The Time Transfer Function as a tool to compute range, Doppler and astrometric observables

In this communication, we will show how the Time Transfer Function (TTF) can be used in the relativistic modeling of range, Doppler and astrometric observables. We will present a method to compute these observables up to second post-Minkowskian order directly from the space-time metric g_¥mu¥nu without explicitly solving the null geodesic. The resulting expressions involve integrals of some functions defined by the metric tensor taken along a straight line between the emitter and the receiver of the electromagnetic signal. Some examples are given within the context of future space missions.