5.12.8 The Age of the Universe

• Hubble’s law can be used to estimate the age of the universe
• The equation for Hubble’s law is:

v = H₀d

• Assuming the recessional speed of a galaxy is constant over the history of the universe, we can find the time since the expansion began, and hence the age of the universe
  • o We must assume that all points in the universe were initially together
  • o If we know how far away a galaxy is from Earth and its recessional speed
  • o We can calculate the time taken to get to reach that distance from the Earth
  • o Using the equation:

time = = 

• o We can also rearrange the Hubble equation to give:

H₀ = 

• Therefore:

time = 

• If we say that all matter was at the same point at the very start of the Big Bang (t = 0), then the time taken for the galaxy to move to its current position will be equal to the age of the universe

 

• Astronomers believe that the universe has been expanding for around 13.7 billion years

   Step 1: List the known quantities

• • H₀ = 67.4 km s⁻¹Mpc⁻¹

   Step 2: Use data booklet

• • 1 parsec ≈ 3.1 x 10¹⁶ m
  • 1 year = 3.16 x 10⁷ s
  • t = H₀^–1

   Step 3: Convert 67.4 km s⁻¹ Mpc⁻¹ to m s⁻¹ Mpc⁻¹

• • 67.4 km s⁻¹ Mpc⁻¹ = 67.4 x 1000 = 6.74 x 10⁴ m s⁻¹ Mpc⁻¹

   Step 4: Convert 1 Mpc to m

• • 1 Mpc = (3.1 x 10¹⁶) x (1 x 10⁶) = 3.1 x 10²² m

   Step 5: Convert 6.74 x 10⁴ m s⁻¹ Mpc⁻¹ to s⁻¹ 

• • 6.74 x 10⁴ m s⁻¹ Mpc⁻¹ =  = 2.17 x 10^–18 s^–1
  • Hence, H₀ = 2.17 x 10^–18 s^–1

   Step 6: Calculate the age of the universe

• • t =  =  = 4.60 x 10¹⁷ s  

   Step 7: Convert 4.60 x 10¹⁷s to years

• • Age of the universe =  = 1.46 x 10¹⁰ years = 14.6 billion years