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
Hubble’s Law states:

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

$v = H_{0} d$

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

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

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:

$T_{0} = \frac{1}{H_{0}}$

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

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”

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

$v = H_{0} d$

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

$H_{0} = \frac{v}{d} = \frac{2.1 \times 10^{7}}{9.5 \times 10^{24}} = 2.2 \times 10^{- 18} s^{- 1}$

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

$T_{0} = \frac{1}{H_{0}} = \frac{1}{2.2 \times 10^{- 18}} = 4.52 \times 10^{17} s$

Step 4: Convert from seconds into years

$T_{0} = \frac{4.52 \times 10^{17}}{(365 \times 24 \times 60 \times 60)} = 1.43 \times 10^{10} years$

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

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