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A LevelPhysicsOCRRevision Notes5. Newtonian World & AstrophysicsCosmologyThe Age of the Universe

The Age of the Universe (OCR A Level Physics)

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Katie M

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Katie M

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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 = fraction numerator bold italic d bold italic i bold italic s bold italic t bold italic a bold italic n bold italic c bold italic e over denominator bold italic s bold italic p bold italic e bold italic e bold italic d end fraction = bold italic d over bold italic v

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

H0 = bold italic v over bold italic d

  • Therefore:

time = 1 over bold italic H subscript 0

  • 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 = fraction numerator 6.74 blank cross times blank 10 to the power of 4 over denominator 3.1 blank cross times blank 10 to the power of 22 end fraction = 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 = 1 over H subscript 0 = fraction numerator 1 over denominator 2.17 blank cross times blank 10 to the power of negative 18 end exponent end fraction = 4.60 x 1017 s  

Step 7: Convert 4.60 x 1017s to years

  • Age of the universe = fraction numerator 4.60 blank cross times blank 10 to the power of 17 over denominator 3.16 blank cross times blank 10 to the power of 7 end fraction = 1.46 x 1010 years = 14.6 billion years

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    Katie M

    Author: Katie M

    Expertise: Physics

    Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.