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An apparent anomalous acceleration of about 8 ? 10^?8 cm/s² (directed towards the Sun) has been detected in the Doppler residuals of Pioneer 10 and 11. A considerable amount of effort has been made in searching for a conclusive origin of this apparent acceleration, however, without success till date. Detailed study of the data has revealed that an annual and a daily variation of the data exist and these can be interpreted as the fluctuating components of the apparent acceleration superimposed on the steady anomalous acceleration. Since these components are definitely related to the Earths motion an explanation has been found for these annual and diurnal fluctuations. The doppler effects due to the motions of the Earth are already incorporated in the model; there should thus be no residual redshift present in the results. It has been shown that the excess redshift of the signal between the Earth and Pioneer 10 due to inertial induction can manifest itself as the apparent acceleration of the spacecraft. It has been shown that the annual and the diurnal components can be accounted for by the excess redshifts due to inertial induction. Both the magnitude and the temporal phase match with the observation.

The apparently anomalous, weak, long-range acceleration of the acceleration  Pioneer 10/11, Galileo and Ulysses spacecraft has been reported recently.  In this paper we show that this observation points to the existence of a velocity dependent inertial interaction which should be included in the theory of gravitation.

The tired-light interpretation of the cosmological redshift is as old as the discovery of the phenomenon itself, and a number of mechanisms have been proposed by researchers in cosmology. This article presents the basic ideas behind the author?s recent proposal of an inertial induction model consisting of both velocity- and acceleration-dependent terms which can explain the cosmological redshift both quantitatively and qualitatively. A major difficulty with the various tired-light mechanisms is that no other reliable experimental verification of the proposed theories is possible, whereas the velocity-dependent inertial induction gives rise to a number of detectable astrophysical and astronomical phenomena. A few of these have been studied, and it has been shown that the predicted effects do exist.

This purpose of this article is to highlight the various aspects of a dynamic model of gravitational interaction proposed by the author in an earlier paper. A number of interesting results are obtained when the proposed velocity and acceleration dependent inertial induction terms are used in conjunction with an extended version of Mach?s principle. Universal induction results in exact equivalence of gravitational and inertial masses, while a cosmological redshift of the proper order of magnitude is obtained, even when a quasistatic, infinite universe is assumed. Inertial induction on a local scale can also explain a number of unexplained or ill-understood observations, viz. the secular retardation of the earth?s spin, the secular acceleration of Phobos and the extra redshift at the solar limb. Velocity dependent inertial induction also provides a servo-mechanism that distributes matter in spiral galaxies in a unique manner, such that a constant rotation curve is observed. Finally, velocity dependent inertial induction can act as a mechanism for the transfer of solar angular momentum, thus explaining the observed distribution of angular omentum. Although there is sufficient indication that the proposed model has validity, a direct observational test would still be desirable. A scheme to test the hypothesis directly is thus proposed.