Pioneer 10 Doppler data analysis: Disentangling periodic and secular anomalies

This paper reports the results of an analysis of the Doppler tracking data of Pioneer probes which did show an anomalous behaviour. A software has been developed for the sake of performing a data analysis as independent as possible from that of Anderson et al. [Anderson, J., Laing, P.A., Lau, E.L., Liu, A.S., Nieto, M.M., Turyshev, S.G. Study of the anomalous acceleration of Pioneer 10 and 11. Phys. Rev. D 65, 082004, 2002], using the same data set. A first output of this new analysis is a confirmation of the existence of a secular anomaly with an amplitude about 0.8 nm s⁻² compatible with that reported by Anderson et al. A second output is the study of periodic variations of the anomaly, which we characterize as functions of the azimuthal angle φ$\phi$ defined by the directions Sun–Earth Antenna and Sun-Pioneer. An improved fit is obtained with periodic variations written as the sum of a secular acceleration and two sinusoids of the angles φ$\phi$ and 2φ$2\phi$. The tests which have been performed for assessing the robustness of these results are presented.