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Redshift and the Big Bang Theory Explained

Redshift

  • When a galaxy or star recedes from Earth, it stretches the wavelength of the light it emits.
  • This is due to the Doppler effect.
  • The Doppler effect causes a shift in wavelength towards the red end of the electromagnetic (EM) spectrum if the star is moving away from us, known as redshift.
  • Reference Wavelength
    • The true wavelength that a star emits is the reference wavelength, denoted as \lambda_0.
  • Apparent Wavelength
    • The wavelength observed on Earth is the apparent wavelength, denoted as \lambda.
  • By observing the shift in wavelength, we can determine the velocity of the star.

Doppler Shift Equation

  • The Doppler shift equation relates the velocity of a star or galaxy to the observed wavelength shift.
  • Equation: v = c \cdot \frac{\Delta \lambda}{\lambda_0}
    • v: Velocity of the star or galaxy.
    • c: Speed of light in a vacuum (approximately 3 \times 10^8 meters per second).
    • \Delta \lambda: Shift in wavelength, calculated as the difference between the apparent wavelength and the reference wavelength (\Delta \lambda = \lambda - \lambda_0).
    • \lambda_0: Reference wavelength.

Example Calculation

  • A star emits light with a reference wavelength of 434 nanometers.
  • The observed wavelength on Earth is 482 nanometers.
  • Calculate the velocity of the star relative to Earth.

Solution

  1. Rearrange the Doppler shift equation to solve for velocity:
    v = c \cdot \frac{\Delta \lambda}{\lambda_0}
  2. Calculate the shift in wavelength:
    \Delta \lambda = 482 \text{ nm} - 434 \text{ nm} = 48 \text{ nm}
  3. Substitute the values into the equation:
    v = (3 \times 10^8 \text{ m/s}) \cdot \frac{48 \text{ nm}}{434 \text{ nm}}
  4. Calculate the velocity:
    v \approx 3.3 \times 10^7 \text{ m/s}

Redshift and Expanding Universe

  • From Earth, galaxies appear to be moving away from us in all directions.
  • The universe is expanding.
  • Evidence for this expansion is the redshift of light from distant galaxies.
  • Explanation for the expansion is the Big Bang theory.

Absorption Spectra

  • Definition: The absorption spectra for visible light emitted from the sun and observed on Earth is a pattern of dark lines. These lines represent wavelengths absorbed by chemicals in the sun's atmosphere.
  • Process:
    • The sun's atmosphere contains various chemicals that absorb specific wavelengths of light.
    • When light reaches Earth, certain wavelengths are missing, creating dark lines in the absorption spectra.
    • Example: Oxygen and hydrogen molecules absorb certain wavelengths, creating gaps in the spectra.

Redshift in Distant Galaxies

  • When analyzing light from distant galaxies, their spectra show the same pattern of black lines but shifted towards the red end of the spectrum.
  • This is called redshift.
  • Redshift occurs because all light waves are stretched as they travel towards Earth.
  • If a gap was at 600 nanometers, it might appear at 650 nanometers due to stretching.

Explanation of Redshift

  • Distant galaxies are moving away from us.
  • Space itself is expanding between us and the galaxies.
  • As space expands, the distance between us and the galaxies increases.

Balloon Model of the Expanding Universe

  • Imagine a balloon covered in markers, where the balloon represents the universe and the markers represent galaxies.
  • As the balloon is inflated (universe expands), the markers (galaxies) move further apart.
  • The galaxies aren't moving across the surface but the space between them is expanding.
  • From a central galaxy, all other galaxies appear to be moving away.
  • The further away a galaxy is, the faster it appears to be moving.

Limitations of Models

  • Models aren't perfect, such as the balloon model.
  • Balloons burst, but the universe isn't likely to burst.
  • Galaxies should be inside the balloon, not just on the surface.
  • Despite limitations, models help us understand difficult concepts.

Big Bang Theory

  • If the universe is expanding, it was smaller in the past.
  • At some point, the universe was tiny.
  • The Big Bang theory proposes that all matter in the universe occupied a tiny space that was dense and hot.
  • Suddenly, it exploded, and space started to expand, which continues today.