The Pioneer Anomaly was inferred from an un-modelled Doppler shift in signals received from both Pioneer 10 & 11. A Doppler shift is where the frequency of a radio signal is changed by the velocity of the transmitter relative to the receiver. Similar to changes in sound as a train passes through a train station. So because the Pioneer craft are moving away from the Earth radio signals from them have their frequency decreased. But over time the Doppler shift slowly varied from that predicted by the velocity of the Pioneer craft. A possible explanation for this is that an acceleration is affecting the velocity of the Pioneer craft. The work carried out to infer this anomalous acceleration (Pioneer Anomaly) is presented in detail below. To summarise: although the anomaly directly affects the
craft’s velocity to analyse it a value known as Doppler velocity is
used. The Doppler velocity for Pioneer
10 over 60 seconds is 5.25x10 Doppler tracking is where a radio signal is transmitted from the Earth to a spacecraft. The signal is then coherently transponded and sent back to the Earth.
(1) The received frequency (f The frequency change of the received signal is compared to the transmitted signal over a period known as the integration time (T). The change in frequency is called the Doppler shift which is directly related to the line of sight velocity of the craft. A Doppler frequency is recorded at the end of each integration period. The craft is tracked for an observation period (τ), during which time the Doppler frequency measurements are made. At the end of an observation period there is a set of Doppler frequency shift measurements, numbering τ/T. The received frequency (f
(2) If the Doppler residual is zero then there are no
un-modelled accelerations acting on the craft. If the residual is not zero there is some
unknown acceleration acting on the craft.
In the case of the Pioneer Anomaly between 1987 and 1998 the Pioneer
Doppler residual varied at a rate of 5.99x10 The Pioneer craft Doppler drift gives an un-modelled
acceleration of -8.168x10 It is the Doppler residual converted into a Doppler
velocity which is used for analysis of the anomalous acceleration. For Pioneer 10 the Doppler residual is
7.7x10 The measured Doppler velocity can be modelled between 1987 and 1998. Graph 1, Plot of the Doppler velocity of
Pioneer 10 between 1987 and 1998, according to the model presented here. This plot corresponds with that presented by Anderson et al.[ii] in 2002 in a report of the Pioneer Anomaly. Graph 1 shows that over an extended observation period the Doppler velocity increases to relatively sizeable values. Over the 11.5 years of this initial observation Pioneer 10 became 57 500 Km out of position compared to a distance travelled of 30 A.U. |

[i]
Anderson, J.D., et al., 2002, ‘Study
of the anomalous acceleration of Pioneer 10 and 11’, Phys. Rev. D **65**, 082004

[ii]

‘Indication
from Pioneer 10/11, Galileo, and Ulysses Data, of an Apparent

Anomalous,
Weak, Long-Range Acceleration’, Phys. Rev. Lett. **81**, 2858