light for very distant galaxies — this is not a violation of relativity because it is space itself expanding, not objects moving through space
- Hubble's law assumes a uniform, linear expansion and breaks down in galaxy clusters (where gravity dominates) and at cosmological distances where dark energy becomes significant
Key Notes
- Formula: v = H₀ × d: Recession velocity v equals the Hubble constant H₀ times the distance d. H₀ ≈ 67–73 km/s/Mpc (there is ongoing debate about the exact value — the "Hubble tension"). A galaxy 100 Mpc away recedes at roughly 7,000 km/s.
- Evidence for the expanding universe: Galaxies show redshifted spectra proportional to their distance — the farther, the faster they recede. This is not objects flying through space; rather, space itself is expanding, carrying galaxies apart.
- Hubble time: 1/H₀ ≈ 14 billion years: The inverse of H₀ gives an approximate age of the universe (exact age requires the full cosmological model). Current best estimate from CMB data: 13.8 billion years — close to the Hubble time.
- Hubble constant uncertainty — the "Hubble tension": Measurements from the early universe (CMB) give H₀ ≈ 67 km/s/Mpc; measurements from the local universe (Cepheids, supernovae) give ≈ 73 km/s/Mpc. This 5-σ discrepancy is one of modern cosmology's major unsolved problems.
- Applications: Hubble's law is used to estimate galaxy distances from redshift measurements, determine the age and size of the observable universe, study large-scale structure formation, and calibrate the cosmic distance ladder.