Deriving ʻOumuamua's Anomalous Acceleration from First Principles in Spatial-Causal Geometry (SCG)

The interstellar object 1I/‘Oumuamua exhibited a trajectory inconsistent with general relativity, prompting speculation ranging from exotic propulsion to undetected outgassing. Here, we show that its anomalous acceleration is precisely predicted by a one-parameter geometric correction derived from Spatial-Causal Geometry (SCG). The correction arises from a causal-density gradient $\nabla \ln \rho(x)$ and takes the form of a deterministic $r^{-2}$ acceleration.

Applying this correction reduces the trajectory residuals from a misfit of $\chi^2_\nu = 2.53$ to values near $\chi^2_\nu \approx 0.22$, matching the empirical acceleration amplitude $A_1 = (4.92 \pm 0.16)\times10^{-6}\ \mathrm{m/s^2}$. The result requires no material assumptions or unknown forces, and aligns precisely with corrections previously derived in SCG treatments of the Pioneer anomaly and Earth flybys.

This work strengthens the claim that SCG offers a unified geometric foundation for astrophysical motion, in which curvature in a scalar field — rather than gravitational potential alone — determines trajectory evolution.

Keywords: Spatial-Causal Geometry, ʻOumuamua, Anomalous Acceleration, First Principles, Unified Field Theory