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On October 5, 1998, the journal Physical Review Letters published, in its issue 81, an article entitled:

Indication, from Pioneer 10/11, Galileo, and Ulysses Data, of an Apparent Anomalous, Weak, Long-Range Acceleration.

John D. Anderson, Philip A. Laing, Eunice L. Lau, Anthony S. Liu, Michael Martin Nieto and Slava G. Turyshev

.....Reference: PACS numbers: 04.80.-y, 95.Eg, 95.55.Pe

.....Below is the abstract, first in English, then its French translation:

Pioneer X

.....Follows a summary of the article with some excerpts.

....The exploration of distant planets began in 1972 with the launch of Pioneer 10, followed by Pioneer 11 in 1973. After undergoing a gravity assist while crossing Jupiter and Saturn, the two probes took hyperbolic trajectories that cause them to leave the solar system. Although Pioneer 10 is still transmitting signals, NASA officially ended this mission on March 31, 1997, when the probe was at a distance of 67 astronomical units from the Sun. The radio system of Pioneer 11, for its part, shut down on October 1, 1990, when this second probe was at 30 astronomical units from the Sun. Nevertheless, due to their excellent spin stabilization, these probes are very good instruments for dynamic studies. Acceleration measurements (in fact, deceleration measurements) can be performed by spacing measurements over five days, leading to an evaluation precision of ~ 10-10 cm/s2. The trajectories of these two vehicles were therefore analyzed at JPL (Jet Propulsion Laboratory) in the DSN (Deep Space Network) department. In this type of analysis, perturbations due to the planets, radiation pressure, the effect of the interplanetary medium, and General Relativity effects were obviously taken into account. In short, all precautions were taken to obtain an analysis result that eliminates all known causes of variations relative to a simple Keplerian trajectory. Starting from 1980, when the effect of radiation pressure (which decreases as r-2) could be neglected—which, at a distance of 20 astronomical units, induces an acceleration lower than 5 x 10-8 cm/s2—the analyses reported an anomalous deceleration component, a "Sun-directed acceleration" (to use the term employed in the article) with a typical value of: (8 ± 3) 10-8 cm/s2. We then considered that this effect could be due to:

• the gravitational field of the Kuiper belt
• the gravitational field of the galaxy
• errors in the ephemerides
• standard errors in the evaluation of the Earth's position
• precession and nutation phenomena.

....But none of these "forces" could justify such an effect: it was off by three orders of magnitude. It was then imagined that the phenomenon could be due to the decrease in power of the electricity generators, the plutonium. But this cause was eliminated, because if it had been so, the phenomenon would have varied over time according to the decrease in power of these onboard electricity sources. Thus we were led to the conclusion that the probes were subject to a Sun-directed acceleration of:

....- ( 8.09 ± 0.20 ) 10-8 cm/s2 for Pioneer 10
....- ( 8.56 ± 0.15 ) 10-8 cm/s2 for Pioneer 11

....These values did not change, within a sensitivity of 2 x 10-8 cm/s2, in a distance range from 40 to 60 astronomical units. We then thought of the effect of a drag force, an action of the viscosity of the ambient medium, proportional to the speed of the probes. But this was hardly credible insofar as the trajectories of these two probes are quite different from a radial trajectory relative to the Sun.

...We then extended our analyses to two other probes: Galileo and the Ulysses probe, whose trajectory lies outside the plane of the ecliptic. Enormous quantities of data were available concerning Doppler effect measurements. It quickly appeared impossible to extract anything from the data related to the Galileo probe, given the non-negligible effect of radiation pressure linked to the Sun. On the other hand, the analysis of the data concerning Ulysses revealed an acceleration of unknown origin, always directed towards the Sun, worth:

...- ( 12 ± 3 ) 10-8 cm/s2

...Finding the same phenomenon with this third vehicle, we then thought that it could be an error linked to the code used. We therefore changed the analysis tool by using CHASMP (Compact High Accuracy Motion Program): no change. We were led to consider that atomic clocks might "drift over time" or even give different values at different points on Earth (...).

...That being said, the same phenomenon was found for Galileo: ( 8 ± 3 ) 10-8 cm/s2. But the proximity of the Sun meant that this value was practically equal to that resulting from the radiation pressure effect (which could, however, be totally neglected for Pioneer 10, Pioneer 11, and Ulysses).

...It was then thought of some unknown interaction between the photons from the waves and the solar wind (...). Discussions then focused on future missions such as "Pluto Express" and "Solar Probe".

..We wondered if this effect could not be attributable to the presence of dark matter in the solar system, but this type of interpretation implied the presence of an amount of dark matter greater than 3 x 10-4 solar masses. But this would then contradict the reliability of the precision of the ephemerides, based on visible mass. One sees that a parasitic mass two orders of magnitude smaller would suffice to create observable perturbations, even for objects as distant as Uranus. The dark matter track therefore had to be abandoned, as well as the hypothesis of a swarm of "massive neutrinos".

..It was then considered to modify the gravitational potential by taking into account the addition of a Yukawa force. The reference is:

..M.M. Nieto and T. Goldman, Phys. Rev. Rep. 205, 221 (1991); 216, 343 (1992).

..The gravitational potential then becomes:

l is the range of this new force. This type of model leads to a constant acceleration:

where a1 is the Newtonian acceleration at the distance r1 = one astronomical unit. We also considered other models where Newton's law is modified. That being said, this modification of Newton's law should then have an influence on the orbits of the planets of the solar system. For planets like Mars, Viking-type probes are capable of detecting variations in orbital parameters of the order of a hundred meters. By combining the effects that Mars and the Earth would undergo, the precision of the measurement would then be 150 meters. Now:

The Pioneer effect is not seen.... a large error here would cause inconsistencies with the overall planetary ephemeris.

Translation: "The Pioneer effect is not found.... such a large error would be in disagreement with the ephemeris data."

...The consequence: if this modification of Newton's law had an effect on the trajectories of Mars and the Earth (and thus claimed universality), the constraints provided by the precision of Viking measurements mean that the effect should be less than 0.1 x 10-8 cm/s2.

..*.*Consequently, if the anomalous radial acceleration acting on spinning spacecraft is gravitational in origin, it is not universal. That is, it must affect bodies in the 1000 kg range more than bodies of planetary size by a factor of 100 or more. This would be a strange violation of the Equivalence Principle.

Translation: Consequently, if the anomalous radial acceleration highlighted for spinning probes had a gravitational origin, the effect would not correspond to a new universal law. Indeed, this would mean that this effect would prove to be more significant for objects whose mass is of the order of a ton than for objects as massive as planets, and this by a factor of one hundred.

...Incidentally, note that the Viking data were also analyzed with a second code (CHASMP), already mentioned above.

...The conclusion of the article: the cause of the effect remains for the moment a complete mystery. Of course, one then wants to ask oneself if such an effect, weak moreover although perfectly measurable, could not be due to the repulsive effect of an environment of twin matter, which tends, at all scales, to infiltrate everywhere where matter is absent. According to my model, the "interstellar vacuum" would contain (in the adjacent universe relative to ours) a density of twin matter much higher than the density of matter that has become very rarefied. A systematic study, a modeling, computer simulations would constitute a very nice thesis topic. Alas, the poor PhD student who ventured into such waters would see his research career immediately obliterated, definitively.

Rémy Chauvin is the author of a sentence that will serve as a conclusion:

...When one wants to undertake something, one immediately has against oneself:

...........- People who do the same thing

...........- Those who do the opposite

...........- Those who do nothing.

A remark in passing: One might think (a detail that was not cited in the article) that this effect of anomalous acceleration could be linked to a "cosmological constant effect". But, as the observed effect acts in the sense of a deceleration, one should then speak of the "attractive power of the vacuum". On the other hand, this effect should increase with distance. Now the Pioneer probes, or at least one of them, are at some 60 astronomical units, that is to say at 1013 meters from the Sun. Placing the (average) orbit of Pluto at five billion km, that is 5 x 1012 meters, one sees that these probes, the oldest of which was launched in 1972, are located at twice the diameter of the solar system. On the other hand, the Ulysses probe, which climbs the cosmos outside the plane of the ecliptic, only climbs to three hundred million km, that is to say one-tenth of Uranus's orbit, or one-sixth of Pluto's orbit. Ulysses is therefore much closer to the Sun. Now the acceleration anomaly observed for Ulysses is 12 x 10-8 cm/s2, that is, 1.4 times greater than the anomalies noted for the Pioneer probes. This therefore seems to exclude a priori the "cosmological constant" track.

...What about an effect that would be linked to an environment of repulsive twin matter? In this perspective, given that matter and twin matter repel each other, where one dominates, the other is absent, and vice-versa. In the scheme I indicated, large conglomerates of twin matter would be located at the center of the "great voids" constituting the large-scale structure of the universe (VLS). Matter would then be arranged in the vicinity of structures evoking "jointed soap bubbles", the galaxy clusters being the junction points of three sheets. In these "plates": galaxies, bathing in an environment of hot twin matter, structured like a kind of gruyère, the galaxies being nested in the gaps. But all this remains schematic. Twin matter tends to infiltrate everywhere it can. A galaxy is not a uniform distribution of matter. With respect to stellar populations, they are tiny grains of matter populating immense voids. In these voids, clouds of interstellar gas, certainly. But matter is not omnipresent. Where it is in a rarefied state, twin matter infiltrates. One can therefore imagine that interstellar space may contain twin matter, at low density. This then brings a contribution to the "confinement" of the system, but a minimal one. The solar system, with respect to gravitation, can to the first order be represented by a point mass: that of the Sun, namely 2 x 1030 kilos. Relative to this mass, the planets are only small perturbing objects. Consequently, if there is a distribution of twin matter, it would, to the first order, have a distribution possessing a quasi-spherical symmetry. Between the stars, far from the Sun, this twin matter would have a quasi-constant density r*, which would drop when approaching the Sun. It is this gap which, having a confining effect, would slow down the space probes. This distribution would have to be evaluated using numerical simulations and then see if such an interpretation would be compatible with the precision of the ephemerides.

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