A new prediction for the shapiro time delay from a unified description of gravity and motion

A novel theoretical framework for gravity is proposed in which the speed of light is a decreasing function of the cumulative gravitational potential, Φ, generated by the matter content of the universe. In this scenario, the total inertial energy of a particle, E, is not conserved when it moves through a non-uniform gravitational field, and the truly conserved quantity is E=cE, where c denotes the effective speed of light, varying with the gravitational potential as c=c₀/Φ. These two fundamental relations, together with hc=const., allow a mathematical construction that reproduces the solar tests proposed by Einstein, while providing the basis for a theory that is, a priori, compatible with Mach’s principle. A noteworthy finding is that the fourth test of general relativity proposed by Shapiro gives rise, in the present framework, to an additional time delay of approximately 20\,, which may not have been accounted for in previous radio-ranging analyses. For the maximum solar encounter in the Cassini geometry, the additional delay produces a Doppler-tracking signature equivalent to an effective Δγeff4.3×10⁻⁵, placing the predicted effect at approximately the sensitivity level of the Cassini experiment.