Hubble & The Age of the Universe (CIE IGCSE Physics)

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• In 1929, the astronomer Edwin Hubble showed that the universe was expanding
  • He did this by observing the absorption line spectra produced from the light of distant galaxies
  • He discovered that the light was shifted towards the red end of the spectrum
• This Doppler shift in the wavelength of the light is evidence that distant galaxies are moving away from the Earth

• Hubble also observed that light from more distant galaxies was more red-shifted than the light from nearer galaxies
  • This observation showed that galaxies or stars which are further away from the Earth are moving faster than galaxies which are closer

Examples of redshifted line spectra for galaxies at different distances from the Earth compared to a laboratory sample

Hubble's Law

• Hubble’s law states:

The recessional velocity v of a galaxy is proportional to its distance from Earth

• Hubble’s law can be expressed as an equation:

• Where:
  • H₀ = Hubble constant (per second)
  • v = recessional velocity of an object, the velocity of an object moving away from an observer (km/s)
  • d = distance between the object and the Earth (km)

• As the equation shows, the Hubble Constant, H₀ is defined as:

The ratio of the speed at which the galaxy is moving away from the Earth, to its distance from the Earth

• The accepted value of the Hubble constant is H₀ = 2.2 × 10^–18 per second

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• Since Hubble's Law states that

• It can be rearranged to show that 

• Hubble’s law shows that the further away a star is from the Earth, the faster it is moving away from us

   

A key aspect of Hubble’s law is that the furthest galaxies appear to move away the fastest

• The gradient of the graph can be used to find the Age of the Universe
  • When the distance equals zero, this represents all the matter in the Universe being at a single point
  • This is the singularity that occurred at the moment of the Big Bang

• The units of the gradient are per second (the same as the units of the Hubble Constant)
  • By taking the reciprocal, or, the units will become seconds
  • Therefore the reciprocal of the gradient represents time and gives the amount of time which the Universe has been expanding for

• Astronomers have used this formula to estimate the age of the Universe at about 13.7 billion years

Step 1: List the known quantities:

• • d = 20 light years
  • H_o = 2.2 x 10^-18 s^-1

Step 2: Convert 20 light-years to m:

• • 1 ly ≈ 9.5 x 10¹⁵ m
  • So, 20 ly = 20 x (9.5 x 10¹⁵) = 1.9 x 10¹⁷ m

Step 3: Substitute values into Hubble's Law: 

• • From the data booklet: v ≈ H₀d 
  • So, v ≈ (2.2 x 10^-18 ) x (1.9 x 10¹⁷) = 0.418 m s^-1

Step 4: Confirm your answer:

• • The velocity of the galaxy as it moves away from Earth 0.42 m s^-1