5.47 Cosmology

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

• 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⁻¹ Mpc⁻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

Step 1: From the data booklet:

Hubble’s Law: v ≈ H₀d

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 =  =  = 66 km s^–1 Mpc^–1

Step 4: Confirm your answer:

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

• 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