Cosmology (Edexcel IAL Physics)

The Hubble Constant

Spec point — 171

• By rearranging the equation for Hubble’s law, we can determine that the Hubble constant, H₀, is:

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

• Where:

  • v = recessional velocity of an object (km s^–1)
  • d = distance between the object and the Earth (Mpc)
  • H_o* *= Hubble constant (km s^–1 Mpc^–1)

• The value for the Hubble constant has been estimated using data for thousands of galaxies

  • The latest estimate of the Hubble constant based on CMB observations by the Planck satellite is:

H₀ = 67.4 ± 0.5 km s⁻¹Mpc⁻¹ (Planck Collaboration VI 2020)

• It is difficult to be certain about just how accurate the values for the Hubble constant are

  • This is due to the random and systematic errors involved when calculating the distance to a galaxy or star

Worked Example The graph shows how the recessional velocity, v, of galaxies varies with their distance, d, measured from the Earth.

Use the graph to determine a value for the Hubble constant and state the unit for this constant.

Answer:

Step 1: From the data booklet:

Hubble’s Law:* v ≈ H **₀d

Step 2: Determine the Hubble constant, H₀, from the graph:**

• y–axis = v = 20, 000
• x–axis = d = 305
• gradient = H₀

Step 3: Calculate the gradient of the graph:

• H₀ = $\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$ = $\frac{20000-0}{305-0}$ = 66 km s^–1 Mpc^–1

Step 4: Confirm your answer:

• The Hubble Constant = 66 km s⁻¹ Mpc⁻¹

Dark Matter

Spec point — 171

• We would expect the velocity of an object within a galaxy to decrease as it moves away from the galaxy's centre because of weakening gravitational field strength

  • This is observed in smaller mass systems, like the solar system where planets orbiting furthest from the Sun have the slowest orbital velocity
  • This is not the case in bigger mass systems like entire galaxies

• Mass is not actually concentrated in the centre of galaxies; it is spread out

  • All the observable mass of a galaxy is, however, concentrated in its centre, so there must be another type of matter we can't see, called Dark Matter

• Dark matter is defined as: Matter which cannot be seen and that does not emit or absorb electromagnetic radiation

• Dark matter cannot be detected directly through telescopes

  • It should make up 27% of the mass in the universe
  • It is detected based on its gravitational effects relating to either the rotation of galaxies or by the gravitational lensing of starlight