Doppler effect

$\dfrac{∆f}{f} = \dfrac{v}{c}$ and $z = \dfrac{∆λ}{λ} = -\dfrac{v}{c}$ for $v≪c$ applied to optical and radio frequencies.

Calculations on binary stars viewed in the plane of orbit.

Galaxies and quasars.

Hubble's law

Red shift $v = Hd$

Simple interpretation as expansion of universe; estimation of age of universe, assuming H is constant.

Qualitative treatment of Big Bang theory including evidence from cosmological microwave background radiation, and relative abundance of hydrogen and helium.

Quasars

Quasars as the most distant measurable objects.

Discovery of quasars as bright radio sources.

Quasars show large optical red shifts; estimation involving distance and power output.

Formation of quasars from active supermassive black holes.

Detection of exoplanets

Difficulties in the direct detection of exoplanets.

Detection techniques will be limited to variation in Doppler shift (radial velocity method) and the transit method.

Typical light curve.