Item | Description of error budget constituents | Bias | Uncertainty |
10–10 m/s2 | 10–10 m/s2 | ||
1 | Systematics generated external to the spacecraft: | ||
a) Solar radiation pressure and mass | +0.03 | ± 0.01 | |
b) Solar wind | ± < 10–5 | ||
c) Solar corona | ± 0.02 | ||
d) Electro-magnetic Lorentz forces | ± < 10–4 | ||
e) Influence of the Kuiper belt’s gravity | ± 0.03 | ||
f) Influence of the Earth’s orientation | ± 0.001 | ||
g) Mechanical and phase stability of DSN antennae | ± < 0.001 | ||
h) Phase stability and clocks | ± < 0.001 | ||
i) DSN station location | ± < 10–5 | ||
j) Troposphere and ionosphere | ± < 0.001 | ||
2 | On-board generated systematics: | ||
a) Radio beam reaction force | +1.10* | ± 0.11 | |
b) RTG heat reflected off the craft | –0.55* | ± 0.55 | |
c) Differential emissivity of the RTGs | ± 0.85 | ||
d) Nonisotropic radiative cooling of the spacecraft | 0.00* | ± 0.48 | |
e) Expelled Helium produced within the RTGs | +0.15 | ± 0.16 | |
f) Gas leakage | ± 0.56 | ||
g) Variation between spacecraft determinations | +0.17 | ± 0.17 | |
3 | Computational systematics: | ||
a) Numerical stability of least-squares estimation | ± 0.02 | ||
b) Accuracy of consistency/model tests | ± 0.13 | ||
c) Mismodeling of maneuvers | ± 0.01 | ||
d) Mismodeling of the solar corona | ± 0.02 | ||
e) Annual/diurnal terms | ± 0.32 | ||
Estimate of total bias/error | +0.90 | ± 1.33 | |
The results of the 2002 study [27] are summarized in Table 5.2. Sources that contribute to the overall
bias and error budget are grouped depending on their origin: external to the spacecraft, generated on-board,
or computational in nature. Sources of error are treated as uncorrelated; the combined error is the root sum
square of the individual error values.
The contribution of effects in the first group in Table 5.2, that is, effects external to the spacecraft to
the overall error budget is negligible: . The second group (on-board effects)
yields the largest error contribution:
. Lastly, computational systematics
amount to
.
Similarly, the largest contribution to bias comes from on-board effects: , a
value that is dominated by the radio beam reaction force. External effects contribute a bias of
, while computational systematics contribute no bias.
Note that several items in Table 5.2 are marked with an asterisk, indicating that these items are the subject of an on-going new investigation of the Pioneer anomaly (discussed in Section 7).
The bias (third column) and error (fourth column) in Table 5.2 give the final acceleration result in the form
where is the reported formal solution for the Pioneer anomaly that was obtained with the data set available prior to 2002 [27 The 2002 analysis demonstrated that after accounting for the gravitational and other large forces
included in standard orbit determination programs [24, 27
, 392
], the anomaly in the Doppler frequency
blue shift drift is uniformly changing with a rate of
[391
] (see
Figure 5.2
). Let us denote the frequency of the signal observed by a DSN antenna as
, and the
predicted frequency of that signal after modeling conventional forces and other signal propagation effects as
. Then, for a one-way signal, the observed anomalous effect to first order in
is given by
. This translates to
Since the publication of the 2002 study [27], many proposals have been put forth offering theoretical
explanations of the anomaly. These are reviewed in the next section (Section 6). On the other hand, our
knowledge of the anomaly also improved. The existence and magnitude of the anomalous acceleration has
been confirmed by several independent researchers. Others have attempted to model the thermal behavior
of the spacecraft, arguing that the magnitude of thermal recoil forces might have been underestimated by
the 2002 study. The recovery of essentially all Pioneer 10 and 11 telemetry, as well as large quantities of
archived project documentation, raised hope that it might be possible to construct a sufficiently
accurate thermal model of the spacecraft using modeling software, and properly estimate the
magnitude of the thermal recoil force. This remains one of several open, unresolved questions
that, hopefully, will be answered in the near future as a result of on-going study, as detailed in
Section 7.
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