In scenario (a), the point of closest approach is frame-independent and represents the moment where there is no change in distance versus time (i.e. dr/dt = 0 where r is the distance between receiver and source) and hence no longitudinal Doppler shift. The source observes the receiver as being illuminated by light of frequency f ′, but also observes the receiver as having a time-dilated clock. In frame S, the receiver is therefore illuminated by blueshifted light of frequency