Study of the Pioneer Anomaly: A Problem Set

Analysis of the radio-metric tracking data from the Pioneer 10 and 11 spacecraft at distances between 20--70 astronomical units (AU) from the Sun has consistently indicated the presence of an anomalous, small, constant Doppler frequency drift. The drift is a blue-shift, uniformly changing at the rate $\dot{\nu} \sim (5.99 \pm 0.01) \times 10^{-9}$ Hz/s. The signal also can be interpreted as a constant acceleration of $a_P = (8.74 \pm 1.33) \times 10^{-8}$ cm/s$^2$ directed towards the Sun. This interpretation has become known as the Pioneer anomaly. The nature of this anomaly remains unexplained. That is to say, up to now no unambiguous explanation of the anomalous signal has been found. To reach this conclusion a complicated interplay between experiment and theory is needed to rule out systematics. However, in the end many of the necessary calculations are amenable to students. To elucidate this students would have a deeper understanding of the workings of physics in space systems. We give a problem set devoted to this cause.