 The radar pulse (which travels at formula_42, the speed of light) travels a total distance, there and back, that is twice the distance to the target, and takes time formula_43, where formula_44 and formula_45 are times recorded by the observer's clock at transmission and reception of the radar pulse.This implies that the distance to the target is

Furthermore, since the speed of light is the same in both directions, the time at which the radar pulse arrives at the target must be, according to the observer, halfway between the transmission and reception times, namely

In the particular case where the radar observer is Alice and the target is Bob (momentarily co-located with Dave) as described previously, by "k"-calculus we have formula_48, and so

As Alice and Bob were co-located at formula_51, the velocity of Bob relative to Alice is given by

This equation expresses velocity as a function of the Bondi "k"-factor.It can be solved for formula_1 to give formula_1 as a function of formula_55