 ...An Exact Classical Mechanics leads toward Quantum Gravitation... Contents
4.7 The Shapiro Time Delay | Fig. 5 Radar reflections from Venus to Earth |
The Shapiro time delay needs a special mention. Equations[36] and [38] show that cT will reduce as light, including radar beams, approaches the Sun. A radar beam bounced from a planet like Venus will therefore take slightly longer to return than if it moved at constant speed: this excess is the Shapiro Time Delay ΔTS. The extended Newtonian yields by simple integration:  | [46] |
Nomenclature is defined in the lower diagram of Figure 3 showing the Earth and Venus orbiting the Sun. The plot shows equation[46] as solid line N, in close agreement with the plot marked GR called the Schwarzschild solution of general relativity and quoted by Shapiro(12) prior to his experimental programme. After the tests he(13) quotes the upper chain dashed curve marked "Shapiro Empirical?". It is this, not the others, which fit the experimental observations! Since only an unpublished source was given it seemed that this curve must be just an empirical match, which is why it is so marked. I found that if the i-ther rotated in a vortex motion centred on the Sun, then a further extra time delay would arise. This was due to light being helped on one path but hindered more on the other, resulting in a small net extra "vortex delay". To fit the discrepancy a velocity distribution was computed described by:  | [47] |
Consequently, since the centre of the Earth is moving at the same speed as the i-ther the null observations of Michelson and Morley no longer seem inexplicable. Furthermore the stellar aberration observed by the astronomer Bradley can also be accommodated. His observations showed stars to move in small circles with annual periodicity. This was consistent with light appearing to be deflected by the orbital motion of the Earth about the Sun, at a speed of 29.7 km/s. The effect was similar to the apparent deflection of raindrops as viewed from a moving vehicle. The Earth would have no apparent speed relative to a co-moving fluid but would be in orbital motion relative to any star. On Christmas Eve 1996 a letter arrived from John Day. It contained a mathematical proof showing he had derived the "Shapiro empirical?" equation from the fundamental metric equation of general relativity. So the latter can provide two solutions but only one is satisfied. | 
