5.2 The 2002 formal solution for the anomalous acceleration

The most definitive study to date of the Pioneer anomaly [27Jump To The Next Citation Point] used Pioneer 10 data from January 3, 1987 to July 22, 1998, and Pioneer 11 data from January 5, 1987 to October 1, 1990 (at this time, Pioneer 11 lost coherent mode capability, as described in Section 2.2.7). The data were again analyzed with two independently developed software packages, JPL’s ODP and The Aerospace Corporation’s CHASMP.

Following an analysis of the anomalous spin behavior of Pioneer 10 (see Section 2.3.7, and also Figure 2.16View Image), the Pioneer 10 data set was further divided into three intervals. Interval I contained data January 3, 1987 to July 17, 1990; Interval II, from July 17, 1990 to July 12, 1992; and Interval III, from July 12, 1992 to July 22, 1998 (Table 5.1).

Analysis of results shown in Table 5.1 let the collaboration develop their estimate for the baseline “experimental” values for Pioneer 10 and 11 [27Jump To The Next Citation Point]. They found the optimally weighted least-squares solution “experimental” number for Pioneer 10:

aPio10= (7.84 ± 0.01) × 10 −10 m ∕s2. (5.1 ) exp
Similarly, the experimental value for Pioneer 11 was found to be:
aPio11= (8.55 ± 0.02) × 10− 10 m ∕s2. (5.2 ) exp
View Image

Figure 5.2: Left: Two-way Doppler residuals (observed Doppler velocity minus model Doppler velocity) for Pioneer 10. On the vertical axis, 1 Hz is equal to 65 mm/s range change per second. Right: The best fit for the Pioneer 10 Doppler residuals with the anomalous acceleration taken out. After adding one more parameter to the model (a constant radial acceleration of aP = (8.74 ± 1.33) × 10− 10 m ∕s2) the residuals are distributed about zero Doppler velocity with a systematic variation ∼ 3.0 mm/s on a time scale of ∼ 3 months [27Jump To The Next Citation Point].



Table 5.1: Acceleration estimates (in units of 10–10 m/s2) published in [27Jump To The Next Citation Point]. Two programs (JPL’s ODP and The Aerospace Corporation’s CHASMP) were used to obtain weighted least squares (WLS) and batch-sequential filtering (BSF, 1-day batch) estimates. CHASMP could also incorporate corrections based on 10.7 cm solar flux observations, called F10.7 corrections.
Program Method Corona P10 (I) P10 (II) P10 (III) P11
ODP WLS no 8.02 ± 0.01 8.65 ± 0.01 7.83 ± 0.01 8.64 ± 0.04
ODP WLS yes 8.00 ± 0.01 8.66 ± 0.01 7.84 ± 0.01 8.44 ± 0.04
ODP BSF yes 7.82 ± 0.29 8.16 ± 0.40 7.59 ± 0.22 8.49 ± 0.33
CHASMP WLS no 8.25 ± 0.02 8.86 ± 0.02 7.85 ± 0.01 8.71 ± 0.03
CHASMP WLS yes 8.22 ± 0.02 8.89 ± 0.02 7.92 ± 0.01 8.69 ± 0.03
CHASMP WLS+F10.7 yes 8.25 ± 0.03 8.90 ± 0.03 7.91 ± 0.01 8.91 ± 0.04

The main conclusions of the 2002 study [27Jump To The Next Citation Point] can be summarized as follows:

Initial announcement of the anomalous acceleration (e.g., [24Jump To The Next Citation Point390Jump To The Next Citation Point]) triggered many proposals that invoked various conventional physics mechanisms, all aimed at explaining the origin of the anomaly. Finding a systematic origin of the proper magnitude and behavior was the main focus of these proposals. Although the most obvious explanation would be that there is a systematic origin to the effect, perhaps generated by the spacecraft themselves from anisotropic heat rejection or propulsive gas leaks, the analysis did not find evidence for either mechanism: That is, no unambiguous, on-board systematic has been discovered.

This initial search was summarized in [27Jump To The Next Citation Point28], where possible contributions of various mechanisms to the final solution for aP were given. The entire error budget was subdivided in three main types of effects, namely i) effects due to sources external to the spacecraft; ii) the contribution of on-board systematics; and iii) computational systematic errors (see Table 5.2.) These three categories are detailed in the following sections.


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