1. Consider the light emitted by a moving source as a sequence of wave crests. Hence derive the classical Doppler formula relating redshift to velocity for a rapidly receding, but non-relativistic, source. Now account for the fact that the emission of the wave crests will be further slowed by relativistic time-dilation, and hence derive the Special Relativistic Doppler formula. Finally, in the framework of General Relativity, derive the relation between scale factor, a, and redshift, z. Compare and discuss your results