PDF《Support for the thermal origin of》

arXiv:1204.

2507v1 [gr-qc]

11 Apr

2012 Support for the thermal origin of the Pioneer anomaly Slava G. Turyshev1 , Viktor T. Toth2 , Gary Kinsella1 , Siu-Chun Lee3 , Shing M. Lok3 , and Jordan Ellis1

1 Jet Propulsion Laboratory, California Institute of Technology,

4800 Oak Grove Drive, Pasadena, CA 91109-0899, USA

2 Ottawa, ON K1N 9H5, Canada and

3 Applied Sciences Laboratory,

13111 Brooks Drive, Suite A, Baldwin Park, CA 91706-7902, USA We investigate the possibility that the anomalous acceleration of the Pioneer

10 and

11 space- craft is due to the recoil force associated with an anisotropic emission of thermal radiation o? the vehicles. To this end, relying on the project and spacecraft design documentation, we constructed a comprehensive ?nite-element thermal model of the two spacecraft. Then, we numerically solve thermal conduction and radiation equations using the actual ?ight telemetry as boundary condi- tions. We use the results of this model to evaluate the e?ect of the thermal recoil force on the Pioneer

10 spacecraft at various heliocentric distances. We found that the magnitude, temporal behavior, and direction of the resulting thermal acceleration are all similar to the properties of the observed anomaly. As a novel element of our investigation, we develop a parameterized model for the thermal recoil force and estimate the coe?cients of this model independently from navigational Doppler data. We ?nd no statistically signi?cant di?erence between the two estimates and conclude that once the thermal recoil force is properly accounted for, no anomalous acceleration remains. PACS numbers: 04.80.-y, 95.10.Eg, 95.55.Pe INTRODUCTION The anomalous acceleration of the Pioneer

10 and

11 spacecraft [1] is a discrepancy between modeled and ob- served radio-metric Doppler data received from the two vehicles. The discrepancy can be eliminated by incorpo- rating a constant sunward acceleration of unknown origin with magnitude of aP = (8.74 ± 1.33) * 10?10 m/s

2 into the orbital model [2]. The presence of this acceleration, which became known as the Pioneer anomaly, was seen by many as a breakdown in the gravitational inverse- square law of general relativity that reveals itself in the dynamics of the outer solar system. There were also pro- posals that this anomaly was due, at least in part, to the waste heat emitted by the spacecrafts'

radioisotope ther- moelectric generators (RTGs) [3], their electrical subsys- tems [4], or both [5], motivating a thorough investigation of the spacecraft systematics (for review, see [6]). Our current investigation began with the recovery of the entire telemetry record of both spacecraft, substan- tial project documentation, and additional Doppler data [7]. The analysis of the extended Doppler data set was completed recently [8], con?rming the existence of the anomaly. This analysis also showed that although the direction of the anomalous acceleration cannot be deter- mined unambiguously, the Doppler residuals improve if one considers a temporally varying acceleration in the direction of the Earth, which is consistent with earlier, similar results [9, 10]. These results are suggestive: If the acceleration were due to thermal recoil force, it would be along the spacecraft spin axis, which generally points in the direction of the Earth and would have temporally decreasing magnitude consistent with the decay of the on-board radioisotope fuel (Pu238 ). In this Letter we report on the completion of a ?nite- element thermal model of the Pioneer

10 spacecraft. This model relies extensively on the project and spacecraft design documentation and was validated using redun- dant ?ight telemetry data. A parameterized form of the thermal force model [11] was also incorporated into a Doppler analysis, which yielded an independent estimate of coe?cients characterizing the thermal recoil force. We compare the outputs of the two independent analyses C Doppler and thermal C to show that no statistically sig- ni?cant anomalous acceleration remains in the data. FINITE-ELEMENT THERMAL MODEL A comprehensive ?nite-element (FE) thermal model (Fig. 1) of the Pioneer