The Density-Gradient Law of Gravitation: Gravity as the Logarithmic Gradient of Ether Plenum Density, and the Derivation of Mercury's Precession From the Medium Alone, Without Spacetime Curvature

This paper reports two results. The first is an expression of gravitational attraction in terms of the medium alone. Rearranging the hydrostatic equilibrium condition already derived in this series, and substituting the equation-of-state parameter forced by the traceless stress-energy tensor of a massless field, gives the gravitational acceleration as negative one third of the squared speed of light times the gradient of the logarithm of the medium's density. The expression contains no masses, no separation, and no gravitational constant, which is what the framework's central claim requires: that gravitation is a local property of the medium a body occupies rather than a relation between distant bodies. It recovers Newton's inverse-square law exactly rather than approximately, satisfies Poisson's equation in vacuum and at a source, and reproduces superposition as a property of the logarithm rather than as an assumption. The paper is explicit that the expression is an identity given the premise of equilibrium, and that its content lies in that premise rather than in the algebra. The second result closes what was previously the framework's most serious failure. Because the density-gradient law returns Newtonian acceleration exactly at every radius, a body governed by it alone would trace a closed ellipse and Mercury's perihelion would not advance. This paper shows that the orbital equation is not governed by acceleration alone: a body moving through the compressed medium ages at the local clock rate and is limited by the local signal speed, and these two effects, both derived earlier in the series for light, apply equally to matter. Constructing the elapsed proper time from them and extremising it yields a post-Newtonian Lagrangian containing exactly two corrections, a velocity-medium coupling contributing a factor of two and a nonlinear-medium coupling arising from the exponential profile contributing one. Their sum gives the coefficient three that the observed precession requires, and a perihelion advance of 42.992 arcseconds per century against a measured 42.98 plus or minus 0.04. The derivation uses no metric, no field equations, and no parametrized post-Newtonian framework. An independent cross-check through the standard parametrization confirms the result and shows that the nonlinearity parameter is likewise derived rather than fitted. The paper closes by establishing that the mechanism is necessarily two-body, since the effect is observed at thirty-five thousand times Mercury's rate in a binary pulsar system containing no third body.