Velocity changes of the Giotto spacecraft induced during the flybys of the comets P/Halley and P/Grigg-Skjellerup

The Giotto Radio-Science Experiment (GRE) was designed to measure the reaction of the spacecraft to its close encounters with the comets P/Halley and P/Grigg-Skjellerup. Radio frequency and signal level data of the downlink carrier signals at X- and S-band, recorded at many ground-based tracking stations, were used for the previous analysis. These signals were transmitted in “one-way” mode (Giotto - Earth) during a few hours about closest approach and in “two-way” mode (Earth - Giotto - Earth) during the adjacent pre-encounter and post-encounter tracking intervals. Unexpectedly large differences for the comet-induced Doppler shift residual of the Giotto signal were implied by the one-way versus the two-way data, a discrepancy which was attributed to instabilities of the on-board oscillator during the encounter. The analysis to date assumed that the two-way Doppler shift residual is exactly twice the one-way residual. As shown in this note, this is not generally the case. The spacecraft's change in velocity, which is measured in a rotating (non-inertial) system, must first be determined in the non-rotating frame by applying the appropriate coordinate transformation. The GRE results should be reinvestigated to account for this previously unrecognized effect.