Hyperbolic Interstellar Trajectories Under Spatial–Causal Geometry (SCG) and the gamma(cause) Invariant

This paper extends the Spatial–Causal Geometry (SCG) framework to the full class of hyperbolic interstellar trajectories. Building on prior SCG treatments of the Earth flyby anomaly and the deterministic derivation of 1I/ʻOumuamua’s anomalous acceleration, the present work develops a unified, parameter-free description of all unbound trajectories passing through a rotating causal–density field.

Using the universal causal–closure invariant γ(cause) ≈ 1.216 and the SCG relation a= c²∇ln⁡ ρ, we show that every hyperbolic visitor—natural or artificial—interacts with the solar coherence field in a way that depends only on its geometric path through the Sun’s rotational frame. Three objects are analyzed in detail:

• 1I/ʻOumuamua, whose strong inclination and small perihelion produce a clear, measurable coherence acceleration.

• 2I/Borisov, whose nearly equatorial trajectory yields a suppressed signature consistent with SCG expectations.

• 3I/ATLAS, a live interstellar case whose early orbit solutions show a measurable perihelion-shift residual that matches the intermediate SCG prediction.

The resulting framework provides both forward predictions and inverse tools, enabling reconstruction of solar coherence parameters from orbital residuals. This unifies the treatment of planetary flybys, interstellar comets, and other hyperbolic probes under a single geometric principle.

The paper establishes SCG as a coherent predictive framework for interpreting all unbound motion through the solar system, setting the foundation for future analysis of additional interstellar visitors.

Keywords

• Spatial–Causal Geometry (SCG)

• γ(cause) invariant

• hyperbolic trajectories

• interstellar objects

• 1I/ʻOumuamua

• 2I/Borisov

• 3I/ATLAS

• solar causal–density field

• non-gravitational acceleration

• rotational coherence

• unbound orbits

• perihelion residuals

• interstellar comets

• dynamical anomalies

• coherence geometry