# 5.47 Cosmology

## The Hubble Constant

• 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)
• Ho = 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

#### 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.

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 Step 3: Calculate the gradient of the graph:

• H0 = = 66 km s–1 Mpc–1

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

## Dark Matter

• 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 ### Get unlimited access

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