Anomalous Energy Change in Open Trajectories from a Radial Substrate Gradient

We present a substrate field model for anomalous energy changes observed in open gravita-tional trajectories, including planetary flybys and interstellar solar passes. In this framework,change is mediated by a finite background substrate whose locally supported rate of change isreduced by mass–energy, producing a radially varying suppression field around a central body.When orbital dynamics are formulated within this non-uniform suppression field, closed trajecto-ries exhibit near-complete cancellation of suppression effects, while open trajectories admit a smallbut non-cancelling contribution between inbound and outbound paths. This results in measurabledeviations in post-encounter energy without introducing additional forces, adjustable parameters,or trajectory fitting. Using reconstructed spacecraft ephemerides and independently constrainedconstants, the model reproduces the observed magnitude and sign of energy changes reported formultiple Earth flybys and predicts the non-gravitational acceleration observed for the interstellarobject 1I’Oumuamua. The results indicate that anomalous energy behavior in open trajectoriesarises naturally from motion through a radial substrate gradient and represents a generic, scale-independent phenomenon.