Falsification of Le Sage Screening Gravity from Planetary Gravitational Constant Measurements

We derive quantitative constraints on Le Sage-type screening gravity, in which an isotropic background field with mass-proportional attenuation produces gravitational attraction. A minimal model with five assumptions (isotropy, linear Beer–Lambert screening, no self-screening, no re-emission, and instantaneous propagation) exactly reproduces Newton’s inverse-square law for spherical mass distributions, including a direct proof of the shell theorem from the screening integral. For oblate spheroids, nonlinear corrections of the form δF/F = R(ε) τchar arise, where ε is the oblateness and τchar = σρ a is the characteristic optical depth. The isotropic part of this correction is absorbed into the measured gravitational constant and is unobservable; the geometry-dependent residual C(ε) = R(ε) − R(0) constitutes the observable non-Newtonian signal. Because optical depth τchar = σρ a differs between solar system bodies, the model predicts body-dependent effective gravitational parameters (GM)eff . Comparing Earth and Jupiter, the predicted fractional difference |ΔG/G| = 3.76 °ø 10−2 at screening cross section σ = 10−12 m2/kg exceeds the precision of Juno’s determination of Jupiter’s GM by a factor of 3.8 °ø 106. The model is falsified for all cross sections above σcrit = (2.8°æ0.2)°ø10−19 m2/kg; below this threshold, it is indistinguishable from Newtonian gravity at current precision.