Formula & Calculator
Hubble's Law
Relates a galaxy's recession velocity to its distance from us due to cosmic expansion.
Interpretation
v = H₀d. The recessional velocity of a galaxy is proportional to its distance. Supports expanding Universe. Used to determine cosmic distances and scale.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| v | Recession velocity | km/s |
| H₀ | Hubble constant | km/s/Mpc |
| d | Distance | Mpc |
What it means
Hubble’s law states that galaxies are receding from us with a velocity (v) proportional to their distance (d), with the constant of proportionality H₀ (Hubble constant). This was the first observational evidence for the expansion of the Universe. It is used to estimate distances to faraway galaxies (using redshift as a proxy for velocity). The Hubble constant is a key parameter in cosmology, influencing the age, size, and fate of the Universe. The law has been refined with more precise measurements and is fundamental to the ΛCDM model. Understanding Hubble’s law is essential for interpreting cosmological observations, for studying galaxy evolution, and for understanding the expansion history of the cosmos.
Worked example
Hubble's Law – Two Detailed Examples
Real‑World| Parameter | Value |
|---|---|
| H₀ (km/s/Mpc) | 67.4 |
| d (Mpc) | 100 |
| Parameter | Value |
|---|---|
| H₀ | 67.4 |
| d | 1500 |
Common mistakes
- Hubble’s law: Recession velocity v = H₀ × d – valid for distant galaxies in the expanding universe.
- Units: H₀ in km/s/Mpc, d in Mpc → v in km/s.
- H₀ value: ~70 km/s/Mpc (current best estimate) – not constant over time.
- Peculiar motion: Nearby galaxies may have random motions that dominate – Hubble’s law applies to large distances.
- Cosmological redshift: v is the recession velocity – not a true space velocity.
Applications
Hubble's law, v = H₀d, states that galaxies recede from us at a speed proportional to their distance, with the Hubble constant H₀ as the proportionality factor. This is the observational basis for the expanding universe and the Big Bang theory. Astronomers use it to measure cosmic distances, to map the large‑scale structure, and to study dark energy. By measuring redshift and distance, the expansion history of the universe can be determined. Hubble's law also allows the estimation of the age of the universe (Hubble time). This relation is essential for cosmology, guiding the interpretation of galaxy surveys and the cosmic microwave background. Understanding Hubble's law is fundamental to modern cosmology.
- Cosmic distance ladder and determination of extragalactic distances
- Study of the expansion rate and dark energy
- Derivation of the age and size of the observable universe
- Interpretation of galaxy redshift surveys
- Calibration of standard candles (e.g., supernovae)
Frequently Asked Questions
v = H₀ d. It states that a galaxy's recession velocity (v) is proportional to its distance (d) from us, with the proportionality constant being the Hubble constant (H₀). This was the first strong evidence for an expanding universe.
H₀ is the current rate of expansion of the universe. Its value is about 70 km/s/Mpc (with uncertainties). The units mean that for every megaparsec (≈ 3.26 million light‑years) of distance, a galaxy recedes at 70 km/s. It can also be expressed in inverse time (s⁻¹).
By measuring the redshift (and thus the recession velocity) of a galaxy, we can compute its distance as d = v / H₀. This is the primary method for determining distances to remote galaxies, forming the basis of the cosmic distance ladder.
The Hubble time is t_H = 1/H₀. With H₀ ≈ 70 km/s/Mpc, t_H ≈ 14 billion years. This is an estimate of the age of the universe if the expansion had been constant. The actual age is about 13.8 billion years, because the expansion rate has changed over time.
Hubble's Law describes the local expansion and the recession of galaxies. The CMB is the residual radiation from the early universe, providing a snapshot of the universe at recombination (about 380,000 years after the Big Bang). Together, they form pillars of the Big Bang model.
H is not constant; it changes with time. In the early universe, H was much larger (the universe expanded faster). The current value, H₀, is the value today. Its evolution depends on the cosmological model (matter, radiation, dark energy).
Observations of distant supernovae show that the expansion is accelerating, driven by dark energy. Hubble's Law is a linear approximation valid for relatively nearby galaxies. At large distances, the relationship between redshift and distance is more complex; the Hubble constant is the local slope of the expansion.
For very nearby galaxies, the recession velocity from cosmic expansion is small and may be overwhelmed by peculiar velocities (motions due to local gravitational interactions). Thus, Hubble's Law is only reliable for distances where the expansion velocity dominates (typically beyond a few tens of Mpc).
If the universe is expanding, then galaxies must have been closer together in the past. Extrapolating backwards leads to a hot, dense state – the Big Bang. This was a paradigm shift, moving cosmology from a static universe model to an evolving one.
The Hubble parameter H(t) is the value of the expansion rate at any cosmic time. The Hubble constant H₀ is its value today. In cosmological models, H(t) evolves with the scale factor, while H₀ is the single number we measure.