# The Anomalous Acceleration of the Pioneer Spacecrafts

#### Garth

Gold Member
A nice review of the anomaly has just been published on the Physics ArXiv as a result of an "Invited talk in Astronomia Dinamica en Latinoamerica. To be published in Revista Mexicana de Astronomia y Astrofisica, Conference Series."

The Anomalous Acceleration of the Pioneer Spacecrafts with the PDF document here.

The Pioneer trajectories have been modeled from radiometric data, considering gravitational and nongravitational forces acting upon the spacecrafts. Starting around 20 AU from the Sun, near the orbit of Uranus, the models deviate from the radiometric data by a small Doppler frequency blue-shifted drift of (5.99±0.01)×10−9 Hz s−1 (Anderson et al. 1998, 2002a). Anderson et al. (2002a) interpreted this Doppler drift either as a constant, unexplained acceleration towards the Sun of (8.74±1.33)×10−10ms−2, or a constant time deceleration of (2.92 ± 0.44) × 10−18 s s−2.
6. CONCLUSIONS
The Pioneer Anomaly consists in an unmodeled constant acceleration of aA = (8.74 ± 1.33) × 10−10 m s−2 towards the Sun detected in radiometric data from the Pioneer 10 and 11 spacecrafts, and also suggested in the radiometric data from Galileo, Ulysses and Cassini spacecrafts. Although there have been many efforts to disentangle its nature, the anomaly still has an uncertain origin. Spurious results introduced by the approximation algorithms, as well as errors in the navigational software used to calculate the trajectories of the Pioneers, have been ruled out after four independent studies have proven evidence of the same anomalous effect. Heat radiation or gas leaks and other on-board causes cannot be completely ruled out, but it is tough to uphold that the same intrinsic effect shows up in five spacecrafts that differ both in designs and trajectories. This circumstance has stimulated the search for extrinsic causes that can explain the anomaly. Hence, different researchers have argued about gravitational disturbances and other conventional forces acting upon the spacecrafts. Although dark matter in the outer Solar System may be a strong candidate to explain the anomaly, it is extremely difficult to prove its effect on the orbits of the planets beyond Saturn.
Another line of research has been held by various groups in the sense that the observed anomaly might be a result of the incompleteness of the current theory of gravitation, or even an indication of new physical phenomena. As speculative as this line of research is, it is undoubtedly very attractive because it can uncover new clues and unexpected physical laws. Scientists are eager to confront unexplained phenomena and therefore new attempts will arise to formulate a solid explanation for the Pioneer anomaly. Perhaps, the mystery of the Pioneer anomaly will not be resolved until a space mission especially devoted to investigate the dynamics in the outer Solar System collects accurate enough data.
Given the necessity and unverified nature of DM and DE in the standard $\Lambda$CDM cosmological model, I would have thought a dedicated mission to explore the PA ought to have the highest priority. It seems our standard theory of gravitation is incomplete in some way.

Garth

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#### robheus

Was't this pioneer anomaly attributed simply to the fact that the region of space (near the Kuiper belt) contains dust, and that the anomolous force (directed towards the sun) thus is an indirect experiment which shows the density of matter in that region?

Also I saw reports which attributed this anomaly to the pioneer instruments themselves causing an a-symetric force on the spaceship (leaking gas or heat effects or something).

#### Garth

Gold Member
Hi robheus, yes there are many suggestions as to the cause of the PA; read the paper, it explores them all.

Several nongravitational, conventional forces have been proposed by different authors to explain the Pioneer anomaly. Hence, drag force due to interplanetary dust have been investigated by Nieto (2005) and Bertolami & Vieira (2006) who calculated that the density of dust necessary to provoke the acceleration would be five orders of magnitude larger than the density calculated for the Kuiper belt dust.
Garth

#### paw

Well it is an interesting read Garth but there's a lot of reliance on the anomaly being constant. Many of the potential causes are dismissed for this reason. But the data, according to Olsen, "is not accurate enough to distinguish between a constant acceleration and acceleration proportional to the remaining plutonium in the RTG's". That kind of blows most of the paper out of the water as far as I'm concerned.

They dismiss the possibility of computation error because the anomaly is present in independant studies using different software. However, using different software doesn't guarantee a different algorithm. And further, different software may still be subject to the same hardware constraints. Math co-processers operate using the same rounding and truncating standards and the sig figs from hardware rounding are of the same order of magnitude as the anomaly. I'd almost bet that's where the anomoly really comes from.

#### Garth

Gold Member
The data is not accurate enough, which is why a dedicated mission is advocated, however it is consistent to within the accuracy of observation.

The 'constancy' of the effect is relative to a 1/r{sup]2[/sup] or 1/r dependence that might be easier to explain or inded relative to a very locally varying effect that might be caused by a 'Planet X', the original reason for the data analysis.

True plutonium radioactive decay is also nearly constant over these timescale but any asymmetric radiation could account for only about an order of magnitude less than the observed effect, with other explanations using 'normal physics' from On-Board Systematics, (source The Study of the Pioneer Anomaly: New Data and Objectives for New Investigation Turyshev et al.), they can so far explain a maximum of:

i Radio Beam Reaction Forc arb = (1.10 ± 0.10) × 10−10 m/s2. .
ii Anisotropic Heat Reflection aah = (−0.55 ± 0.55) × 10−10 m/s2. .
iii Differential Change of the RTG’s Radiant Emissivity are = 0.85 × 10−10 m/s2. .
iv Constant Electrical Heat Radiation as the Source: not viable.
v Helium Expulsion from the RTGs ahe = (0.15 ± 0.16) × 10−10 m/s2. .
vi Propulsive Mass Expulsion apme = ±0.56 × 10−10 m/s2.

This makes a maximum total of an = (2.1 ± 0.8) × 10−10 m/s2 that can be caused by normal physics leaving at least a minimum anomalous acceleration of ax = (6.6 ± 2.1) × 10−10 m/s2 to be explained.

I agree the data needs to be more accurate, nevertheless with the present data is inconsistent with GR with the present error bars on the various possible causes.

Garth

#### Garth

Gold Member
Pioneer Doppler data analysis: study of periodic anomalies submitted on today's physics ArXiv by Prof. Dr. Reynaud of the Laboratoire Kastler Brossel, Université Pierre et Matie Curie, Paris.
This paper reports the results of an analysis of the Doppler tracking data of Pioneer probes which did show an anomalous behaviour. A software has been developed for the sake of performing a data analysis as independent as possible from that of J. Anderson et al. (Phys. Rev. D65, 082004, 2002), using the same data set. A first output of this new analysis is a confirmation of the existence of a secular anomaly with an amplitude about 0.8 nms$^{-2}$ compatible with that reported by Anderson et al. A second output is the study of periodic variations of the anomaly, which we characterize as functions of the azimuthal angle $\varphi$ defined by the directions Sun-Earth Antenna and Sun-Pioneer. An improved fit is obtained with periodic variations written as the sum of a secular acceleration and two sinusoids of the angles $\varphi$ and $2\varphi$. The tests which have been performed for assessing the robustness of these results are presented.
Garth

#### tony873004

Gold Member
Jon Giorgini of JPL Horizons was asked about the Pioneer Anomaly during the Q&A following his acceptance speech for the Masursky Award. He said:

"It's been studied fairly intensively. The conclusion is that it's very well described by the thermal radiation model. Discrepancies or inadequacies in the model of how heat is radiated off of it explains this anomalous acceleration. If you correct the heat model you can reduce this mysterious effect, so it doesn't represent new physics. It appears to represent mis modeling of thermal radiation."

You can view his speech here:
Skip forward to 1:30:10 for the Pioneer Anomaly question.

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#### Enthalpy

Hello everybody!

I'd like to recommend to everybody to read at least the chapter titles of the original paper by Anderson, Turyshev and many others. Available for free on ArXiv. They really analysed many possible causes and ruled them out. This does include dust, additional planets, radiation pressure from the radioisotopic generator and the Sun, Solar wind, relativistic corrections and many many more.

This should avoid to suggest explanations that are already ruled out.

#### Enthalpy

- I believe Turysha and others more than Giorgini, for they made the analysis (page 34), not he. Any publication by Turysha saying that?

- Worse: you can easily compute by yourself what the maximum radiation force is. It's 39nm/s2 if fully asymmetrical, or about 50 times the anomaly. Even if the craft wasn't modelled that precisely before flight, any rough estimation is better than 2% anisotropy. Remember this is heat radiation at the tip of a boom.

#### Enthalpy

Software:

Yes, two teams contracted by Anderson et al used really different softwares based on different algorithms - that is, different libraries, but same physics. Already checked in the initial paper.

This will rule out rounding errors as well: they won't add up identically in two different programs.