Range, Doppler and astrometric observables computed from Time Transfer Functions: a survey

Determining range, Doppler and astrometric observables is of crucial interest for modelling and analyzing space observations. We recall how these observables can be computed when the travel time of a light ray is known as a function of the positions of the emitter and the receiver for a given instant of reception (or emission). For a long time, such a function--called a reception (or emission) time transfer function--has been almost exclusively calculated by integrating the null geodesic equations describing the light rays. However, other methods avoiding such an integration have been considerably developped in the last twelve years. We give a survey of the analytical results obtained with these new methods up to the third order in the gravitational constant G for a mass monopole. We briefly discuss the case of quasi-conjunctions, where higher-order enhanced terms must be taken into account for correctly calculating the effects. We summarize the results obtained at the first order in G when the multipole structure and the motion of an axisymmetric body is taken into account. We present some applications to on-going or future missions like Gaia and Juno. We give a short review of the recent works devoted to the numerical estimates of the time transfer functions and their derivatives