An important paper by Anderson et al available atupdates the discussion about the anomaly that has been observed in the behaviour of the space probes Pioneer 10 and 11, Ulysses and Galileo. It all began in 1980 when Pioneer 10 was 20 Astronomical Units (AU) from the Sun. One AU is equal to the radius of the earth’s orbit. At 20 AU the spacecraft was sufficiently far from the Sun for the pressure of solar radiation to have dropped to a level where the 252 kilogram probe could no longer be accelerated by the pressure.  Some time after this, a systematic error became apparent which could be interpreted as an un-modeled acceleration, directed towards the Sun, that has been present ever since in all four spacecraft. The magnitude of this anomalous acceleration is (8.74 +/- 1.33) x 10-8 cm/s2. The Pioneer 10 data used in the determination of this anomaly extended from 3rd January 1987 to 22nd July 1998. For Pioneer 11 the data spans the period 5th January 1987 to the loss of coherent data on 1st October 1990.

In order to isolate the cause of the anomaly, every aspect of the probes’ constituent parts has been assessed. This included the radio beam reaction force, the heat radiated and/or reflected from the craft using all sources, gas leakage and expelled helium. Systematics external to the craft that have been assessed included solar radiation pressure and mass, the effects of the solar wind and solar corona, electromagnetic Lorentz forces, the influence of Kuiper Belt gravity, as well as the mechanical and phase stability of all clocks involved. When these and all other factors are taken into account, the anomaly remains.

The possible physical origin of the anomaly was then discussed in detail. First was Crawford’s suggestion that a gravitational frequency shift of signals has occurred that is proportional to the distance of the spacecraft and the density of the dust in the interstellar medium. However, the known properties of the interstellar medium and the quantities and densities of dust are not large enough to produce an acceleration of the required magnitude. Dark matter or modified gravity, such as Milgrom’s MOND model, fail because there should be observable effects on the orbits and distances of Earth and Mars as well as elsewhere in the solar system. These effects are not seen. Problems with atomic clocks have been considered, but the behaviour of the entire system of clocks precludes this. A number of new suggestions are followed through and all seem to fall short of a satisfactory explanation since they must also accord with known data.

In view of the apparent failure of these proposals to come up with an adequate answer, it may be well to look at what is really being measured. There are only two places in the paper where this is clearly delineated. First, under Section X titled “Error budget and Final Result”, we find these words: “It is important to realize that our experimental observable is a Doppler frequency shift…”  If  fo refers to the observed frequency, fm refers to the modeled frequency and fr is the reference frequency, then the actual equation by Anderson et al reads

fo – fm = - fr (2at/c) = - fr (2v/c)                 (1)

In this equation, a is the acceleration, which, when multiplied by time t, gives a velocity v while c is the velocity of light. It is important to note that the frequency has been measured as decreasing at a rate of 6 x 10-9 hertz per second or 1.5 Hz over a period of 8 years.

In all this, therefore, it emerges that the term (2at/c) is the cause of the dilemma. Since t is known, and it has been assumed that c is known, the only option has been to consider that the term a, the acceleration, is the source of the problem. However, the option which has not been considered has been that a is behaving just as predicted and that lightspeed, c, is changing. The behaviour of c was first noted in the 1987 Report for SRI International and Flinders University entitled The Atomic Constants, Light and Time by Trevor Norman and Barry Setterfield. In that Report it was established that c had been dropping with time. However, in Section V (D) the Report mentioned that the value of c had bottomed out and may increase again. This increase has been suggested by data obtained post 1985 from the gyro-magnetic ratio, the Hall resistance or the Von Klitzing constant and others.   This oscillation effect is also discussed in “Modifications to Light-Speed Model”,  as well as in parts viii and ix of Appendix 4 of Behavior of the Zero Point Energy and Atomic Constants.

This becomes immediately relevant to the behaviour of these space probes as they potentially provide information on the way that lightspeed has behaved. If the quantity t is known, and a, the acceleration towards the Sun, is in fact unchanged, as most theories suggest, then the only other item for consideration becomes lightspeed, c. Now the data indicate that the observed Doppler frequency, fo, is dropping with time. If we isolate fo in the above equation, we obtain

fo = fm - fr (2at/c) = fm - fr (2v/c)                 (2)

Therefore, in equation (2), since fm remains unchanged, a decrease in observed frequency can only be achieved if the factor [fr (2v/c)] gets larger. With the constancy of all the other terms in this factor being maintained in the approach adopted here, this requires the speed of light, c, to be dropping over the period of these observations.

In order to see what is happening, let us consider small changes in lightspeed so that it changes from the accepted value of c at launch by a factor of c(1- b) at the time of signal emission. In that case, equation (2) becomes

fo = fm - fr (2at/c) = fm - fr (2v/c) = fm - fr (2v/[c{1 - b}])                 (3)

Let us now gather the terms 2v/c together and include them together with reference frequency fr so that these unchanging terms then become Fr. The observed frequency then becomes

fo = fm - Fr/(1 - b)                                               (4)

However, since b is small, 1/(1 – b) can be closely approximated as (1 + b). The equation then becomes

fo =  fm - Fr/(1 - b) =  fm -  Fr (1 + b)                         (5)

For the observed frequency, fo, to decrease with fm being fixed means that Fr (1 + b) must increase. Since unchanging terms make up Fr, this requires the term b to increase. As a consequence, lightspeed must have changed from the time of the launch of the probe to the time of signal reception by a factor of (1 – b).


Barry Setterfield.
10th September 2003