# The Age of the Universe(OCR A Level Physics)

Author

Katie M

Expertise

Physics

## 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.

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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