Mathematical Physics

    

Three—Body Problem: Recurrence, Alignment, and Temporal Structure in the Sun—Earth—Moon System

Authors: Pedro A. Kubitschek Homem de Carvalho

The classical three—body problem is traditionally formulated as the predictionof complete spatial trajectories of three interacting masses under gravitation, a taskknown to be generally non—integrable and chaotic. In this work, we adopt a complementary perspective focused on the Sun—Earth—Moon system, where the most stable and observable features arise not from translational motion but from rotational recurrence and angular phase closure. We introduce an angular—toroidal phase formalism in which the three bodies are represented by periodic phase variables associated with Earth rotation, Earth orbital motion, and lunar orbital motion. These phasesnaturally define a three—torus T 3, within which the system evolves as a helical flow.

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[v1] 2025-12-18 21:58:56

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