HUBBLE’S LAW & THE BIG BANG THEORY
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 - This can be calculated using:
$
\mathbf{v}=\mathbf{H}_0 \mathbf{d}
$
- Where:
- $v=$ the galaxy’s recessional velocity $\left(\mathrm{m} \mathrm{s}^{-1}\right)$
- $\mathrm{d}=$ distance between the galaxy and Earth $(\mathrm{m})$
- $\mathrm{H}_0=$ Hubble’s constant, or the rate of expansion of the universe $\left(\mathrm{s}^{-1}\right)$
- 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
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 $T_0$ is equal to:
$
\mathrm{T}_0=\frac{1}{H_0}
$
- Current estimates of the age of the universe range from $\mathbf{1 3}-14$ 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
Worked example: Age of the universe
A galaxy is found to be moving away with a speed of $2.1 \times 10^7 \mathrm{~m} \mathrm{~s}^{-1}$. The galaxy is at a distance of $9.5 \times 10^{24} \mathrm{~m}$. Assuming the speed has remained constant, what is the age of the universe, in years?
Answer/Explanation
Step 1: $\quad$ Write down Hubble’s Law
$
\mathbf{v}=\mathbf{H}_0 \mathbf{d}
$
Step 2:
Rearrange for the Hubble constant $\mathrm{H}_0$, and calculate
$
\mathrm{H}_0=\frac{v}{d}=\frac{2.1 \times 10^7}{9.5 \times 10^{24}}=2.2 \times 10^{-18} \mathrm{~s}^{-1}
$
Step 3:
Write the equation for the age of the universe $T_0$, and calculate
$
\mathrm{T}_0=\frac{1}{H_0}=\frac{1}{2.2 \times 10^{-18}}=4.52 \times 10^{17} \mathrm{~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} \text { years }
$
Therefore, the age of the universe is estimated to be about $\mathbf{1 4 . 3}$ billion years