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

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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 space equals space H subscript 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

Hubbles Law Graph, downloadable AS & A Level Physics revision notes

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 subscript 0 space equals space 1 over H subscript 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

Big Bang, downloadable AS & A Level Physics revision notes

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

Worked example

A galaxy is found to be moving away with a speed of 2.1 × 107 m s-1. The galaxy is at a distance of 9.5 × 1024 m from Earth.

Assuming the speed has remained constant, what is the age of the universe in years?

Answer:

Step 1: Write down Hubble’s Law

v space equals space H subscript 0 d

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

H subscript 0 space equals fraction numerator space v over denominator d end fraction space equals space fraction numerator 2.1 space cross times space 10 to the power of 7 space over denominator 9.5 space cross times space 10 to the power of 24 end fraction space equals space 2.2 space cross times space 10 to the power of negative 18 end exponent space straight s to the power of negative 1 end exponent

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

T subscript 0 space equals 1 over H subscript 0 space equals fraction numerator space 1 over denominator 2.2 space cross times space 10 to the power of negative 18 end exponent end fraction space equals space 4.52 space cross times space 10 to the power of 17 space straight s

Step 4: Convert from seconds into years

T subscript 0 space equals space fraction numerator 4.52 space cross times space 10 to the power of 17 space over denominator open parentheses 365 space cross times space 24 space cross times space 60 space cross times space 60 close parentheses end fraction space equals space 1.43 space cross times space 10 to the power of 10 space years

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

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Ashika

Author: Ashika

Expertise: Physics Project Lead

Ashika graduated with a first-class Physics degree from Manchester University and, having worked as a software engineer, focused on Physics education, creating engaging content to help students across all levels. Now an experienced GCSE and A Level Physics and Maths tutor, Ashika helps to grow and improve our Physics resources.