Study of the anomalous acceleration of Pioneer 10 and 11 John D. Anderson,∗a Philip A. Laing,†b Eunice L. Lau,‡a Anthony S. Liu,§c Michael Martin Nieto,¶d and Slava G. Turyshev∗∗a aJet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109 bThe Aerospace Corporation, 2350 E. El Segundo Blvd., El Segundo, CA 90245-4691 cAstrodynamic Sciences, 2393 Silver Ridge Ave., Los Angeles, CA 90039 dTheoretical Division (MS-B285), Los Alamos National Laboratory, University of California, Los Alamos, NM 87545 (Dated: 11 April 2002) Our previous analyses of radio Doppler and ranging data from distant spacecraft in the solar system indicated that an apparent anomalous acceleration is acting on Pioneer 10 and 11, with a −8 2 magnitude aP ∼ 8 × 10 cm/s , directed towards the Sun. Much effort has been expended looking for possible systematic origins of the residuals, but none has been found. A detailed investigation of effects both external to and internal to the spacecraft, as well as those due to modeling and compu- tational techniques, is provided. We also discuss the methods, theoretical models, and experimental techniques used to detect and study small forces acting on interplanetary spacecraft. These include the methods of radio Doppler data collection, data editing, and data reduction. There is now further data for the Pioneer 10 orbit determination. The extended Pioneer 10 data set spans 3 January 1987 to 22 July 1998. [For Pioneer 11 the shorter span goes from 5 January 1987 to the time of loss of coherent data on 1 October 1990.] With these data sets and more −8 2 detailed studies of all the systematics, we now give a result, of aP = (8.74 ± 1.33) × 10 cm/s . (Annual/diurnal variations on top of aP , that leave aP unchanged, are also reported and discussed.) PACS numbers: 04.80.-y, 95.10.Eg, 95.55.Pe I. INTRODUCTION at approximately 4.28 and 7.8 revolutions per minute (rpm), respectively, with the spin axes running through the centers of the dish antennae. Their spin-stabilizations Some thirty years ago, on 2 March 1972, Pioneer 10 and great distances from the Earth imply a minimum was launched on an Atlas/Centaur rocket from Cape number of Earth-attitude reorientation maneuvers are re- Canaveral. Pioneer 10 was Earth’s first space probe to quired. This permits precise acceleration estimations, to an outer planet. Surviving intense radiation, it success- the level of 10−8 cm/s2 (single measurement accuracy av- fully encountered Jupiter on 4 December 1973 [1]-[6]. In eraged over 5 days). Contrariwise, a Voyager-type three- trail-blazing the exploration of the outer solar system, axis stabilized spacecraft is not well suited for a precise Pioneer 10 paved the way for, among others, Pioneer celestial mechanics experiment as its numerous attitude- 11 (launched on 5 April 1973), the Voyagers, Galileo, control maneuvers can overwhelm the signal of a small Ulysses, and the upcoming Cassini encounter with Sat- external acceleration. urn. After Jupiter and (for Pioneer 11) Saturn encoun- In summary, Pioneer spacecraft represent an ideal sys- arXiv:gr-qc/0104064v5 10 Mar 2005 ters, the two spacecraft followed hyperbolic orbits near tem to perform precision celestial mechanics experiments. the plane of the ecliptic to opposite sides of the solar sys- It is relatively easy to model the spacecraft’s behavior tem. Pioneer 10 was also the first mission to enter the and, therefore, to study small forces affecting its motion edge of interstellar space. That major event occurred in in the dynamical environment of the solar system. In- June 1983, when Pioneer 10 became the first spacecraft deed, one of the main objectives of the Pioneer extended to “leave the solar system” as it passed beyond the orbit missions (post Jupiter/Saturn encounters) [5] was to per- of the farthest known planet. form accurate celestial mechanics experiments. For in- The scientific data collected by Pioneer 10/11 has stance, an attempt was made to detect the presence of yielded unique information about the outer region of the small bodies in the solar system, primarily in the Kuiper solar system. This is due in part to the spin-stabilization belt. It was hoped that a small perturbation of the of the Pioneer spacecraft. At launch they were spinning spacecraft’s trajectory would reveal the presence of these objects [7]-[9]. Furthermore, due to extremely precise navigation and a high quality tracking data, the Pioneer 10 scientific program also included a search for low fre- ∗Electronic address: [email protected] quency gravitational waves [10, 11]. †Electronic address: [email protected] ‡ Beginning in 1980, when at a distance of 20 astronom- Electronic address: [email protected] ical units (AU) from the Sun the solar-radiation-pressure §Deceased (13 November 2000). ¶Electronic address: [email protected] acceleration on Pioneer 10 away from the Sun had de- ∗∗[email protected] creased to < 5 10−8 cm/s2, we found that the largest × 2 systematic error in the acceleration residuals was a con- and attitude control systems, as well as thermal and com- stant bias, aP , directed toward the Sun. Such anoma- munication systems. lous data have been continuously received ever since. Jet Since our analysis addresses certain results from the Propulsion Laboratory (JPL) and The Aerospace Corpo- Galileo and Ulysses missions, we also give short descrip- ration produced independent orbit determination analy- tions of these missions in the final subsection. ses of the Pioneer data extending up to July 1998. We ultimately concluded [12, 13], that there is an unmodeled −8 2 acceleration, aP , towards the Sun of 8 10 cm/s A. General description of the Pioneer spacecraft for both Pioneer 10 and Pioneer 11. ∼ × The purpose of this paper is to present a detailed expla- Although some of the more precise details are often nation of the analysis of the apparent anomalous, weak, difficult to uncover, the general parameters of the Pi- long-range acceleration of the Pioneer spacecraft that we oneer spacecraft are known and well documented [1]-[6]. detected in the outer regions of the solar system. We at- The two spacecraft are identical in design [14]. At launch tempt to survey all sensible forces and to estimate their each had a “weight” (mass) of 259 kg. The “dry weight” contributions to the anomalous acceleration. We will dis- of the total module was 223 kg as there were 36 kg of cuss the effects of these small non-gravitational forces hydrazine propellant [15, 16]. The spacecraft were de- (both generated on-board and external to the vehicle) on signed to fit within the three meter diameter shroud of the motion of the distant spacecraft together with the an added third stage to the Atlas/Centaur launch vehi- methods used to collect and process the radio Doppler cle. Each spacecraft is 2.9 m long from its base to its navigational data. cone-shaped medium-gain antenna. The high gain an- We begin with descriptions of the spacecraft and other tenna (HGA) is made of aluminum honeycomb sandwich systems and the strategies for obtaining and analyzing material. It is 2.74 m in diameter and 46 cm deep in the information from them. In Section II we describe the shape of a parabolic dish. (See Figures 1 and 2.) Pioneer (and other) spacecraft. We provide the reader with important technical information on the spacecraft, much of which is not easily accessible. In Section III we describe how raw data is obtained and analyzed and in Section IV we discuss the basic elements of a theoretical foundation for spacecraft navigation in the solar system. The next major part of this manuscript is a description and analysis of the results of this investigation. We first describe how the anomalous acceleration was originally identified from the data of all the spacecraft in Section V [12, 13]. We then give our recent results in Section VI. In the following three sections we discuss possible experimental systematic origins for the signal. These in- clude systematics generated by physical phenomena from sources external to (Section VII) and internal to (Sec- tion VIII) the spacecraft. This is followed by Section IX, where the accuracy of the solution for aP is discussed. In the process we go over possible numerical/calculational errors/systematics. Sections VII-IX are then summarized in the total error budget of Section X. We end our presentation by first considering possible unexpected physical origins for the anomaly (Section XI). In our conclusion, Section XII, we summarize our results and suggest venues for further study of the discovered anomaly. FIG. 1: NASA photo #72HC94, with caption “The Pioneer F spacecraft during a checkout with the launch vehicle third stage at Cape Kennedy.” Pioneer F became Pioneer 10. II. THE PIONEER AND OTHER SPACECRAFT The main equipment compartment is 36 cm deep. In this section we describe in some detail the Pioneer The hexagonal flat top and bottom have 71 cm long 10 and 11 spacecraft and their missions. We concentrate sides. The equipment compartment provides a thermally on those spacecraft systems that play important roles in controlled environment for scientific instruments. Two maintaining the continued function of the vehicles and three-rod trusses, 120 degrees apart, project from two in determining their dynamical behavior in the solar sys- sides of the equipment compartment. At their ends, each tem. Specifically we present an overview of propulsion holds two SNAP-19 (Space Nuclear Auxiliary Power, 3 FIG. 2: A drawing of the Pioneer spacecraft. model 19) RTGs (Radioisotope Thermoelectric Gener- B. Propulsion and attitude control systems ators) built by Teledyne Isotopes for the Atomic En- ergy Commission.