Hubble’s Law and Cosmic Expansion Study Pack

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Last updated May 21, 2026

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Hubble’s Law and Cosmic Expansion Study Guide

Trace the expanding universe from Hubble's foundational equation — v = H₀ × d — through the redshift evidence, the Hubble constant's measurement, and the role of dark energy in accelerating expansion. This pack clarifies why space itself stretches rather than galaxies moving outward, and how tracing expansion backward points to the Big Bang roughly 13.8 billion years ago.

Key Takeaways

  • •Hubble's Law states that a galaxy's recession velocity is directly proportional to its distance from Earth, expressed as v = H₀ × d, where H₀ is the Hubble constant.
  • •The observed redshift of light from distant galaxies provides the primary observational evidence that the universe is expanding in all directions.
  • •The Hubble constant (H₀) is currently estimated at approximately 70 km/s/Mpc, meaning a galaxy 1 megaparsec away recedes at roughly 70 km/s.
  • •Cosmic expansion does not mean galaxies move through space from a central point — space itself stretches, carrying galaxies apart, which is why no single location qualifies as the 'center' of the universe.
  • •Hubble's Law implies that the universe had a definite beginning: tracing expansion backward leads to an extremely hot, dense initial state known as the Big Bang, approximately 13.8 billion years ago.
  • •At very large scales, the recession speeds inferred from Hubble's Law can exceed the speed of light without violating special relativity, because it is space expanding rather than objects moving through space.
  • •Dark energy is the leading explanation for the observed acceleration of cosmic expansion, first confirmed through Type Ia supernova observations in the late 1990s.

Observational Foundation: Galaxy Redshifts and Recession

The discovery that the universe is expanding rests on a specific pattern in the light arriving from distant galaxies — a systematic shift toward longer wavelengths that reveals those galaxies are moving away from us.

Cosmological Redshift as Evidence of Expansion

  • •When a light source moves away from an observer, the wavelength of its emitted light is stretched, shifting spectral lines toward the red end of the electromagnetic spectrum — a phenomenon called the cosmological redshift.
  • •Astronomers measure redshift by comparing the observed wavelength of known spectral lines (such as hydrogen's Balmer series) against their laboratory wavelengths; the fractional shift gives the recession velocity.
  • •Edwin Hubble and Milton Humason compiled systematic redshift measurements for dozens of galaxies in the late 1920s, establishing that nearly every galaxy outside the Local Group shows a positive redshift — meaning nearly all are receding.

Distinguishing Cosmological Redshift from Doppler Shift

  • •A true Doppler shift occurs when an object moves through space, compressing or stretching sound or light waves relative to a stationary medium.
  • •Cosmological redshift arises differently: space itself expands while light travels through it, physically stretching the photon's wavelength during transit rather than at the moment of emission.
  • •This distinction matters at large distances, where cosmological redshift dominates over any peculiar (local) motion a galaxy might have through its own neighborhood of space.

Hubble's Law: The Velocity–Distance Relationship

Hubble's Law is the quantitative backbone of observational cosmology, linking how fast a galaxy appears to recede to how far away it is.

Mathematical Form of Hubble's Law

  • •The law is written v = H₀ × d, where v is the galaxy's recession velocity in km/s, d is its distance in megaparsecs (Mpc), and H₀ is the Hubble constant.
  • •The relationship is linear: doubling a galaxy's distance doubles its recession speed, which means the universe expands proportionally — every region of space stretches at the same rate.
  • •On a velocity–distance plot, galaxies scatter around a straight line through the origin; the slope of that line is H₀.

The Hubble Constant H₀

  • •Current best estimates place H₀ near 70 km/s/Mpc, though measurements using different techniques — the cosmic microwave background versus local distance ladders — yield slightly different values, a tension that remains an active area of research.
  • •H₀ has units of velocity per distance, which means it can also be expressed as an inverse time (roughly 1/H₀ ≈ 14 billion years), providing a rough estimate of the age of the universe.
  • •Because H₀ encodes the current expansion rate, its precise value affects every cosmological calculation, including estimates of the universe's size, age, and energy content.

Using Hubble's Law to Measure Distance

  • •For galaxies too remote for direct parallax or standard candle measurements, astronomers use the measured redshift to infer recession velocity and then divide by H₀ to estimate distance.
  • •This method assumes the galaxy's redshift is dominated by cosmic expansion rather than peculiar motion, an assumption that holds well beyond distances of roughly 10–20 Mpc.

About this Study Pack

Created by Kibin to help students review key concepts, prepare for exams, and study more effectively. This Study Pack was checked for accuracy and curriculum alignment using authoritative educational sources. See sources below.

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