Hubble's Law & the Big Bang Theory (CIE A Level Physics)

• 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
• Hubble’s Law states:

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

• This can be calculated using:

v = H₀d

• 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, the faster it’s recession velocity
  • The gradient of a graph of recession velocity against distance is equal to the Hubble constant

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

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

• 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

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

Step 1: Write down Hubble’s Law

v = H₀d

Step 2: Rearrange for the Hubble constant H₀, and calculate

Step 3: Write the equation for the age of the universe T₀, and calculate

Step 4: Convert from seconds into years

Therefore, the age of the universe is estimated to be about 14.3 billion years