Study of the Pioneer anomaly: A problem set

American Journal of Physics

Volumn 73, Issue 11, 2005, Pages 1033-1044

  Turyshev, Slava G ^a   Nieto, Michael Martin ^b   Anderson, John D ^a  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^b LOS ALAMOS NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 27744432568     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.2008300     Document Type: Article

References (29)

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3. To be precise, the data analyzed in Ref. 2 was taken between 3 January 1987 and 22 July 1998 for Pioneer 10 (when the craft was 40 to 70.5 AU distant from the Sun), and that from Pioneer 11 was obtained between 5 January 1987 and 1 October 1990 (22.4 to 31.7 AU).
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25. -5 G.
26. G. W. Null, "Gravity field of Jupiter and its satellites from Pioneer 10 and Pioneer 11 tracking data," Astron. J. 81, 1153-1161 (1976).
27. The NASA Deep Space Network (DSN) is an international network of antennae spread nearly equidistantly around the Earth with one complex being situated in Goldstone, CA, the second one near Canberra, Australia, and the third one near Madrid, Spain (Ref. 2). For more details, see (http://deepspace.jpl.nasa.gov/ dsn/).
28. To determine the state of the spacecraft at any given time, the Jet Propulsion Laboratory's orbit determination program uses a batch-sequential filtering and smoothing algorithm with process noise (Ref. 2). For this algorithm, any small anomalous forces may be treated as stochastic pa-rameters affecting the spacecraft's trajectory. As such, these parameters are also responsible for the stochastic noise in the observational data. To better characterize these noise sources, the data interval is split into a number of constant or variable size intervals, called "batches," and assumptions are made for statistical properties of these noise factors. The mean values and the second moments of the unknown parameters are estimated within the batch. In batch sequential filtering, the reference trajectory is updated after each batch to reflect the best estimate of the true trajectory. (For more details consult Ref. 2 and references therein.)
29. We use the symbol b to identify biases in the measured value of the Pioneer anomaly produced by various sources of acceleration noise. The uncertainty in the contribution of these noise sources to the anomalous acceleration is conventionally denoted by σ. See an example of this usage in Eq. (21).