The Pioneer anomaly or Pioneer effect is the observed deviation from predicted accelerations of the Pioneer 10 and Pioneer 11 spacecraft after they passed about 20 astronomical units (3×109 km; 2×109 mi) on their trajectories out of the Solar System. The apparent anomaly was a matter of tremendous interest for many years.
Both Pioneer spacecraft are escaping the Solar System, but are slowing under the influence of the Sun's gravity. Upon very close examination of navigational data, the spacecraft were found to be slowing slightly more than expected. The effect is an extremely small acceleration towards the Sun, of 8.74±1.33)×10−10 m/s2, which is equivalent to slowly accelerating to a velocity of 1 (kilometre per hour (0.6 mph) over a period of ten years. The two spacecraft were launched in 1972 and 1973 and the anomalous acceleration was first noticed as early as 1980, but not seriously investigated until 1994. The last communication with either spacecraft was in 2003, but analysis of recorded data continues.
Various explanations, both of spacecraft behavior and of gravitation itself, were proposed to explain the anomaly. Over the period 1998–2012, one particular explanation became accepted. The spacecraft, which are surrounded by an ultra-high vacuum and are each powered by a radioisotope thermoelectric generator (RTG), can shed heat only via thermal radiation. If, due to the design of the spacecraft, more heat is emitted in a particular direction—what is known as a radiative anisotropy—then the spacecraft would exhibit a small acceleration in the direction opposite that of the excess emitted radiation due to radiation pressure. Because this force is due to the recoil of thermal photons, it is also called the thermal recoil force. If the excess radiation and attendant radiation pressure were pointed in a general direction opposite the Sun, the spacecrafts’ velocity away from the Sun would be decelerating at a greater rate than could be explained by previously recognized forces, such as gravity and trace friction, due to the interplanetary medium (imperfect vacuum).
By 2012 several papers by different groups, all reanalyzing the thermal radiation pressure forces inherent in the spacecraft, showed that a careful accounting of this could explain the entire anomaly, and thus the cause was mundane and did not point to any new phenomena or need for a different physical paradigm. The most detailed analysis to date, by some of the original investigators, explicitly looks at two methods of estimating thermal forces, then states "We find no statistically significant difference between the two estimates and conclude that once the thermal recoil force is properly accounted for, no anomalous acceleration remains."
- 1 Description
- 2 Explanation: thermal recoil force
- 3 Previously proposed causes
- 4 Indications from other missions
- 5 Potential issues with the thermal solution
- 6 Proposed explanations
- 6.1 The deceleration model
- 6.2 Observational or recording errors
- 6.3 New physics
- 7 Further research avenues
- 8 Meetings and conferences about the anomaly
- 9 See also
- 10 Notes
- 11 References
- 12 Further reading
- 13 External links
Pioneer 10 and 11 were sent on missions to Jupiter and Jupiter/Saturn respectively. Each spacecraft was spin-stabilised in order to keep its high-gain antenna pointed towards Earth using gyroscopic forces. Although the spacecraft included thrusters, after the planetary encounters they were used only for semiannual conical scanning maneuvers to track Earth in its orbit, leaving them on a long "cruise" phase through the outer Solar System. During this period, both spacecraft were repeatedly contacted to obtain various measurements on their physical environment, providing valuable information long after their initial missions were complete.
Because the spacecraft were flying with almost no additional stabilization thrusts during their "cruise", it is possible to characterize the density of the solar medium by its effect on the spacecraft's motion. In the outer Solar System this effect would be easily calculable, based on ground-based measurements of the deep space environment. When these effects were taken into account, along with all other known effects, the calculated position of the Pioneers did not agree with measurements based on timing the return of the radio signals being sent back from the spacecraft. These consistently showed that both spacecraft were closer to the inner Solar System than they should be, by thousands of kilometres—small compared to their distance from the Sun, but still statistically significant. This apparent discrepancy grew over time as the measurements were repeated, suggesting that whatever was causing the anomaly was still acting on the spacecraft.
As the anomaly was growing, it appeared that the spacecraft were moving more slowly than expected. Measurements of the spacecraft's speed using the Doppler effect demonstrated the same thing: the observed redshift was less than expected, which meant that the Pioneers had slowed down more than expected.
When all known forces acting on the spacecraft were taken into consideration, a very small but unexplained force remained. It appeared to cause an approximately constant sunward acceleration of 8.74±1.33)×10−10m/s2}} for both spacecraft. If the positions of the spacecraft were predicted one year in advance based on measured velocity and known forces (mostly gravity), they were actually found to be some 400 km closer to the sun at the end of the year. This anomaly is now believed to be accounted for by thermal recoil forces. (
Explanation: thermal recoil force
Starting in 1998, there were suggestions that the thermal recoil force was under-estimated, and perhaps could account for the entire anomaly. However, accurately accounting for thermal forces was hard, because it needed telemetry records of the spacecraft temperatures and a detailed thermal model, neither of which was available at the time. Furthermore, all thermal models predicted a decrease in the effect with time, which did not appear in the initial analysis.
One by one these objections were addressed. Many of the old telemetry records were found, and converted to modern formats. This gave power consumption figures and some temperatures for parts of the spacecraft. Several groups built detailed thermal models, which could be checked against the known temperatures and powers, and allowed a quantitative calculation of the recoil force. The longer span of navigational records showed the acceleration was in fact decreasing.
"We investigate the possibility that the anomalous acceleration of the Pioneer 10 and 11 spacecraft is due to the recoil force associated with an anisotropic emission of thermal radiation off the vehicles. To this end, relying on the project and spacecraft design documentation, we constructed a comprehensive finite-element thermal model of the two spacecraft. Then, we numerically solve thermal conduction and radiation equations using the actual flight telemetry as boundary conditions. We use the results of this model to evaluate the effect 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 coefficients of this model independently from navigational Doppler data. We find no statistically significant difference between the two estimates and conclude that once the thermal recoil force is properly accounted for, no anomalous acceleration remains."
Although the above reference has the most detailed analysis to date, the explanation based on thermal recoil force has the support of other independent research groups, using a variety of computational techniques. Examples include "thermal recoil pressure is not the cause of the Rosetta flyby anomaly but likely resolves the anomalous acceleration observed for Pioneer 10." and "It is shown that the whole anomalous acceleration can be explained by thermal effects".
Previously proposed causes
Before the thermal recoil explanation became accepted, other proposed explanations fell into two classes — "mundane causes" or "new physics". Mundane causes include conventional effects that were overlooked or mis-modeled in the initial analysis, such as measurement error, thrust from gas leakage, or uneven heat radiation. The "new physics" explanations proposed revision of our understanding of gravitational physics.
If the Pioneer anomaly had been a gravitational effect due to some long-range modifications of the known laws of gravity, it did not affect the orbital motions of the major natural bodies in the same way (in particular those moving in the regions in which the Pioneer anomaly manifested itself in its presently known form). Hence a gravitational explanation would need to violate the equivalence principle, which states that all objects are affected the same way by gravity. It was therefore argued that increasingly accurate measurements and modelling of the motions of the outer planets and their satellites undermined the possibility that the Pioneer anomaly is a phenomenon of gravitational origin. However, others believed that our knowledge of the motions of the outer planets and dwarf planet Pluto was still insufficient to disprove the gravitational nature of the Pioneer anomaly. The same authors ruled out the existence of a gravitational Pioneer-type extra-acceleration in the outskirts of the Solar System by using a sample of Trans-Neptunian objects.
The magnitude of the Pioneer effect (8.74±1.33)×10−10 m/s2) is numerically quite close to the product ( (6.59±0.075)×10−10 m/s2) of the (speed of light and the Hubble constant , hinting at a cosmological connection, but this is now believed to be of no particular significance. In fact the latest Jet Propulsion Laboratory review (2010) undertaken by Turyshev and Toth claims to rule out the cosmological connection by considering rather conventional sources whereas other scientists provided a disproof based on the physical implications of cosmological models themselves.
Gravitationally bound objects such as the Solar System, or even the Milky Way, are not supposed to partake of the expansion of the universe—this is known both from conventional theory and by direct measurement. This does not necessarily interfere with paths new physics can take with drag effects from planetary secular accelerations of possible cosmological origin.
Indications from other missions
The Pioneers were uniquely suited to discover the effect because they have been flying for long periods of time without additional course corrections. Most deep-space probes launched after the Pioneers either stopped at one of the planets, or used thrusting throughout their mission.
The Voyagers flew a mission profile similar to the Pioneers, but were not spin stabilized. Instead, they required frequent firings of their thrusters for attitude control to stay aligned with Earth. Spacecraft like the Voyagers acquire small and unpredictable changes in speed as a side effect of the frequent attitude control firings. This 'noise' makes it impractical to measure small accelerations such as the Pioneer effect; accelerations as large as 10−9 m/s2 would be undetectable.
Newer spacecraft have used spin stabilization for some or all of their mission, including both Galileo and Ulysses. These spacecraft indicate a similar effect, although for various reasons (such as their relative proximity to the Sun) firm conclusions cannot be drawn from these sources. The Cassini mission has reaction wheels as well as thrusters for attitude control, and during cruise could rely for long periods on the reaction wheels alone, thus enabling precision measurements. It also had radioisotope thermoelectric generators (RTGs) mounted close to the spacecraft body, radiating kilowatts of heat in hard-to-predict directions.
After Cassini arrived at Saturn, it shed a large fraction of its mass from the fuel used in the insertion burn and the release of the Huygens probe. This increases the acceleration caused by the radiation forces because they are acting on less mass. This change in acceleration allows the radiation forces to be measured independently of any gravitational acceleration. Comparing cruise and Saturn-orbit results shows that for Cassini, almost all the unmodelled acceleration was due to radiation forces, with only a small residual acceleration, much smaller than the Pioneer acceleration, and with opposite sign.
Potential issues with the thermal solution
There are two features of the anomaly, as originally reported, that are not addressed by the thermal solution: periodic variations in the anomaly, and the onset of the anomaly near the orbit of Saturn.
First, the anomaly has an apparent annual periodicity and an apparent Earth sidereal daily periodicity with amplitudes that are formally greater than the error budget. However, the same paper also states this problem is most likely not related to the anomaly: "The annual and diurnal terms are very likely different manifestations of the same modeling problem. [...] Such a modeling problem arises when there are errors in any of the parameters of the spacecraft orientation with respect to the chosen reference frame."
Second, the value of the anomaly measured over a period during and after the Pioneer 11 Saturn encounter had a relatively high uncertainty and a significantly lower value. The Turyshev, et al. 2012 paper compared the thermal analysis to the Pioneer 10 only. The Pioneer anomaly was unnoticed until after Pioneer 10 passed its Saturn encounter. However, the most recent analysis states: "Figure 2 is strongly suggestive that the previously reported "onset" of the Pioneer anomaly may in fact be a simple result of mis-modeling of the solar thermal contribution; this question may be resolved with further analysis of early trajectory data".
A number of proposed explanations for acceleration towards the sun have been pursued, mostly before asymmetrical thermal emission emerged as a leading contender. These are categorized under the following: an unaccounted for real deceleration, observational errors, and explanations that would essentially be New Physics. During March 2011, experts proposed new calculations that seem to confirm that heat is the cause of the spacecraft slowing down.
The deceleration model
It has been viewed as possible that a real deceleration is not accounted for in the current model for several reasons.
Thermal radiation pressure
A real deceleration not accounted for in the model could result from asymmetrical thermal radiation pressure of the heat from the spacecraft (the effect cannot be from the radiation pressure of sunlight or the spacecraft's radio emissions as it is too small at this distance, and points in the wrong direction).
Possibilities include the asymmetrical radiation of heat from the RTGs (See Radioisotope rocket) or the spacecraft electronics. Even if the RTGs themselves radiate symmetrically, some of their radiation will reflect from the back of the spacecraft's dish-like main antenna, causing a recoil like sunlight striking a solar sail.
The asymmetrical radiation of heat remains a prime suspect, as presented at the second ISSI meeting in Bern, February 2007. A presentation at the APS April 2008 meeting suggests that differential heating may account for as much as one third of the observed acceleration.
A research team from Portugal has proposed that previous modelling used to predict the directions of radiation pressures was incorrect. By using the Phong reflection model to model diffusive and specular reflections they believe that the observed and theoretical results no longer diverge. This proposed explanation finds most of the diverging thrust in the heat from the main equipment compartment reflecting off the back of the main antenna, which would tend to produce a thrust in the direction of the sun. The Jet Propulsion Laboratory is currently attempting to confirm this explanation by studying their own thermal data.
According to Slava Turyshev of JPL in the paper "Support for temporally varying behavior of the Pioneer anomaly from the extended Pioneer 10 and 11 data sets," published in Physical Review Letters in 2011, the anomaly has a temporally-decaying (not constant as previously thought) nature and points towards Earth. This strengthens the case for on-board generated recoil forces as the reason behind the anomaly. A more recent 2012 analysis by the same group concludes that thermal forces can explain all the anomalous acceleration.
It is possible that deceleration is caused by gravitational forces from unidentified sources such as the Kuiper belt or dark matter. However, this acceleration does not show up in the orbits of the outer planets, so any generic gravitational answer would need to violate the equivalence principle (see modified inertia below). Likewise, the anomaly does not appear in the orbits of Neptune's moons, challenging the possibility that the Pioneer anomaly may be an unconventional gravitational phenomenon based on range from the Sun.
Observational or recording errors
The possibility of observational errors, which include measurement and computational errors, has been advanced as a reason for interpreting the data as an anomaly. Hence, this would result in approximation and statistical errors. However, further analysis has determined that significant errors are not likely because seven independent analyses have shown the existence of the Pioneer anomaly as of March 2010.
The effect is so small that it could be a statistical anomaly caused by differences in the way data were collected over the lifetime of the probes. Numerous changes were made over this period, including changes in the receiving instruments, reception sites, data recording systems and recording formats.
Because the "Pioneer anomaly" does not show up as an effect on the planets, Anderson et al. speculated that this would be interesting if this was new physics. Later, with the Doppler shifted signal confirmed, the team again speculated that one explanation may lie with new physics, if not some unknown systemic explanation.
Clock acceleration is an alternate explanation to anomalous acceleration of the spacecraft towards the Sun. This theory takes notice of an expanding universe, which creates an increasing background 'gravitational potential'. The increased gravitational potential then accelerates cosmological time. It is proposed that this particular effect causes the observed deviation from predicted trajectories and velocities of Pioneer 10 and Pioneer 11.
From their data, Anderson's team deduced a steady frequency drift of 1.5 Hz over 8 years. This could be mapped on to a clock acceleration theory, which means all clocks would be changing in relation to a constant acceleration. In other words, that there would be a non-uniformity of time. Moreover, for such a distortion related to time, Anderson's team reviewed several models in which time distortion as a phenomenon is considered. They arrived at the "clock acceleration" model after completion of the review. Although the best model adds a quadratic term to defined International Atomic Time, the team encountered problems with this theory. This then led to non-uniform time in relation to a constant acceleration as the most likely theory.[note 1]
Definition of gravity modified
|This section's factual accuracy is disputed. (January 2014)|
The Modified Newtonian dynamics or MOND hypothesis proposes that the force of gravity deviates from the traditional Newtonian value to a very different force law at very low accelerations on the order of 10−10 m/s2. Given the low accelerations placed on the spacecraft while in the outer Solar System, MOND may be in effect, modifying the normal gravitational equations. The Lunar Laser Ranging experiment combined with data of LAGEOS satellites refutes that simple gravity modification is the cause of the Pioneer anomaly. The precession of the longitudes of perihelia of the solar planets or the trajectories of long-period comets have not been reported to experience an anomalous gravitational field toward the Sun of the magnitude capable of describing the Pioneer anomaly.
Definition of inertia modified
MOND can also be interpreted as a modification of inertia, perhaps due to an interaction with vacuum energy, and such a trajectory-dependent theory could account for the different accelerations apparently acting on the orbiting planets and the Pioneer craft on their escape trajectories. A model of inertia using Unruh radiation and a Hubble-scale Casimir effect, which, unlike MOND, has no adjustable parameters, has been proposed to explain the Pioneer anomaly and the flyby anomaly. A possible terrestrial test for evidence of a different model of modified inertia has also been proposed.
Another theoretical explanation is based on a possible non-equivalence of the atomic time and the astronomical time, which can give the same observational fingerprint as the anomaly.
Celestial ephemerides in an expanding universe
A rather straightforward explanation of Pioneer anomaly can be achieved if one takes into account that the background spacetime is described by cosmological Friedmann–Lemaître–Robertson–Walker metric that is not Minkowski flat. In this model of spacetime manifold, light moves uniformly with respect to the conformal cosmological time whereas physical measurements are performed with the help of atomic clocks that count the proper time of observer coinciding with the cosmic time. The difference between the conformal and cosmic times yields exactly the same numerical value and signature of the anomalous, blue Doppler shift effect that was measured in the Pioneer experiment. A small discrepancy between this theoretical prediction and the measured value of the Pioneer effect is a clear evidence of the presence of the thermal recoil that accounts up only to 10–20 percent of the overall effect. If the origin of the Pioneer effect is cosmological, it gives a direct access to measuring the numerical value of the Hubble constant independently of observations of the cosmic microwave background radiation or supernova explosions in distant galaxies (Supernova Cosmology Project).
Further research avenues
It is possible, but not proven, that this anomaly is linked to the flyby anomaly, which has been observed in other spacecraft. Although the circumstances are very different (planet flyby vs. deep space cruise), the overall effect is similar—a small but unexplained velocity change is observed on top of a much larger conventional gravitational acceleration.
The Pioneer spacecraft are no longer providing new data (the last contact having been on 23 January 2003) and Galileo was deliberately burned up in Jupiter's atmosphere at the end of its mission. So far, attempts to use data from current missions such as Cassini have not yielded any conclusive results. There are several remaining options for further research:
- Further analysis of the retrieved Pioneer data. This includes not only the data that was first used to detect the anomaly, but additional data that until recently was saved only in older, inaccessible computer formats and media. This data was recovered in 2006, converted to more modern formats, and is now available for analysis.
- The New Horizons spacecraft to Pluto is spin-stabilised for much of its cruise, and there is a possibility that it can be used to investigate the anomaly. New Horizons may have the same problem that precluded good data from the Cassini mission—its RTG is mounted close to the spacecraft body, so thermal radiation from it, bouncing off the spacecraft, may produce a systematic thrust of a not-easily predicted magnitude, several times as large as the Pioneer effect. Nevertheless efforts are underway to study the non-gravimetric accelerations on the spacecraft, in the hopes of having them well modeled for the long cruise to Pluto after the Jupiter fly-by that occurred in February 2007. In particular, despite any large systematic bias from the RTG, the 'onset' of the anomaly at or near the orbit of Saturn might be observed.
- A dedicated mission has also been proposed. Such a mission would probably need to surpass 200 AU from the Sun in a hyperbolic escape orbit.
- Observations of asteroids around 20 AU may provide insights if the anomaly's cause is gravitational.
Meetings and conferences about the anomaly
The Pioneer Explorer Collaboration was formed to study the Pioneer Anomaly and has hosted three meetings (2005, 2007, and 2008) at International Space Science Institute in Bern, Switzerland to discuss the anomaly, and discuss possible means for resolving the source.
- Flyby anomaly
- Galaxy rotation problem
- Modified Newtonian dynamics
- General relativity
- Unsolved problems in physics
- non-uniform time in relation to a constant acceleration is a summarized term derived from the source or sources used for this sub-section.
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- Nieto, M. M.; Turyshev, S. G.; Anderson, J. D. (2005). "Directly measured limit on the interplanetary matter density from Pioneer 10 and 11". Physics Letters B 613 (1–2): 11. arXiv:astro-ph/0501626. Bibcode:2005PhLB..613...11N. doi:10.1016/j.physletb.2005.03.035.
- Milgrom, M. (1999). "The Modified Dynamics as a vacuum effect". Physics Letters A 253 (5–6): 273. arXiv:astro-ph/9805346. Bibcode:1999PhLA..253..273M. doi:10.1016/S0375-9601(99)00077-8.
- McCulloch, M. E. (2007). "Modelling the Pioneer anomaly as modified inertia". Monthly Notices of the Royal Astronomical Society 376 (1): 338–342. arXiv:astro-ph/0612599. Bibcode:2007MNRAS.376..338M. doi:10.1111/j.1365-2966.2007.11433.x.
- McCulloch, M. E. (2008). "Modelling the flyby anomalies using a modification of inertia". Monthly Notices of the Royal Astronomical Society Letters 389 (1): L57–60. arXiv:0806.4159. Bibcode:2008MNRAS.389L..57M. doi:10.1111/j.1745-3933.2008.00523.x.
- Ignatiev, A. Yu. (2007). "Is violation of Newton's second law possible?". Physical Review Letters 98 (10): 101101. arXiv:gr-qc/0612159. Bibcode:2007PhRvL..98j1101I. doi:10.1103/PhysRevLett.98.101101.
- Rañada, A. F.; Tiemblo, A. (2012). "Parametric invariance and the Pioneer anomaly". Canadian Journal of Physics 90: 931–937. arXiv:1106.4400. Bibcode:2012CaJPh..90..931R. doi:10.1139/p2012-086. Antonio Fernández-Rañada and Alfredo Tiemblo-Ramos propose "an explanation of the Pioneer anomaly that is a refinement of a previous one and is fully compatible with the cartography of the solar system. It is based on the non-equivalence of the atomic time and the astronomical time that happens to have the same observational fingerprint as the anomaly."
- Kopeikin, S. M. (2012). "Celestial Ephemerides in an Expanding Universe". Physical Review D 86: 064004. arXiv:1207.3873. Bibcode:2012PhRvD..86f4004K. doi:10.1103/PhysRevD.86.064004.
- Choi, C. Q. (3 March 2008). "NASA Baffled by Unexplained Force Acting on Space Probes". Space.com. Retrieved 2011-02-12.
- "The Pioneer Missions". NASA. 26 July 2003. Retrieved 2015-05-07.
- "Data Saved!". Planetary Society. 1 June 2006. Archived from the original on 2012-04-18.
- Nieto, M. M. (2008). "New Horizons and the Onset of the Pioneer Anomaly". Physics Letters B 659 (3): 483. arXiv:0710.5135. Bibcode:2008PhLB..659..483N. doi:10.1016/j.physletb.2007.11.067.
- "Pioneer anomaly put to the test". Physics World. 1 September 2004. Retrieved 2009-05-17.
- Clark, S. (10 May 2005). "Lost asteroid clue to Pioneer puzzle". New Scientist. Retrieved 2009-01-10.
- "Conference on The Pioneer Anomaly - Observations, Attempts at Explanation, Further Exploration". Center of Applied Space Technology and Microgravity. Retrieved 2012-02-12.
- "The Pioneer Explorer Collaboration: Investigation of the Pioneer Anomaly at ISSI". International Space Science Institute. 18 February 2008. Retrieved 2015-05-07.
- Anderson, J D.; Laing, P. A.; Lau, E. L.; Liu, A. S.; Nieto, M. M.; Turyshev, S. G. (1998). "Indication, from Pioneer 10/11, Galileo, and Ulysses Data, of an Apparent Anomalous, Weak, Long-Range Acceleration". Physical Review Letters 81 (14): 2858–2861. arXiv:gr-qc/9808081. Bibcode:1998PhRvL..81.2858A. doi:10.1103/PhysRevLett.81.2858.
- The original paper describing the anomaly
- Anderson, J D.; Laing, P. A.; Lau, E. L.; Liu, A. S.; Nieto, M. M.; Turyshev, S. G. (2002). "Study of the anomalous acceleration of Pioneer 10 and 11". Physical Review D 65 (8): 082004. arXiv:gr-qc/0104064. Bibcode:2002PhRvD..65h2004A. doi:10.1103/PhysRevD.65.082004.
- A lengthy survey of several years of debate by the authors of the original 1998 paper documenting the anomaly. The authors conclude, "Until more is known, we must admit that the most likely cause of this effect is an unknown systematic. (We ourselves are divided as to whether 'gas leaks' or 'heat' is this 'most likely cause.')"
The ISSI meeting above has an excellent reference list divided into sections such as primary references, attempts at explanation, proposals for new physics, possible new missions, popular press, and so on. A sampling of these are shown here:
- Musser, George (December 1998). "Pioneering Gas Leak?". Scientific American 279 (6): 26–27. Bibcode:1998SciAm.279f..26M. doi:10.1038/scientificamerican1298-26b.
- Reardon, A. C. (2011). "Gravitational Analysis of V541 Cygni, DI Herculis, and the Pioneer anomaly". Astrophysics and Space Science, Vol. 336, No. 2 369–377,  Theory establishes a gravitational connection between the unexplained periastron advance observed in two binary star systems and the Pioneer anomaly.
- Anderson, J. D.; Turyshev, S. G.; Nieto, M. M. (2002). "A mission to test the Pioneer anomaly". International Journal of Modern Physics D 11 (10): 1545. arXiv:gr-qc/0205059. Bibcode:2002IJMPD..11.1545A. doi:10.1142/S0218271802002876.
- Turyshev, S. G.; Nieto, M. M.; Anderson, J. D. (2005). "A Route to Understanding of the Pioneer Anomaly". In Chen, P.; Bloom, E.; Madejski, G.; Petrosian, V. The XXII Texas Symposium on Relativistic Astrophysics 2004 (752). pp. 13–17. arXiv:gr-qc/0503021. Bibcode:2005tsra.conf..121T. Stanford e-Conf #C04, paper #0310.
- Dittus H et al. (2005). "A Mission to Explore the Pioneer Anomaly". ESA Spec.Publ. 588: 3–10. arXiv:gr-qc/0506139. Bibcode:2005gr.qc.....6139T.
- Nieto, M. M.; Turyshev, S.G. (2004). "Finding the origin of the Pioneer anomaly". Classical and Quantum Gravity 21 (17): 4005. Bibcode:2004CQGra..21.4005N. doi:10.1088/0264-9381/21/17/001.
- Further elaboration on a dedicated mission plan (restricted access)
- Page, J. F.; Dixon, David S.; Wallin, John F. (2005). "Can Minor Planets be Used to Assess Gravity in the Outer Solar System?". The Astrophysical Journal 642: 606. arXiv:astro-ph/0504367. Bibcode:2006ApJ...642..606P. doi:10.1086/500796.
- Johnson, J. (January 2, 2005). "Opening New Doors in Space". Seattle Times. Retrieved 2012-01-12.
- Nieto, M. M.; Anderson, J. D. (2005). "Using Early Data to Illuminate the Pioneer Anomaly". Classical and Quantum Gravity 22 (24): 5343–5354. arXiv:gr-qc/0507052. Bibcode:2005CQGra..22.5343N. doi:10.1088/0264-9381/22/24/008.
- Hellemans, Alexander (October 2005). "A Force to Reckon With". Scientific American 293 (4): 24–25. Bibcode:2005SciAm.293d..24H. doi:10.1038/scientificamerican1005-24.
- Brownstein, J. R.; Moffat, J. W. (2006). "Gravitational solution to the Pioneer 10/11 anomaly". Classical and Quantum Gravity 23 (10): 3427–3436. arXiv:gr-qc/0511026. Bibcode:2006CQGra..23.3427B. doi:10.1088/0264-9381/23/10/013.
- Anderson, J. (January 28, 2009). "March 2009: Is there something we don't know about gravity?". Astronomy Magazine 37 (3): 22–27.
- "Pioneer Anomaly Solved By 1970s Computer Graphics Technique" (March 2011)
- "Pioneering Gas Leak? The strange motions of two space probes have mundane explanations--probably" Scientific American (December 1998)
- "A Force to Reckon With: What applied the brakes on Pioneer 10 and 11?" Scientific American (October 2005)
- "Gravity theory dispenses with dark matter" - STVG (Scalar-tensor-vector gravity) theory claims to predict Pioneer anomaly
- Planetary Society data recovery effort enables study
- Shows number of publications about the Pioneer anomaly on arXiv.org, by year.
- Space.com: The Problem with Gravity: New Mission Would Probe Strange Puzzle
- "Wanted - Einstein Jr". the Economist. March 2008.
- The Pioneer Anomaly, a 30-Year-Old Cosmic Mystery, May Be Resolved At Last - Popular Science (December 2010)[dead link]
- Robbins, Stuart (May 2014). "Exposing PseudoAstronomy, Episode 110: Solar System Mysteries "Solved" by PseudoScience, Part 2 - The Pioneer Anomaly". Exposing PseudoAstronomy Podcast.