Impact-Triggered Lunar Angular-Momentum Reversal I: Conservation-Law Constraints and Collision Phase Space

This preprint develops a conservation-law and collision-phase-space framework for an impact-triggered lunar angular-momentum-reversal pathway. The analysis asks whether a Moon-scale collision could, in principle, generate an Earth-bound retrograde remnant or debris reservoir carrying sufficient negative geocentric orbital angular momentum to permit a subsequent reversal of the terrestrial spin component. The study deliberately separates necessary mechanical conditions from hydrodynamic sufficiency. It uses exact finite-mass two-body angular momentum for the principal benchmark, a restricted geocentric model for post-impact orbital screening, an impulse-level collision parameterization, a fluid Roche-limit screen, and a Darwin-type angular-momentum stability criterion. No tidal quality factor, constant time lag, reversal timescale, or successful hydrodynamic collision outcome is assumed. For the ideal reversed-present-Moon benchmark, the finite-mass calculation gives a terrestrial spin-zero radius of 243,191.59 km. Eccentric retrograde post-impact configurations reduce the ideal anti-tangential velocity change required relative to an equal-radius circular reversal, while simultaneously increasing the required surviving retrograde mass fraction. Representative Moon-scale impactor mass and velocity combinations define a mechanically admissible region of collision phase space. These results do not demonstrate that a realistic lunar collision produces the required retrograde reservoir. The decisive unresolved test is hydrodynamic retention of sufficiently large negative Earth-centered orbital angular momentum. Strength-aware SPH simulations, fragment reconstruction, and post-impact N-body persistence analysis are therefore treated as subsequent computational gates. The accompanying reproducibility package provides the frozen constants, source code, machine-readable tables, numerical outputs, and claim-boundary documentation used for Paper I of the ITLAMR sequence.