C20: Cosmology (the Big Bang)

• Stellar parallax 


  Technique used to determine the distance to stars that are relatively close to the Earth (less than 100pc) by comparing their apparent positions against distant stars at times 6 months apart.
• Parallax angle 


  The angle of apparent shift in the position of a relatively close star against the backdrop of fixed more distant star as the Earth makes a quarter of an orbit around the Sun.
• Astronomical unit (AU) 


  The average/mean distance from the Earth to the Sun, i.e. 150 million km or 1.50 x 10^11 m.
• Light-year (ly)


  The distance travelled by light in a vacuum in a time of 1 year. (9.64 x 10^15 m)
• Calculate the distance of 1 light-year.

  s = v•t = 3.0 x 10^8 x (365 x 24 x 60 x 60) = 9.64 x 10^15 m ≈ 9.5 x 10^15 m.
• Parsec (pc)


  The distance at which a radius of 1 AU subtends an angle of one arcsecond.
• Calculate 1 pc in metres.

  tan (1 arcsecond) = 1AU/1pc = 1pc = 1.50 x 10^11/ tan(1/3600) = 3.1 x 10^6m (≈3.26 ly)
• Arcminute

  1/60th of a degree
• 1 arcsecond = 1/3600 of a degree
• 1 AU = 1 parsec
• Draw diagram 


  Remember diagram

  
• Why can’t parallax angle method only be used for stars that are relatively close to Earth?

  Analyze diagram

  
• Doppler effect

  The change in frequency and wavelength of waves as the source moves away from or towards the observer.
• Eqn relating the parallax p in seconds of arc and the distance d in parsec?

  p = 1/d
• Cosmological principle

  The universe is homogeneous, isotropic and the laws of physics are universal.
• Isotropic

  The same in all directions (for example the Universe, appearing the same to any observer regardless of position).
• Homogeneous

  Uniform in terms of the distribution of matter across the Universe when viewed on a sufficiently large scale.
• Doppler effect equation.

  fΔ/f​ ≈ Δλ​/λ ≈ v/c , for a source of electromagnetic radiation moving relative to an observer.
• Can you describe the Doppler shift of electromagnetic radiation?

  • If the galaxy is moving towards the Earth the absorption lines will be blue-shifted — they move towards the blue end of the spectrum, because the λ appears shorter.
  • If the galaxy is moving away from the Earth (‘receding’) the absorption lines will be red-shifted — they all move towards the red end of the spectrum, because the λ appears stretched.
• Hubble’s law

  The recessional speed v of a galaxy is almost directly proportional to its distance d from the Earth.