All subjects · Physics · WPH15 (Unit 5)

Redshift, Hubble's law and the fate of the universe

Light from distant galaxies is stretched to longer wavelengths. This redshift shows the universe is expanding, and leads to estimates of its age.

The Doppler effect

When a wave source moves relative to an observer, the observed frequency changes. A source moving towards the observer gives a higher frequency (shorter wavelength); moving away gives a lower frequency (longer wavelength). For light from a receding source, spectral lines shift towards the red end: redshift.

Redshift

For speeds much less than c:

z = Δλ / λ ≈ Δf / f ≈ v / c

where Δλ is the shift in wavelength from the laboratory value λ, and v is the speed of recession. Almost all galaxies show redshift, so they are moving away from us.

Hubble's law

The recession speed of a galaxy is proportional to its distance:

v = H_0d

where H_0 is the Hubble constant (about 70 km/s per Mpc, or about 2.3 x 10-18 s-1). This is evidence that the universe is expanding. If it has always expanded at the same rate, its age is about 1 / H_0, around 1.4 x 1010 years.

Age and fate: an open debate

Worked example

A hydrogen line with laboratory wavelength 656 nm is observed at 670 nm in a galaxy's spectrum. Find the galaxy's speed of recession.

  1. z = Δλ / λ = 14 / 656 = 0.0213
  2. v = zc = 0.0213 x 3.00 x 108

Answer: v = 6.4 x 106 m/s, moving away

Key idea: Redshift z = Δλ/λ ≈ v/c means recession; v = H_0d; age ≈ 1/H_0; fate depends on density, which is uncertain because of dark matter.

Check yourself

  1. A spectral line with laboratory wavelength 656 nm is observed at 670 nm. Find the redshift z, to 3 s.f.
    Show answer

    0.0213. z = Δλ / λ = 14 / 656 = 0.0213.

  2. Using that redshift (656 nm observed at 670 nm), find the recession speed, in units of 106 m/s, to 3 s.f.
    Show answer

    6.40 x 106 m/s. v = zc = (14 / 656) x 3.00 x 108 = 6.40 x 106 m/s.

  3. A galaxy recedes at 4.6 x 106 m/s. Taking H_0 = 2.3 x 10-18 s-1, find its distance, in units of 1024 m.
    Show answer

    2 x 1024 m. d = v / H_0 = 4.6 x 106 / 2.3 x 10-18 = 2.0 x 1024 m.

  4. Estimate the age of the universe from H_0 = 2.3 x 10-18 s-1, in units of 1010 years, to 3 s.f. (1 year = 3.15 x 107 s)
    Show answer

    1.38 x 1010 years. Age ≈ 1 / H_0 = 4.35 x 1017 s; divide by 3.15 x 107 to get 1.38 x 1010 years.

  5. Convert H_0 = 70 km/s per Mpc into s-1, in units of 10-18 s-1, to 3 s.f. (1 Mpc = 3.09 x 1022 m)
    Show answer

    2.27 x 10-18 s-1. H_0 = 7.0 x 104 m/s / 3.09 x 1022 m = 2.27 x 10-18 s-1.

  6. The spectral lines from a distant galaxy are redshifted. What does this show?
    • The galaxy is moving away from us
    • The galaxy is moving towards us
    • The galaxy is very hot
    • The galaxy is made of hydrogen only
    Show answer

    The galaxy is moving away from us. A receding source has its wavelengths stretched.

  7. Why is the ultimate fate of the universe uncertain?
    • Galaxies are not really moving
    • Redshift cannot be measured
    • Its average density is uncertain, partly because the amount of dark matter is unknown
    • The speed of light is changing
    Show answer

    Its average density is uncertain, partly because the amount of dark matter is unknown. Whether expansion continues depends on density, which depends on dark matter (and dark energy).

  8. Which observation provides evidence for dark matter?
    • Distant galaxies are redshifted
    • Stars have black body spectra
    • Nearby stars show parallax
    • Stars at the edges of galaxies orbit faster than the visible mass can explain
    Show answer

    Stars at the edges of galaxies orbit faster than the visible mass can explain. Extra unseen mass is needed to provide the centripetal force.

Practise with instant feedback

Sources

Last updated 7 November 2026. Spotted a mistake? Tell us.