Hubble’s Law And The Big Bang Theory (Copy)

1. Redshift in Spectra from Distant Objects

• Light from distant stars and galaxies shows emission or absorption lines.
• In many distant galaxies, these spectral lines are shifted towards the red end of the spectrum.
• This redshift means that wavelengths (λ) appear longer than expected compared to laboratory values on Earth.
• Let:
  • λ = original/rest wavelength (measured in lab)
  • ∆λ = λ_observed − λ_rest = amount of shift
• The fractional redshift z is given by:

  z = ∆λ / λ = ∆f / f = v / c

• Where:
  • v = velocity of the object moving away
  • c = speed of light (≈ 3.00 × 10⁸ m/s)
  • ∆f = change in observed frequency (a decrease if redshifted)
• For most astronomical objects, v << c, so non-relativistic Doppler approximation holds.

2. Meaning and Implication of Redshift

• If all galaxies are redshifted, they must be moving away from us.
• The farther the galaxy, the greater the redshift — indicating it is receding faster.
• This provides evidence that:
  • Space itself is expanding
  • The universe is not static, but dynamic and evolving
• Therefore, redshift is direct evidence for:
  • The expanding universe
  • The Big Bang theory (a past point of origin from a dense, hot state)

3. Hubble’s Law: Velocity-Distance Relationship

• Hubble discovered that the velocity v at which a galaxy moves away is proportional to its distance d from us.
• Hubble’s Law:

  v = H₀d

• Where:
  • v = recessional velocity (m/s)
  • H₀ = Hubble constant (≈ 70 km/s/Mpc or 2.27 × 10⁻¹⁸ s⁻¹ in SI units)
  • d = distance to the galaxy (m)
• This relationship is linear:
  • Plotting v against d gives a straight line through the origin.
  • Slope = H₀

4. Estimating the Age of the Universe

• If v = H₀d, then the time since galaxies started moving apart is roughly:

  t ≈ 1 / H₀

• This gives a rough estimate of the age of the universe, assuming constant expansion.
• For H₀ ≈ 2.27 × 10⁻¹⁸ s⁻¹:

  t ≈ 4.4 × 10¹⁷ s ≈ 14 billion years

5. The Big Bang Theory

• Hubble’s law supports the Big Bang theory:
  • At one point in the past, the universe was infinitely small and dense.
  • All matter and space originated from a single point.
  • The expansion began at the Big Bang and continues today.
• Redshift, cosmic microwave background radiation (CMBR), and distribution of galaxies all provide observational support.

6. Summary of Key Equations

• Redshift:

  z = ∆λ / λ = ∆f / f = v / c

• Hubble’s Law:

  v = H₀d

• Age of Universe estimate:

  t ≈ 1 / H₀

Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change A2 Level Physics Full Scale Course