Hubble's Law & the Big Bang Theory (Cambridge (CIE) A Level Physics): Revision Note

Hubble's law & the Big Bang theory

• Edwin Hubble investigated the light spectra emitted from a large number of galaxies

• He used redshift data to determine the recession velocities of these galaxies, and standard candles  to determine the distances

• From these measurements, he formulated a relationship, now known as Hubble’s law, which states:

  The recession speed of galaxies moving away from Earth is proportional to their distance from the Earth

• This can be calculated using:

$v=H_{0}d$

• Where:

  • v = the galaxy's recessional velocity (m s^-1)

  • d = distance between the galaxy and Earth (m)

  • H₀ = Hubble's constant, or the rate of expansion of the universe (s^-1)

• This equation tells us:

  • The further away a galaxy is, the faster its recession velocity

  • The gradient of a graph of recession velocity against distance is equal to the Hubble constant

Hubble's law graph

A key aspect of Hubble’s law is that the furthest galaxies appear to move away the fastest

Age of the Universe

• If the galaxies are moving away from each other, then they must’ve started from the same point at some time in the past

• If this is true, the universe likely began in an extremely hot, dense singular point which subsequently began to expand very quickly

  • This idea is known as the Big Bang Theory

• The redshift of galaxies and the expansion of the universe are now some of the most prominent pieces of evidence to suggest this theory is true

• The data from Hubble’s law can be extrapolated back to the point that the universe started expanding i.e. the beginning of the Universe

• Therefore, the age of the universe T₀ is equal to:

$T_0=\frac{1}{H_0}$

• Current estimates of the age of the universe range from 13 – 14 billion years

• There is still some discussion about the exact age of the universe, therefore, obtaining accurate measurements for the Hubble constant is a top priority for cosmologists

Expansion of the Universe

Tracing the expansion of the universe back to the beginning of time leads to the idea the universe began with a “big bang”