Thursday, November 04, 2004

The Pioneer anomaly

The last paper on gr-qc today is about the Pioneer anomaly:

It seems that it is a rather attractive topic for many people - and there have even been conferences dedicated to this problem. See, for example,

What's the problem?

Two spacecrafts (Pioneer 10 and Pioneer 11) were launched in 1972 and 1973. They have done a good job and informed us about the distant planets in our solar system. Eventually NASA lost contact with them.

Nevertheless, the radio measurements of the position of the spacecrafts during the last years of their existence seem to show a puzzle: it seems that there is a universal unexpected contribution to the acceleration towards the Sun whose magnitude is roughly

a = (8 +- 1) x 10^{-10} meters/second^2

A shocking feature of this value of a is that it seems to be the same acceleration as the critical acceleration relevant for the MOND theories that replace dark matter, see another article on this blog


More precisely, the value of this acceleration is again a=Hc - it is the Hubble constant multiplied by the speed of light, plus minus roughly ten percent. If I calculated correctly, the usual Newtonian acceleration at the distance of 70 AU from the Sun (where the Pioneer anomaly was measured) is roughly 1.2 times 10^{-6} meters per second squared which is approximately 1500 times bigger than the anomalous acceleration a.

In other words, the integrated deviation from the expected position of both spacecrafts is roughly 400,000 kilometers in both cases - that's like 10 thousand of marathones!

Most particle physicists and string theorists would of course be skeptical about the existence of this new effect: we know from the observation of planets that such a large effect does not seem to exist for planets. Moreover, we have tested the equivalence principle pretty well, and a special "universal force acting on the spacecrafts" violates the equivalence principle. Furthermore, we have already learned that the people in NASA are sometimes capable to make as stupid errors as confusing inches and centimeters.

Nevertheless the numerical value of the acceleration and the possible relations with MOND (and holography) makes this topic sufficiently interesting for me so that I decided to write this short article, and encourage you to write your knowledge and opinions about this topic. Don't you think that there can be some new effect, associated with the breakdown of GR at very small accelerations, at least for small enough objects, associated with the breakdown of locality in holographic theories?

Obviously, Europe finds this topic more attractive, and some proposals to launch a spacecraft (well, NASA with LANL with the University of Bremen) whose only purpose is to measure its own motion have been suggested:

These new probes could increase the precision by a factor of one thousand, and they should almost definitely settle the question whether the anomaly is a result of
  • a stupid systematic error,
  • the influence of new dark matter at the boundary of the Solar system
  • or a proof of new physics.


  1. Dear Lubos,

    there is also another, not so well known and (should one cautiously add here 'even'?) less well established anomaly associated with the solar system. There is evidence that planets are in an accelerating motion so that the size of their orbits is gradually decreasing in the coordinate system where Newton's equations hold true. The two phenomena seem to be aspects of one and the same phenomenon.

    There are two means of determining the positions of planets in the solar system. The first method is based on optical measurements and determines the position of planets with respect to the distant stars. Already thirty years ago came the first indications that the planetary positions determined in this manner drift from their predicted values as if planets were in accelerated motion. The second method determines the relative positions of planets using radar ranging: this method does not reveal any such acceleration.

    C. J. Masreliez (2001), Do the planets accelerate?

    C. J. Masreliez (2001), Expanding Space-Time Theory},

    Y. B. Kolesnik (2000), Applied Historical Astronomy, 24th meeting of the IAU}, Joint Discussion 6, Manchester, England. Ibid (2001a), Journees 2000, Systemes de reference spatio-temporels, J2000, a fundamental epoch for origins of reference systems and astronomomical models, Paris.

    C. J. Masreliez, who contacted me during this year, is probably one of the first researchers who have proposed a model for the origin of the anomaly. I do not claim that I understand his model but on basis of his finding that the magnitude of the acceleration relates to Hubble constant, I developed my own explanation based on many-sheeted space-time.

    The idea is simple: altough the space-time sheet of solar system co-moves in cosmological expansion it does not co-stretch so that there is a genuine inwards acceleration in the local Robertson-Walker coordinates compensating for cosmological expansion.

    The same mechanism would explain the anomalous acceleration of space-crafts and predict correctly the acceleration in both cases. The only difference would be that nearly radial motion would be in question now.

    The model can be found at my homepage .


    Matti Pitkanen

  2. Lubos,

    If you don't mind Silly Guesses:

    1. The universe is expanding. On the average. The effect would be to drag apart test particles that are initially at rest w.r.t. each other. Well within a gravitationally (or otherwise) bound system, like our solar system, this expansion should be invisible. But as one moves from the center to the edge of a gravitationally bound system, the universal expansion might become significant. Of course, even at the edge of our solar system, we are well within the potential well of our galaxy, etc., :), but silly wild guesses are acceptable, are they not?

    2. This wild guess is only slightly more serious. For very high precision solar system predictions and measurements, the coordinate system has to be determined with high precision. What I mean is, I imagine that theory, with all its post-Newtonian corrections, provides in terms of an ideal coordinate system, a set of expressions relating the relative positions of the sun, earth, jupiter etc., at a given time, that is full of parameters that have to be determined from observations. We can then convert other observations into this ideal coordinate system. But measurement errors in time and in observations result in some indeterminacy of the coordinate system. I have some vague memory of an astronomer telling me about the 1995 set of parameters would soon be superceded by a much improved set.

  3. Thanks guys for your comments! It's interesting how the proposals with the expansion of the Universe is shared by many people who try to solve it. ;-)

    Nevertheless, the effect for the spacecrafts should be absent for the planets; does not it kill some of your ideas?

  4. Are we sure that the effect does not happen with planets? A poster above seemed to point out the contrary.

    A doubt I see here. How is that the Pionner effect is about a constant force but the MoND effect is about a 1/r effect, and still they are presented as related?

  5. Hey Leucipo! The Pioneer acceleration also seems different to me from the rotation curves - 1 vs. 1/r.

    Which poster says that the planets also experience an anomaly??

  6. Hey Lubos (btw Blog asked me for a nickname, so I used that one... It is clear from content of posts that I am Alejandro). If I read matti well enough, he seems to be telling that this obscure Masreliez is claiming acceleration effect in planets, isn't he?

  7. Yes. There is evidence for the acceleration of planets coming from the determination of the planetary motion with respect to distant stars defining a coordinate system naturally approximating the coordinate system defined by Robertson Walker coordinates.

    I discovered only relatively recently that the model for the claimed acceleration of planets explains also the anomalous acceleration of space crafts if the method used (Doppler shift) to measure their position measures their space-time position with respect to Robertson-Walker coordinates.

    Using the terminology of TGD: space-time surface corresponds to a hierarchy of space-time sheets, each sheet having boundary and representing physical object, be it elementary particle or galaxy. The space-time sheets are connected by extremely tiny wormhole contacts of size about 10^4 Planck lengths. Imagine pieces of plane of increasing size glued to each other and having transversal distances of about 10^4 Planck lengths in 3-D space.

    The space-time sheet of solar system would not co-stretch with the space-time sheet defined by the distant stars. It would be like a rigid ship in expanding and storming ocean keeping its size and shape.


  8. Lubos,

    I suppose the planets rule out the anomalous acceleration of the Pioneer spacecraft as a gravitational effect, and I suppose someone has done the calculations to prove so.

    Without looking at any of that - the planets are not in highly eccentric orbits, and stay pretty much at the same distance from the sun. In that case, a small constant acceleration would simply show up as a small difference in the effective value of Newton's constant, which is known only to an accuracy of about 1 part in 2000.


  9. Hello Dear Lubos,
    I have more to say to those who are intereested in the planetary acceleration. I am working now on a paper relates to this issue. I would like to draw your attentio to the two papres at
    and another two at
    conatct me please at
    Arbab, A.I

  10. Dear Lubos,
    I have recently found this site and make the following comment:

    The Pioneer Anomaly,the acceleration of planetary motion, and a spinning up of the Earth's rotation after tidal breaking has been accounted for obtained from ancient eclipse records, all are of the order of cH or H.

    They may all be explained by a clock drift between atomic and ephemeris clocks.

    The coincidences between these anomalies may well mean the effects are cosmological in nature and indicative of a failure of the present GR paradigm.

    An alternative published theory able to resolve the problem is Self Creation Cosmology and may be found at and reference therein.