The JPL team continued to monitor the unexpected anomalous accelerations of Pioneer 10 and 11. Eventually, a proposal was made to NASA to initiate a formal study. The proposal argued that the anomaly is evident in the data of both spacecraft; that no physical model available can explain the puzzling behavior; and that, perhaps, an investigation with two independent software codes is needed to exclude the possibility of a systematic error in the navigational software. NASA supported the proposed investigation and, in 1995, the formal study was initiated at JPL and, independently, at the Aerospace Corporation, focusing solely on the acceleration anomaly detected in the radiometric Doppler data of both spacecraft Pioneer 10 and 11.
Acceleration estimates for Pioneer 10 and 11 were developed at the JPL using the Orbit Determination Program (ODP). The independent analysis performed by The Aerospace Corporation utilized a different software package called Compact High Accuracy Satellite Motion Program (CHASMP). This effort confirmed the presence of the anomalous acceleration, excluded computational systematics as a likely cause, and also indicated a possible detection of a sunward acceleration anomaly in the Galileo and Ulysses spacecrafts’ signals.
Standard navigational models account for a number of post-Newtonian perturbations in the dynamics of the planets, the Moon, and spacecraft. Models for light propagation are correct to order . The equations of motion of extended celestial bodies are valid to order . Nongravitational effects, such as solar radiation pressure and precessional attitude-control maneuvers, make small contributions to the apparent acceleration we have observed. The solar radiation pressure decreases as ; at distances 10 – 15 AU it produces an acceleration in the case of the Pioneer 10 and 11 spacecraft that is much less than , directed away from the Sun. (The acceleration due to the solar wind is roughly a hundred times smaller than this.)
The initial results of both teams (JPL and The Aerospace Corporation) were published in 1998 . The JPL group concluded that there is indeed an unmodeled acceleration, , towards the Sun, the magnitude of which is for Pioneer 10 and for Pioneer 11. The formal error is determined by the use of a five-day batch sequential filter with radial acceleration as a stochastic parameter, subject to white Gaussian noise ( 500 independent five-day samples of radial acceleration). No magnitude variation of with distance was found, within a sensitivity of over a range of 40 to 60 AU.
To determine whether or not the anomalous acceleration is specific to the spacecraft, an attempt was made to detect any anomalous acceleration signal in the tracking data of the Galileo and Ulysses spacecraft. It soon became clear that in the case of Galileo, the effects of solar radiation and an anomalous acceleration component cannot be separated. For Ulysses, however, a possible sunward anomalous acceleration was seen in the data, at . Thus, the data from the Galileo and Ulysses spacecraft yielded ambiguous results for the anomalous acceleration. Nevertheless, the analysis of data from these two additional spacecraft was useful in that it ruled out the possibility of a systematic error in the DSN Doppler system that could easily have been mistaken as a spacecraft acceleration.
The systematic error found in the Pioneer 10/11 post-fit residuals could not be eliminated by taking into account all known gravitational and nongravitational forces, both internal and external to the spacecraft. A number of potential causes have been ruled out. Continuing the search for an explanation, the authors considered the following forces and effects:
Other possible sources of error were considered but none found to be able to explain the puzzling behavior of the two Pioneer spacecraft.
The availability of further data (the data spanned January 1987 to July 1998) from the then-still-active Pioneer 10 spacecraft allowed the collaboration to publish a revised solution for . In 1999, based partially on this extended data set, they published a new estimate of the average Pioneer 10 acceleration directed towards the Sun, which was found to be . The analyses used JPL’s Export Planetary Ephemeris DE200, and modeled planetary perturbations, general relativistic corrections, the Earth’s nonuniform rotation and polar rotation, and effects of radiation pressure and the interplanetary medium.
A possible systematic explanation of the anomalous residuals is nonisotropic thermal radiation. The thermal power of the spacecrafts’ radioisotope thermoelectric generators was in excess of 2500 W at launch with a half-life for the 238Pu fuel of 87.74 years, and most of this power was thermally radiated into space. The power needed to explain the anomalous acceleration is 65 W. Nonetheless, anisotropically emitted thermal radiation was not seen as a likely explanation, for two reasons: first, it was assumed, after an initial analysis of the spacecraft’s geometry, that the thermal radiation would be largely isotropic, and further, the observed acceleration did not appear to be consistent with the decay rate of the radioactive fuel.
As a result of this work, it became clear that a detailed investigation of the Pioneer anomaly was needed.
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