Age of the Universe (Cambridge International IGCSE Physics)

The Hubble constant

Spec point — 6.2.7 · Define the Hubble constant H0 as the ratio of the speed at which the galaxy is moving away from the Earth to its distance from the Earth;

• recall
• and use the equation H0 = v/d Know that the current estimate for H0 is 2.2 × 10^–18 per second

The Hubble constant

Extended Tier Only

• When Edwin Hubble looked at the absorption spectra of distant galaxies, he determined a relationship between the speed of a galaxy and its distance from Earth

Hubble discovered that all galaxies show redshift, but the galaxies that are further away show a greater increase in redshift

• This is Hubble's law, which states

The speed of recession is proportional to the distance of the galaxy away from Earth

• 'Recession' speed means the speed at which something is moving away

• This means that the further away a galaxy is from Earth:

  • the faster it is moving away
  • the greater the increase in redshift

Hubble's law tells us the greater the distance to a galaxy, the greater the redshift, or the speed it moves away from Earth

• Hubble’s law can be expressed as an equation:

$H_{0}=\frac{v}{d}$

• Where:

  • $H_{0}$ = Hubble constant (per second)
  • $v$ = recessional velocity of an object, the velocity of an object moving away from an observer (km/s)
  • $d$ = distance between the object and the Earth (km)

• From this equation, the Hubble constant $H_{0}$ can be defined as:

The ratio of the speed at which the galaxy is moving away from the Earth, to its distance from the Earth

• The accepted value of the Hubble constant is $H_{0}$ = 2.2 × 10^-18per second

Exam Hint Make sure to learn the currently accepted value of the Hubble constant.

You will be expected to know that the current estimate for H₀ is 2.2 × 10^-18 per second.

Measuring recession speed & distance

Spec point — 6.2.7 · - Know that the speed (v) at which a galaxy is moving away from the Earth can be found from the change in wavelength of the galaxy’s starlight due to redshift

• Know that the distance of a far galaxy (d) can be determined using the brightness of a supernova in that galaxy

Measuring recession speed & distance

Extended Tier Only

• The Hubble constant $H_{0}$ can be determined from measurements of:

  • redshift of the light emitted by a galaxy
  • the brightness of supernovae in the galaxy

Measuring recession speeds of galaxies

• The speed of recession $v$ of a galaxy (i.e. how fast it is moving away from the Earth) can be found from the change in wavelength of the galaxy’s starlight due to redshift

Measuring distance using supernovae

• The distance $d$ to a galaxy can be determined using the brightness of a supernova in that galaxy

• Supernovae are exploding stars

  • Certain types of supernovae have the same peak level of brightness (absolute magnitude), meaning they can be used as standard candles
  • These supernovae are so bright that they can be used for measuring distances to the most distant galaxies

Age of the Universe

Spec point — 6.2.7 · Know that the equation d/v = 1/H0

• represents an estimate for the age of the Universe and
• that this is evidence for the idea that all the matter in the Universe was present at a single point

Age of the Universe

Extended Tier Only

• Hubble's law can be rearranged to give the expression:

$\frac{1}{H_{0}}=\frac{d}{v}$

• Since time is equal to distance divided by speed, the term $\frac{1}{H_{0}}$ represents an estimate of the age of the Universe

• Hubble's law provides further evidence for the Big Bang

• It shows that the Universe has been expanding since the beginning of time

  • If we looked at time in reverse, we would see galaxies were closer together in the past
  • This suggests that the Universe must have originated from a single point and has been expanding outwards ever since

Hubble's law graph

• Using measurements from galactic redshift and brightness of supernovae, a graph of recession velocity against distance can be plotted

Graph of galaxy recession velocity against distance

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

• The gradient of the graph represents the age of the Universe

  • When the distance equals zero, this represents all the matter in the Universe being at a single point
  • This is the singularity that occurred at the moment of the Big Bang

• Astronomers have used this formula to estimate the age of the Universe is about 13.8 billion years

Worked Example A distant galaxy is 20 light-years away from Earth.

Use Hubble’s law to determine the velocity at which the galaxy moves away from Earth.

[3]

Answer:

Step 1: List the known quantities

• Distance to the galaxy, $d$ = 20 light-years
• 1 light year = 9.5 × 10¹⁵ m
• Hubble constant, $H_{0}$ = 2.2 × 10⁻¹⁸ per second

Step 2: Convert 20 light-years to m

$d = 20 \text{ly} = 20 \times ( 9.5 \times 10^{15} )$

$d=1.9\times10^{17}m$ [1 mark]

Step 3: Substitute values into Hubble's Law

$v=H_{0}d$

$v = ( 2.2 \times 10^{- 18} ) \times ( 1.9 \times 10^{17} )$ [1 mark]

$v=0.418m/s$

• The galaxy moves away from Earth at a velocity of 0.42 m/s [1 mark]

Exam Hint If you are taking the Extended paper, remember that you have to learn the values for a light year and the Hubble constant.