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Anomalous acceleration of Pioneer 10 and 11

  1. Dec 28, 2006 #1
    I came upon a very interresting paper that describes the analysis of the anomalous acceleration of Pioneer 10 and 11, an unexplained perturbation of the trajectories of these spacecraft launched in the early 70's and observed during several decades.

    After a first reading, I have already two questions:

    • The equations (3) in the paper provides the system of differential equations that represents the motions of the planets as well as test bodies. It includes SR and GR corrections. First, I wonder how this equation can be derived, specially for the GR corrections. Any link to a readable derivation and comments on the meaning of each of these 10 and more terms in the rhs?
    • Secondly, I would like to know how much this "experiment" can be considered as a test for the Equivalence Principle? At first sight it might be that it doesn't test the EP, since one given Pioneer probe is involved in each analysis. Nevertheless, the set of equations (3) somehow integrates the EP, since it is a full set of equations of motion. Therefore, maybe, the Pioneer data could also be relevant to checking the EP. Any idea?


    Last edited: Dec 28, 2006
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  3. Dec 28, 2006 #2


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    This appears to me to be a combination of the PPN equations (a well known approximation to GR) along with the Nasa ephermides, also referenced in the paper and online at http://iau-comm4.jpl.nasa.gov/

    The PPN approximation is only good for weak fields, but as the authors of the paper mention, it's good enough for solar system tests and there's nothing about the approximation that should be "broken" by the Pioneer orbit computation.

    You'll find the PPN approximation (which can be used for other metric theories of gravity other than GR as well), along with an explanation of some of its constants (beta, gamma, etc) in many textbooks, including MTW's gravitation.
    Last edited: Dec 28, 2006
  4. Dec 29, 2006 #3
    I'm rather surprised by the low number of responses to the Pioneer 10 anomaly. While the so-called missing mass problem presents itself on a galactic scale and larger, this anomaly is present in our own solar system. It is also not explained by GR. Something fundamental is missing (and I don't mean dark matter). There seems to be some kind of large-scale, space-time (or quantum-vacuum) distortion in addition to the curvature induced by the sun and the individual planets.
  5. Dec 29, 2006 #4
    The Pioneer 10 anomaly is not related to the "missing" mass problem.
    You are looking for a connection that is not there.
    It has likely something to do with the spaceship. I believe the Voyagers do not have the same problem.

    I would not hold my breath for finding the next Nobel price clue on this one. :smile:
  6. Dec 29, 2006 #5
    Exactly: data. :wink:
  7. Dec 29, 2006 #6


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    There is plenty of data - what is missing is a epistemological analysis of the data: Where might our long-held assumptions be wrong? We have indications that GR and our BB model of cosmology might break down at some levels. The errors that have demanded the invocation of Dark Matter, Dark Energy, and Inflation should be telling us that something is wrong with our understanding of the universe. Like a lobster in water that is brought up to boiling very slowly, the scientific community has swallowed these conundrums one by one with no realization that something might be dreadfully wrong. Might our understanding of gravity be flawed? Might the speed of light in a vacuum not be constant? Either of these could give rise to the Pioneer anomaly.
  8. Dec 29, 2006 #7


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    But you, on the other hand, should also not be so quick to jump up to the conclusion that the sky is falling. Every time something comes up that appears to not fit into what we already know, you are very quick into chucking out the baby with the bath water. That isn't how physics is done, and it isn't how it is supposed to be done. Why? Because we know that the things we have fully understood have worked! That evidence is a very compelling reason to hold on to it until there is unequivocal evidence that it doesn't work all the time.

    Furthermore, and this is something you continue to neglect every time you offer your criticism of "the scientific community", the whole point of being a scientist IS to go looking for things we have not understood or could not explain! That's the whole reason why scientists are employed in the first place! We WANT to find out where what we understand doesn't work and come up with new and better formulation! You may find that difficult to believe, but it is true nonetheless! The only difference between you and the scientists is that we have to do it very carefully and make sure the evidence cannot be explained with existing, established theories that we do know work. There must be enough data, and not just from one spacecraft but not from another. There must be account that the data is real and not an artifact of something else. As an experimentalist, I have to deal with such thing all the time and must always be conservative in claiming of anything new. You can only cry wolf so many times before your reputation goes down the drain.

    I strongly suggest you cease pursuing this line of "attack" if you have nothing substantial to add to the discussion beyond accusing the scientific establishment of not wanting to pursue something new. This is a very tired and obsolete argument that only crackpots who are ignorant of the workings of scientists would continue to push.

  9. Dec 29, 2006 #8

    Ivan Seeking

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  10. Dec 29, 2006 #9


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    Dark matter certainly is weird. But the last I heard, there was at least some evidence that it had been "found" - for instance (a popular report)


    I don't know if these latest results have been replicated, so they should probably be viewed with some caution. But though dark matter is certainly weird and not expected, it at least appears to be meeting the experimental tests to which it has been put, including the above.

    I also seem to recall that dark matter had been ruled out as an explanation for the pioneer anomaly, though I don't recall the details.
  11. Dec 30, 2006 #10
    Hi Pervect, I knew about this so-called dark matter proof (your ref) but to me it is no proof at all. A real proof of dark matter would have to be much nore direct (for instance recreate it in accelerators, determine its properties, show that it is a very likely outcome of present particle physical models, etc.). Bending of light can be the result of anything (such as new physics, unknown solutions of the Einstein Field equations, etc.).

    I woul like to point out that there is a parallel tread running in the Astronomy & Cosmology - General Astronomy section under the topic : "The Pioneer Anomaly".
  12. Dec 30, 2006 #11
    I am not running for a Nobel price, but I am interrested by the subject.
    It is not so often that we have an opportunity to look at an experiment from many sides: experimental, historical, technical, theoretical. The long list of possible explanations given in this paper covers quite a range of physics.

    Even without considering alternative theories (like the Mond theory), I would be happy to check by myself the equations of motion (eq 3 in the paper), understand the origin and meaning of each terms, understand the approximations, check the calculations, try to see if and where something could be missing, and at least become familiar with such an application of General relativity. For example, I would find it interresting to see the influence of each terms of eq (3) on the solution and how it compares with the anomalous acceleration. Nothing more than a nice exercice based on real-life physics, but maybe quite a lot work anyway.

    Last edited: Dec 30, 2006
  13. Dec 30, 2006 #12


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    MTW "Gravitation" covers this for sure (see pg 1088 for the PPN equations of motion, I haven't cross checked them with the ones in your paper because they are such a mess).

    I don't recall seeing any treatment of this topic in Wald.

    A textbook is the shortest route to your goal, but I don't know if you have enough background to dive in this deep yet.
  14. Dec 31, 2006 #13

    Yesterday I have checked MTW, that I read in 1983. (At that time this was already one of my hobbies. I was very enthousiastic about this book ... )Indeed MTW chapters 30 and 18 are a path of investigation.

    I also took the JPL, GAIA and the IERS as starting points on the web and found some papers by Soffer and Klioner on the subject. This already illustrated me how much GR is of practical use in space programs as well as geodesy. It also illustrates real-life aspects like earth deformations to be taken into account in the data processing.

    I have also ordered to Amazon a copy of "Theory and Experiment in Gravitational Physics" by Clifford M. Will.

    And finally I checked quickly §106 in "Field Theory" by Landau and Lifchitz. This last reference, again, fits better to my mindset. I specially like the action principle as starting point as well as the neat separation between technicalities and principles. (in addition I am not interrested in the PPN aspects, GR is enough for me today)

    You may wonder why I am asking here then?

    The reason is that, as an evening and weekend hobbyist, I have little time to crunch pages of equations and I try therefore to find the answers before doing the calculations (a well known principle ...). In this process interresting discussions are extremely useful. Comprehensive references or reports can help too.

    Thanks for your many interresting contributions here,

    Last edited: Dec 31, 2006
  15. Jan 12, 2007 #14
    Dear All,

    By reading this paper:

    I was surprised that General Relativity corrections in the equations of motion were totally negligible (see page 6). However, the clock slowing-down by gravity is not negligible to analyse the data. Therefore, only this aspect can be checked from the Pioneer data.

    Would you have some comments or further papers on this topic?
    I would also be interrested in a list of all GR checks based on clock slowing down.


  16. Jan 12, 2007 #15

    Chris Hillman

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    I beg to differ...

    Hi, notknowing,

    "Low number of responses"?! I think not! See http://arxiv.org/find/grp_physics/1/AND+all:+Pioneer+all:+anomaly/0/1/0/all/0/1

    IMO, you are now venturing far beyong the available evidence into the realm of wild conjecture.

    If you look at the papers above, you'll see that quite a few researchers have suggested that the alleged effect might be due to (broadly speaking),

    1. misanalysis of the data (the alleged "effect" might be entirely spurious),

    2. conventional nonrelativistic physics,

    3. conventional relativistic physics.

    In addition to these "prosaic" proposals, you will find many more exotic ones, such as interpretations favoring one of gtr's classical field theory competitors, some kind of "dark matter" or "dark energy" effect, or some kind of new physical field. Usually, the last few possibilities are modeled within in the framework of gtr. In fact, overall, comparatively few of the proposed resolutions of the alleged effect would involve replacing gtr with an alternative theory of gravitation.

    I don't wish to "argue" with you about the relative plausibility of the many extant proposed "resolutions" of the alleged effect; my point is that as far as I can tell, every proposed resolution to date appears to be highly controversial; at the present time, no one proposed resolution appears to me to be dominant.

    One essential point which amateurs might find hard to grasp is that none of the spacecraft being tracked were designed to answer the question: "does the effect exist at all?", and if so to try to measure it accurately. The point is that when dealing with very small effects, you need to try to very carefully eliminate all possible "conventional sources of error", which can be almost impossible if you are analyzing data from "experiments" designed for another purpose entirely. There is a proposal being touted to design a mission specifically intended to try to verify and measure the alleged "Pioneer effect".

    Regarding (1) above, another essential point which might be difficult for many to appreciate is that conventional spacecraft tracking involves rather cumbersome "relativistic corrections" overlaid on a Newtonian foundation. Currently there is also considerable interest in exploring fully relativistic beaconing navigation systems (which would eliminate at one stroke all the classical topological difficulties with calendars and of geographical coordinates), so it is likely that such a mission will use such a beaconing system.

    Well, it might turn out that indeed there is some yet unknown "stuff" responsible for the effect (if it indeed exists), but at this point I think it would be fair to say that no-one really knows what is going on, but contrary to your assertion, there is obviously a great deal of interest in trying to figure out what if anything is going on, and there seems to be considerable consensus that the place to start is with a special purpose spacecraft mission designed to yield clean and unambiguous data. I for one would certainly enthusiastically support a mission designed to test schemes like the Coll positioning system as well as to try to verify and measure the alleged "Pioneer effect".
  17. Jan 13, 2007 #16


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    While I fully endorse your statement
    I feel that you may be dismissing the "alleged" PA too lightly.

    The data has been analysed and re-analysed for many years now – it is definitely there in the data and not “entirely spurious”.

    Conventional non-relativistic physics may explain part of the anomaly, but not all of it.

    It is true that, as with the precession of Mercury’s perihelion, GR effects are ‘cobbled’ onto Newtonian gravitation. However the Mercury precession has always been accepted as correct by the GR community (because it is predicted by GR) where GM/rc2 ~ 10-8, so why call upon un-modelled relativistic corrections in the outer Solar System to explain the PA where GM/rc2 ~ 10-10? (Note: the PA is OOM 10-3 the Newtonian sunwards acceleration at that range.)

    The discovery of the PA was indeed serendipitous, for they initially analysed the data to look for a possible Planet X but found a constant effect equal in both spacecraft. That does not negate the discovery, for example, the discovery of the Van Allen Belts was also serendipitous and they proved to be real! (Explorer I’s Geiger counter was designed to detect cosmic rays and sometimes reported an expected ~30 counts per second, but at certain heights from the Earth it reported 0 counts per second, which was interpreted as the Geiger counter being overwhelmed by a dense layer of radiation there.)

    It is important to note that:

    1. The PA is measured as a residual blue Doppler shift on signals returned back to Earth. The value of the frequency change or time acceleration is equal to:

    ad = (2.92 ± 0.44) × 10−18 s-1.

    2. This can be interpreted as an acceleration (either towards the Sun or the Earth) equal to
    aP = (8.74 ± 1.33) × 10−10 m/s2.

    3. The effect has been constant and equal for both spacecraft from 10AU - 90AU. (Pioneer 10 - Feb 2003) (Other effects swamped it when they were closer than than 10AU from the Sun.)

    4. It does not show up in the orbital dynamics of the outer planets. This alone indicates to me that it cannot be modelled by modification in the gravitational field of the Sun. See Iorio's eprint Can the Pioneer anomaly be of gravitational origin? - answer: negative.

    (However, as a caveat, remember the residuals in Uranus’ orbit that led to the discovery of Neptune? Once Neptune was discovered there was still a residual that led to a search for Planet X. Pluto was found and the search discontinued. However Pluto was not Planet X, it is 2 OOM too small, so a residual in Uranus’ orbital elements still appears to exist!)

    5. That 'normal physics' from On-Board Systematics, (source The Study of the Pioneer Anomaly: New Data and Objectives for New Investigation Turyshev et al.), 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.

    This may be expressed as a minimum Doppler shift or clock drift of

    ad residual = (2.20 ± 0.70) × 10−18 s-1.

    6. Furthermore note that Hubble's constant in similar units (1/(Hubble Time) expressed in seconds) is equal to:

    H = (2.4 ± 0.2) × 10−18 s-1 (with h=0.73) and where I have given H ±10% error bars, which is consistent with that unexplained residual ad residual in the PA.

    The PA may therefore be cosmological and not local in nature and viable gravitational theories that predict such a clock drift (such as SCC) should be given due consideration.

    Last edited: Jan 13, 2007
  18. Jan 13, 2007 #17

    Chris Hillman

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    I wrote, in part,

    Garth quoted the last sentence but then commented:

    I don't feel that I have offered unreasonable counsel, but I won't argue with you if you feel otherwise. However, please do not attribute to me a view I do not hold and which I did not express; quite the opposite.
  19. Jan 13, 2007 #18


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    Chris, no intention to attribute false views. Sorry if I have given that impression.

    We agree then that there is something here that requires further investigation; we live in interesting times!

  20. Jan 13, 2007 #19

    Chris Hillman

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    Now THAT I can agree with!

    Hi, Garth,

    I appreciate the clarification, and am glad that we agree on the important point. I feel that it is too early to offer any firm opinion about how the alleged Pioneer effect (sorry, but I too cautious to omit the A word) will turn out, but it will be interesting to follow this in the years to come. I think it is clear that this question is in no danger of being ignored.
    Last edited: Jan 13, 2007
  21. Jan 13, 2007 #20


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    Hi Chris,

    then perhaps where we differ is I would drop (for reasons given in #16) the "alleged". :wink:

    Last edited: Jan 13, 2007
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