Hubble's Law
Hubble's Law is the empirical observation that the recession velocity of a galaxy is directly proportional to its distance from the observer, expressed as v = H₀d, where H₀ is the Hubble constant. First published by Edwin Hubble in 1929 based on measurements of galaxy redshifts, it provided the first direct observational evidence for the expanding universe predicted by general relativity. The Hubble constant H₀, currently estimated at approximately 67–73 km/s/Mpc from different methods, also allows astronomers to estimate the age of the universe as roughly 1/H₀.
Key Formula
v = H₀ × d; Hubble time t_H = 1/H₀
LaTeX: v = H_0 \, d, \quad t_H = \frac{1}{H_0}
| Symbol | Meaning | Unit |
|---|---|---|
| v | Recession velocity | km/s |
| H₀ | Hubble constant | km/s/Mpc |
| d | Distance to galaxy | Mpc |
| t_H | Hubble time (approximate age of universe) | seconds (or Gyr) |
Worked Example
Problem
Using H₀ = 70 km/s/Mpc, estimate the Hubble time (approximate age of the universe) in years.
Solution
Step 1 – Convert H₀ to SI units: H₀ = 70 km/s/Mpc 1 Mpc = 3.086 × 10²² m H₀ = 70 × 10³ m/s / (3.086 × 10²² m) = 2.269 × 10⁻¹⁸ s⁻¹ Step 2 – Hubble time: t_H = 1/H₀ = 1 / (2.269 × 10⁻¹⁸ s⁻¹) = 4.407 × 10¹⁷ s Step 3 – Convert to years: t_H = 4.407 × 10¹⁷ s / (3.156 × 10⁷ s/yr) ≈ 1.40 × 10¹⁰ yr = 14.0 Gyr
Answer
Hubble time ≈ 14.0 billion years (close to the accepted age of 13.8 Gyr).
Hubble Constant Measurements from Different Methods
| Method | H₀ (km/s/Mpc) | Source | Year |
|---|---|---|---|
| CMB (Planck) | 67.4 ± 0.5 | Planck Collaboration | 2018 |
| Type Ia Supernovae | 73.2 ± 1.3 | Riess et al. (SH0ES) | 2022 |
| Strong Lensing (H0LiCOW) | 73.3 ± 1.7 | Wong et al. | 2020 |
| Tip of Red Giant Branch | 69.8 ± 1.9 | Freedman et al. | 2020 |
| Gravitational Waves | ~68 | LIGO/Virgo | 2021 |
Interactive Tools
Wikimedia Commons, CC BY-SA
Related Terms
Expanding Universe
The expanding universe is the observational discovery that the fabric of space itself is stretching over time, causing galaxies that are not gravitationally bound to each other to recede from one another at velocities proportional to their separating distances. First confirmed observationally by Edwin Hubble in 1929 through measurements of galaxy redshifts, this expansion is described by the Friedmann–Lemaître–Robertson–Walker (FLRW) metric in general relativity. The rate of expansion, parameterised by the Hubble constant H₀ ≈ 67–73 km/s/Mpc, has been measured to be accelerating due to dark energy.
Cosmological Redshift
Cosmological redshift is the increase in the wavelength of photons as they travel through an expanding universe, caused by the stretching of space itself rather than by the relative motion of source and observer (Doppler effect). Quantified by the redshift parameter z = (λ_observed − λ_emitted) / λ_emitted, it is directly related to the expansion factor of the universe: 1 + z = a(t_now) / a(t_emit). Cosmological redshift allows astronomers to determine the distance and lookback time to distant galaxies and serves as a primary tool for mapping the large-scale structure of the universe.
Big Bang Theory
The Big Bang Theory is the prevailing cosmological model describing the origin and evolution of the universe, proposing that all matter, energy, space, and time originated from an extremely hot, dense singularity approximately 13.8 billion years ago. The rapid expansion from this primordial state led to cooling, the formation of fundamental particles, and eventually atoms, stars, and galaxies. Evidence supporting this model includes the observed expansion of the universe, the cosmic microwave background radiation, and the abundance of light elements like hydrogen and helium.
Named after American astronomer Edwin Powell Hubble (1889–1953), who published the velocity-distance relationship in 1929. "Law" derives from Old English "lagu" (rule, regulation), reflecting an empirical regularity in nature. The relationship had been theoretically anticipated by Georges Lemaître in 1927.