Periodic Pioneer anomaly points to modified general relativity


The Pioneer anomaly grows ever more fascinating.

Here’s the background: Pioneer 10 and 11 were launched in 1972 and 1973 respectively and, after sweeping past a number of the outer gas giants, have been heading out of the solar system ever since.

NASA has been accurately tracking their position and speed using Doppler tracking measurements of radio signals from the craft. But this data has thrown up a problem. Both probes appear to be decelerating faster than can be explained by the Sun’s gravity. All that has been widely discussed and numerous explanations have been put forward to explain this discrepancy.

What isn’t so well known is that there is a periodic component to the anomaly. The team at the NASA’s Jet Propulsion Lab who have been collecting the data say that it’s unlikely that this variation is a from the spacecraft. Instead, they think probably the result of something at our end such as a tiny variation in Earth’s orbit.

Now Bruno Christophe and pals from the French aerospace lab, ONERA, near Paris and various other French institutions, have carried the most detailed analysis yet on these periodic variations and raise another interesting possibility.

A number of people have suggested modifications to general relativity that would explain the Pioneer anomaly. But there has never been a way to test these modifications.

Now Christophe and co say that the periodic variations are compatible with the effects on radio signals that some of these modifications might cause.

That’s an extraordinary claim. Obviously, more analysis is needed and it always pays to be cautious with these kinds of ideas. But could it really be possible that the Pioneer anomaly is the first evidence of physics beyond Einstein’s version of general relativity?

Ref: Pioneer Doppler Data Analysis: Study of Periodic Anomalies

20 Responses to “Periodic Pioneer anomaly points to modified general relativity”

  1. diggers says:

    Didn’t we figure this out just the other week? With the satellites in earth orbit and slight deviations there could be explained via proper application of special relativity to the doppler shift involving the ground receiving station. Is this not related?

  2. ZEPHIR says:

    Yes, the corresponding KFC’s article is here:

    The problem is, SR and GR are mutually interconnected each other by the way, which isn’t quite transparent from mathematical point of view. Many important results, derived by SR (Hafele-Keating experiment, the twins paradox), which were derived by using of SR, are GR effects, in fact. The SR relies on GR on background: for example, the fact we can interpret the inertial motion around Earth by SR is in fact the result of Earth gravitational field and it’s potential. Correspondingly, the equivalence principle analysis of the twin paradox does provide more detailed analysis of the subject.

  3. caoimh says:

    Pioneer anomaly is NOT the same as the fly by anomaly.

  4. […] Periodic Pioneer anomaly points to modified general relativity […]

  5. Qasem says:

    Are the raw data of the Poineer anomaly available for others?

  6. Bent Schmidt-Nielsen says:

    A question on both the pioneer anomaly and the flyby anomalies: Has the variable refractive index at the appropriate radio frequencies of the earth’s magnetosphere been taken into account? How large is this (and other subtle effects) effect compared to the small anomalies being reported?

  7. Rhymer says:

    Hello Zephir,

    you got the point. I suppose you are an expert. STR is on the one hand basis for GTR, providing the infinitesimal Lorentz tangent space, on the other hand it gives the boundary condition to physical solutions of the equations of GTR. Would be interesting to talk to you directly on the simple solution of the twin paradox which involves gravitation simply through the EP already given in 1920 by August Kopff. It can be given either approximately in Newtonian Gravity or exactly using GTR.

    Back to flyby:

    Jean Paul Mbelek’s solution relies on some assumptions:

    a) JPL’s analysis does not include the transverse Doppler effect and just uses the non-relativistic Doppler formula; I would (i) very much doubt that JPL uses the non-relativistic formula and (ii) I also have doubts that they do not include the transverse Doppler effect. Here, one should simply ask Anderson et al.

    b) Mbelek uses the strict transverse Doppler formula – which, however, is only valid for the earth’s velocity being orthogonal to the spacecraft’s velocity. This is only the case at the point of closest approach!

    (I would think instead that the JPL people use the full STR Doppler formula including longitudinal and transverse velocities.)

    c) Mbelek claims that JPL’s analysis uses the non-relativistic Doppler formula: Here the order v/c term appears in his own analysis. However, this formula is, assuming it was used, only valid far from the point of closest approach. (But as I said, I doubt that JPL is relying on the non-relativistic Doppler formula anyway.).

    d) Mbelek adds the velocities of earth and spacecraft. I would instead assume a difference velocity between earth and spacecraft. Note that we do not deal with absolute space…


    Under the assumptions he bases his analysis on, Mbelek claims to be deriving the empirical formula of Anderson et al. However,

    – Mbelek’s Doppler ansatz (4) is only valid at the point of closest approach (b). the measurements of the NEAR flyby for instance have a gap of about 3 hours around the point of closest approach. The data are measured when definitely the transverse Doppler effect is very small on the incoming and outgoing trajectory outside this gap, i.e. when the velocities of the satellite and the earth stations are nearly parallel;

    – using the correct difference velocities instead he would get simply the wrong sign for the formula (d);

    – Mbelek claims that the effect is spurious as it is simply caused by deriving the velocity with the wrong Doppler formula. But then, the effect should vanish outside the gap because it is – according to him – not a physical one and the transverse formula will not give a contribution as the velocities are aligned.


  8. Philip Carter says:

    Could Dark Matter permeating the solar system cause this effect?

  9. Zephir says:

    By my opinion, the modified relativity theory including stress tensor (used in Yilmaz’s, Heim or MOND theories) can provide explanation of Pioneer anomaly, Alais effect or flyby anomalies disputed. The modified relativity considers the existence of global reference frame, in which the energy density of space-time curvature manifest itself as additional matter density, while exhibiting additional gravitating effects. The Aether theory just makes it’s understanding easier – by AWT the vacuum is formed by dense foam, the density gradient of which manifests as a space-time curvature. Every density gradient exhibits a surface tension phenomena, which are modifying behavior of space-time curvature.

    In addition, the rotation of gravitating objects shakes the Aether foam by such a way, a more dense ring in the plane of rotation is formed. Such rings were observed already at the case of large rotating galaxy clusters, where they can be observed as a rings of dark matter, but they should surround every rotating massive object, including solar system and the Earth. Due the nature of gravity, all these phenomena are related to omni-directional expansion of Universe, which cannot occur quite uniformly from long term/distance perspective.

  10. Rhymer says:

    MOND is a serious attempt to phenomenologically describe rotation curves of galaxies. It gives much better fits than any CDM model. It has been discussed repeatedly to apply MOND to the pioneer anomaly. However, such attempts failed as the effects of MOND would be detectable on the ephemerides of the outer planets.

    Heim’s theory or Yilmaz theory are not consistent theories. Both are incomplete.

  11. Zephir says:

    Well, the relativity and quantum mechanics aren’t consistent as well, finished the less – and we are using them without problem.

  12. Rhymer says:

    Relativity is self-consistent seen as predictive scheme and quantum mechanics is as well. This does allow for a theory that encompasses both, however, which will be self-consistent.

    Yilmaz’ and Heim’s theories simply are not self-consistent.

  13. Zephir says:

    Re: Maybe “simply”, but “actually”? Can you give us some “simple” proof of their inconsistency? If not, why we should consider such proclamations seriously?

  14. Rhymer says:

    Heim never was accepted by a serious journal. If it is correct, Heim would have been able to defend any critics. This is at least my experience with referees. Hauser and Droescher gave an extension to Heim. It was shown by Bruhn, however, that the HD-metrics g_jk is positive definite. But GR requires g_jk to be indefinite and locally be transformable to the Minkowski-metrics diag(1, 1, 1, −1). Tis is a simple proof, given by Bruhn, of the inconsistency of the Heim/HD theory.

    What are the new predictions to test Heim’s theory?

  15. Micheal E. Murphy says:

    Since you are considering the positions of the planets so accurately I thought of something about the position of the outer planets. During the forming of the Solar System with the density of gas…..What would the Sun sound like if it had air around it and would this affect the positions of the axis of some of the outer planets. Is there a sound function to the Solar Wind and other particles in our Solar System?

  16. Exirifard says:

    Although the covariant resolution of the Pioneer anomaly leads to some periodic terms with periodicity of one day and one year in the effective acceleration assigned to the space-craft, the order of magnitude of the amplitude of these periodic terms are smaller than of the residual of the fit of the Doppler shift with constant anomalous acceleration [Page 5 of

  17. tof tof says:

    Dear Rhymer,

    Mbelek’s assumptions are totally flawed. It is absolutly wrong to claim that the JPL’s analysis does not include the transverse Doppler effect and just uses the non-relativistic Doppler formula.

    A monograph from T. Moyer is available on the Decanso JPL server. The relativistic scheme is explained with full details. Mainly is included:
    -full 1PN equation of motion for the probe
    -Use of planetary ephemerides consistent with General Relativity
    -Position of the ground station in the GCRS then transformation to the BRCS (GCRS and BCRS are the two IAU relativistic reference systems, based on the work of Damour, Soffel and Xu)
    – Light time are calculated in the approximation of N stationary mass-monopole up to the ordre G^2/c^4 (including the Shapiro delay)

    Everything have been done in the framewortk of general relativity, that’s it. Many relativistic people have checked the sheme and claim that this is ok.

    NB : the supposed Pioneer anomaly has an amplitude bigger than Newtonian indirect planetary perturbation… It is not only a question of general relativity, but the full description of gravity. If of course, this anomaly is real.

  18. Jean Paul Mbelek says:

    The software the Jet Propulsion Laboratory uses is relativistic but not fully relativistic, in particular as regards to the rotation of the Earth and the other planets.

  19. Jim Gerrish says:

    I have been investigating doppler anomalies in connection with a hypothesis I developed that space/time is caused by the inflation of space at about the constant C. It occurred to me that if true, this might cause a doppler anomaly or two that would puzzle astronomers who don’t see the universe as I hypothesize. I happened on this site and besides the Pioneer anomaly discussed here, have found that there are other doppler anomalies that are being discussed elsewhere with regards to the red shift results noticed in certain galaxies. The existence of these anomalies doesn’t prove anything, but it is exciting to me that I was able to use the hypothesis to deduce that such anomalies might exist, and that space/time itself might be able to cause them and thus possibly create a “time shift”, whatever that might mean.

  20. Jim Gerrish says:

    Distant Galaxies seem to be moving away from us (and one another) and accelerating as they go, according to the doppler red shit readings. We have no way to know actually how fast they were going before in order to compare what we are observing today. However, in the case of the Pioneer Probes, we do know the speed at which they were going from the time they left earth until the time the doppler anomalies began showing up. The probes appear to be decelerating given the doppler analysis. However, if my inflation of space/time hypothesis is correct, the probes, freed from our space/time neighborhood effects could be exhibiting their own space/time inflation which results in the doppler shift anomaly. They may still be proceeding at the same speed as before, but the doppler reading of the combined speed and inflation makes it appear to be deceleration.

    The only way to test this is with data from additional spacecraft sent from earth at a known speed.