On one-way Doppler measurements of space craft and celestial objects

Abstract

The orbital velocity of a spacecraft and other celestial objects is monitored by observing the Doppler frequency shift of the signals received at the ground station. This is possible one-way in case the transmitted frequency is stable enough. In most spacecraft a calibrated transponder allows two-way Doppler frequency registrations. In general, the factor 2 is expected as the quotient between two- and one-way frequencies. However, this is no longer the case when the motion of the observed object deviates from the orbit as predicted. Frequency differences appear. Porsche (1999) has published a formula to describe these differences based on the assumption of a double projection of the true velocity vector. In the present paper a more sophisticated analysis of the influence of state errors on the track-ing results is deduced. This theory has been tested by the Doppler measurements during flybys of the comet space probe GIOTTO penetrating through the comae of the comets P/Halley and P/Grigg-Skjellerup. One-way Doppler measurements of the low Earth satellites CHAMP and TERRASAR-X show a tendency for the applicability of this approach. Finally, some conse-quences for the observation of other celestial objects are discussed.