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 phaseformalism in which the three bodies are represented by periodic phase variablesassociated with Earth rotation, Earth orbital motion, and lunar orbital motion. These phases naturally define a three—torus T3, within which the system evolves as a helical flow. Observable cycles such as the solar day, the synodic month, and the year emerge as alignment events corresponding to phase closure conditions. An alignment operator is proposed to characterize the temporal coherence of these events. The approach does not aim to recover full three—body trajectories, but in stead provides an analytic and geometrically transparent description of recurrence and temporal structure in the restricted three—body problem.