Past exam of the mathematics course of the University of Cambridge / 2008 / iii / Paper 73 / 1 / ii / Solution

Take $v>0$ for recession. By the definition of kinematic redshift, $1+z_{\mathrm{kin}}={\nu }_e/{\nu }_0$. Inverting the supplied relativistic Doppler effect and expanding with $\beta =v/c$ givesThusA negative radial velocity gives a blueshift at this order.