Empirical cosmological relation
Hubble-
Lemaitre Law
On sufficiently large, nearby cosmological scales, a galaxy's recession velocity is approximately proportional to its distance. The relation turned scattered redshifts and distance estimates into evidence for an evolving universe.
Build a nearby-universe observation.
Choose a galaxy distance, a value for the present-day Hubble constant, and a local peculiar velocity. The model separates smooth cosmological recession from motion caused by nearby structure.
At this distance, local motion adds scatter but the large-scale expansion signal dominates.
A proportional law with a carefully defined domain.
For galaxies participating in the smooth large-scale expansion and at sufficiently low redshift, the recession velocity v is approximately the present Hubble constant H0 multiplied by proper distance d. NASA summarizes the relation as V = H0 x d.[4]
The unit is part of the insight. A value near 70 km/s/Mpc says that each additional megaparsec of separation corresponds, in the local linear approximation, to roughly 70 km/s more recession velocity. It is not a speed assigned to one universal boundary.
"The farther the galaxy, the larger the recession signal - but the straight line is a local window into a much richer cosmic history."
No center is required inside the model.
In a homogeneous expanding model, distances between unbound, comoving galaxies grow with the cosmic scale factor. Every such observer sees distant galaxies receding, with more distant galaxies separating faster. This does not select Earth as the center.
Move cosmic time. The grid expands while each galaxy keeps its comoving address.
Redshift alone is not the law.
A Hubble diagram needs two independently constructed axes. Spectroscopy supplies redshift. Standard candles, geometric anchors, or other distance indicators supply distance. The slope emerges only after those measurements are paired.
Parallax and geometric anchors calibrate nearby distances.
Period-luminosity behavior transfers the scale to nearby galaxies.
Bright standardized events extend the ladder into the Hubble flow.
NASA describes the distance ladder as a linked sequence in which each measurement technique calibrates the next.[6] This dependence is powerful but makes systematic error control central.
Theory, spectra, distances, and recognition.
The discovery was not one isolated observation by one person. It depended on general relativity, solutions for a dynamic universe, galaxy spectra, stellar distance indicators, and the eventual velocity-distance plot.
Vesto Slipher measures large radial velocities for spiral nebulae, providing much of the redshift evidence later reused.
Alexander Friedmann publishes expanding and contracting solutions to Einstein's field equations.
Georges Lemaitre derives an expanding model, connects it to observations, and estimates the proportionality between distance and velocity.[1]
Edwin Hubble publishes a distance-velocity relation for extragalactic nebulae using available distances and radial velocities.[2]
IAU members approve a resolution recommending the term Hubble-Lemaitre law to recognize both theoretical and observational contributions.[3]
The straight line is the nearby approximation.
The compact equation works best when redshift is small enough that velocity can be treated approximately as cz and when peculiar velocities are modest compared with the Hubble flow. Nearby galaxies can deviate strongly because local gravitational motion is a large fraction of their observed velocity.
Andromeda is approaching the Milky Way despite cosmic expansion. The linear law is not a command applied to every galaxy.
Averaging across many galaxies reveals an approximately proportional trend with scatter.
Distance definitions diverge, H changes with time, and recession cannot be reduced to the low-z Doppler approximation.
The Hubble parameter is the fractional rate of change of the scale factor. H0 is its value at the present epoch.
Two precise routes do not land on the same H0.
The Hubble tension compares a local, late-universe distance-ladder measurement with an early-universe inference from the cosmic microwave background under the standard flat Lambda-CDM model. It is not simply two telescopes timing the same galaxy.
km/s/Mpc
km/s/Mpc
Planck reported H0 = 67.4 +/- 0.5 km/s/Mpc within base Lambda-CDM.[7] The 2022 SH0ES analysis reported 73.04 +/- 1.04 km/s/Mpc from its Cepheid-supernova distance ladder.[8] NASA reported in 2024 that Webb observations supported the reliability of Hubble's Cepheid measurements while the puzzle persisted.[9]
A calibration, population, selection, or modeling effect remains underestimated.
New early-universe physics or another extension changes the inference bridge.
Several smaller issues may contribute rather than one dramatic failure.
What the law does not say.
"Earth is at the center."
A homogeneous expansion produces the same large-scale relation for every comoving observer.
"Everything expands."
Bound systems resist cosmological expansion through gravity or other forces.
"Redshift is always ordinary Doppler motion."
Cosmological redshift is associated with light propagating through an evolving spacetime geometry.
"H0 is known exactly."
Its measured or inferred value depends on evidence, calibration, uncertainty, and cosmological assumptions.
"v = H0d works at every redshift."
The simple velocity interpretation is a low-redshift approximation; full cosmology is nonlinear.
"Hubble worked alone."
The result combined theoretical and observational contributions from multiple researchers.
Sources and further reading.
Original papers, official scientific organizations, mission results, and peer-reviewed analyses are prioritized.
- Georges Lemaitre (1927) - A Homogeneous Universe of Constant Mass and Increasing RadiusFaithful translation with editorial history and analysis of Lemaitre's theoretical and observational synthesis.arxiv.org/abs/1305.6470
- Edwin Hubble (1929) - A Relation Between Distance and Radial Velocity Among Extra-Galactic NebulaeThe original PNAS paper presenting the observational distance-velocity relation.doi.org/10.1073/pnas.15.3.168
- International Astronomical Union - Resolution B4 documentationOfficial documentation for recommending the name Hubble-Lemaitre law.iau.org/static/archives/announcements/pdf/ann18048a.pdf
- NASA Science - Hubble GlossaryOfficial concise definition of Hubble's Law, its variables, and related observational terms.science.nasa.gov/mission/hubble/multimedia/hubble-glossary/
- NASA Science - Cosmological RedshiftExplanation of wavelength stretching, spectra, distance, and expansion observations.science.nasa.gov/mission/hubble/science/science-behind-the-discoveries/hubble-cosmological-redshift/
- NASA Science - Three Steps to Measuring the Hubble ConstantOfficial overview of the geometric, Cepheid, and supernova distance-ladder sequence.science.nasa.gov/asset/hubble/three-steps-to-measuring-the-hubble-constant/
- Planck Collaboration (2020) - Planck 2018 Results VI: Cosmological ParametersFinal Planck cosmological parameter analysis, including the base Lambda-CDM inference H0 = 67.4 +/- 0.5 km/s/Mpc.doi.org/10.1051/0004-6361/201833910
- Riess et al. (2022) - A Comprehensive Measurement of the Local Value of H0SH0ES distance-ladder analysis reporting H0 = 73.04 +/- 1.04 km/s/Mpc.arxiv.org/abs/2112.04510
- NASA Science (2024) - Webb and Hubble Affirm Expansion-Rate MeasurementsWebb cross-check of Cepheid measurements and NASA's account of the continuing Hubble tension.science.nasa.gov/missions/webb/...expansion-rate-puzzle-persists/
- ESA - Galaxies and the Expanding UniverseEducational overview distinguishing expanding space, galaxy recession, redshift, and the use of Hubble's relation.sci.esa.int/web/education/-/36827-galaxies-and-the-expanding-universe