The Age of the Universe (OCR A Level Physics): Revision Note
Exam code: H556
Estimating 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
Worked Example
In 2020, the best estimate for the Hubble constant, H0 was 67.4 km s−1 Mpc−1. Use this value to calculate the age of the universe.
Answer:
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
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