C33 — Oscillation and Orbital Equality

This conceptual and preliminary mathematical paper examines the proposed relation between pendulum oscillation and circular orbital motion. It derives the small-angle pendulum relation T ≈ 2π√(L/g), yielding g ≈ 4π²L/T², and the circular-orbit relation a_c = 4π²r/T_o². It explains why the expressions are mathematically comparable but arise from different physical conditions: a pendulum bob does not complete a full circle during one oscillation, and string tension contributes to its radial acceleration. The paper distinguishes observations, established mechanics, source-derived interpretation, deductions, and open questions. No new experimental data are claimed; a test programme is proposed for future work.