Space Dependence of Light Velocity May Explain Anomalous Effect Seen in Distant Spacecraft
The Maxwellian electromagnetic wave nature of light is assumed. This theory requires a medium of propagation. There is evidence that this medium is generated by (and therefore attached to and carried along by) large celestial bodies. It is explained how this theory may account for the anomalous effect seen in distant spacecraft. This leads to the practical idea of an "optical translational velocimeter".
Matter-generated light-wave-medium, hierarchical schesis, optical translational velocimeter.
03.50.D Maxwell theory
41.20.Jb Electromagnetic wave propagation
42.25.Bs Light propagation
07.07.Df Optical sensors
42.81.Pa Sensors, gyros
04.80.Cc Experimental tests of gravitational theories
95.55.Pe Lunar, planetary, and deep-space probes
95.10.Eg Orbit determination and improvement
Anderson et al [1,2] reported an anomalous effect seen in distant spacecraft and investigated various possible causes, but failed to find a satisfactory explanation. A new candidate for a potential explanation is put forward here.
Anderson et al remarked that "it is interesting to speculate on the possibility that the origin of the anomalous signal is new physics".  It is not so much new physics that is proposed here; rather it is a new version of quite old physics which regrettably was unjustifiably neglected. What follows is an outline of a theory that may explain the anomalous effect.
Anderson et al also commented that "one can speculate that there is some unknown interaction of the radio signals with the solar wind".  The speculation here is that there is a well-defined connection of the electromagnetic-wave radio signals with the (admittedly imperfectly known) electromagnetic-wave medium - "Maxwell's Ether". 
In order to understand better the properties of radio signals over large (interplanetary) distances, one has to consider the nature and large-scale structure of the medium of radio signals. There is considerable evidence that this medium is generated by (and therefore attached to and carried along by) large celestial bodies.  Thus for the Earth observer, the speed of radio signals is the universal constant c only in the neighbourhood of the Earth. Elsewhere, it is c with respect to the nearest dominant body (which invariably moves with respect to the Earth), and it is probably this that gives rise to the anomalous effect. This theory is corroborated by the Anderson et al remark that "our [anomalous] effect could only be seen … further than 10-15 Astronomical Units". 
The best way to visualise the situation is to consider a "fluid" and "turbulent", so to speak, medium (of waves propagated through it) with "currents" or "streams" or "winds" or "fluxes" flowing in this fluid medium. Examples : (i) ocean-currents in the ocean-wave-medium (i.e. ocean); (ii) winds in the sound-wave-medium (i.e. air); (iii) "ether-fluxes" in the light-wave-medium (i.e. ether); etc. 
Elementary observation discloses a well-defined hierarchical (non-static but non-chaotic and dynamically stable) organisation of matter in the universe: planet, star, galaxy, cluster, etc. More careful study than is commonly done, shows that it is one of these material frames, and no others, which provide the scientists (and specifically the NASA investigators) with the concrete natural standard with respect to which all velocities (including c) and all accelerations which enter into the true laws of nature must be referred - in order to obtain consistent results. Alfred O'Rahilly's 1938 term "schesis" has been adopted  to denote these all-important concrete natural standards. Assuming that each celestial body generates in its vicinity its own light-medium, it follows that the speed of a radio signal near a celestial body B is the universal constant c with respect to the schesis B only, and c with respect to nothing else.
The inexorable fact is that the various scheses move with respect to each other, and from this follows that there are "ether-fluxes" (and not the nineteenth century misconceived "ether-wind") and it may be this that the NASA deep space missions have unknowingly been detecting for decades. It also follows that (although in reality the numerical value c is in a certain general sense still a universal constant) for an observer on schesis E the speed of a radio signal near a schesis B is not c, even when the radio signal is sent from E.
In a certain sense, this unknowingly detected (by NASA) positive result is the outcome of a Michelson-Morley type of experiment on a grand (interplanetary) scale. Significantly, Michelson's own and substantially correct explanation of the null result of the original (laboratory scale) Michelson-Morley experiment was that it contradicted Fresnel's "ether-wind" model of the light-medium and instead supported Stokes's "ether-drag" model of the light-medium. Moreover, Michelson never endorsed the popular tendency of neglecting (or, worse, denying) the existence of the light-medium of the light(-electromagnetic)-waves. 
The above ideas lead one to suspect that a source of the anomalous effect (and possibly the only one) lies in the analysis of the ranging data (when dealing with large distances, spanning more than one planet), and specifically in the (in this problem) inappropriate use of the formula:
(probe distance) = (speed of light)(radio signal transit time)
The probably inaccurate value of the probe distance incorrectly derived from this inappropriate formula predictably fails to agree with the probably accurate value of the probe distance correctly derived from the initial conditions plus the integration of Newton's law of dynamical motion:
F = dp/dt
In order to correctly account for the anomalous effect, it is suggested that in the analysis of the ranging data the following formula must be used:
dt = dx/c(x)
This formula is evidently simple, and it evidently applies to small distances dx and small durations dt. The great difficulty has always lain in the in effect space-dependence (over large distances, spanning more than one planet) of c(x), which is non-trivial and not so obvious. In order to obtain correct results over large distances, one has got to do some non-trivial integration.
The exact function c(x) is not known, and it must be the business of space agencies to determine it experimentally. In the same way that oceanographers have meticulously mapped (for example) the Gulf stream in the Atlantic ocean, the various space agencies ought to have started mapping the "ether fluxes" in space from the dawn of the space age. The most efficient mapping these "ether fluxes" in space can be done by equipping all space probes with what has been termed the "optical translational velocimeter". [5, 6]
In the same way that the apparatus of the Sagnac experiment has been painstakingly developed into the now very useful "optical rotational velocimeter", the present theory predicts the development of the apparatus of the Michelson-Morley experiment into the "optical translational velocimeter", which may turn out to be equally (if not more) useful. [5, 6]
 J. D. Anderson, P. A. Laing, E L. Lau, A. S. Liu, M. M. Nieto, and S. G. Turyshev, Phys. Rev. Lett. 81 (1998) 2858.
 J. D. Anderson, P. A. Laing, E L. Lau, A. S. Liu, M. M. Nieto, and S. G. Turyshev, Phys. Rev. Lett. 83 (1999) 1891.
 T. Theocharis, Lettere al Nuovo Cimento 36 (1983) 325.
 T. Theocharis, Physics Education 17 (1982) 148.
 M. Psimopoulos, and T. Theocharis, Nature, 319 (1986) 269.
 M. Psimopoulos, and T. Theocharis, Electronics & Power, 32 (1986) 789.
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[A presentation of the author is given at the end of his previous paper published in this same issue of Episteme]
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