Past exam of the physics course of the year 4 of the natural sciences course of the University of Cambridge / 2014 / Paper 1 / B4 / b

A photon reaching spacecraft position $x(t)$ at Earth time $t$ was emitted at $t_e=t-x(t)/c$. Differentiating gives $d{t}_e/dt=1-\beta$. Since $Rd{t}_e$ photons arrive in $dt$,The emission rate and impact rate refer to different events, even though both are expressed in Earth coordinate time.