From Center to Orbit: Electromagnetic Architecture — Radial Acceleration, Cyclic Motion, and the 4π²r²v² Geometry in the Earth–Moon System

This work develops a theoretical framework based on the Earth–Moon system in which radial acceleration, cyclic orbital motion, and electromagnetic organization are interpreted as different geometrical manifestations of a common central dynamics. The model takes (v^2) as a mass-independent measure of instantaneous central activity and proposes that the same central organization may appear simultaneously as inward radial acceleration and circumferential motion. A central quantitative result is obtained by expressing acceleration in an equivalent velocity form through (v=√ar). Using Earth’s surface acceleration and mean radius gives an equivalent cyclic velocity of approximately 7.9 km/s. When the same radial field is geometrically scaled to the mean Earth–Moon distance, the corresponding velocity is approximately 1.018 km/s, closely matching the Moon’s observed mean orbital velocity of approximately 1.022 km/s. The framework further introduces the quantities (2π rv^2), (4π rv^2), and (4π^2r^2v^2=(2π r)^2v^2) as progressively extended geometrical representations of cyclic electromagnetic activity. Previous calculations across the lunar orbit showed that (4π^2r^2v^2) remains highly stable, varying by only about 0.3%. The model also introduces the concept of effective electromagnetic path length in atom-dense environments and proposes that radial binding and cyclic orbital motion may represent different manifestations of a single central electromagnetic architecture. The Earth–Moon system is used as a starting point for a broader, testable framework in which orbital velocity, radial acceleration, surface gravity equivalents, and kinematic electromagnetic-field indicators may be inferred from purely geometrical and kinematic parameters without explicitly introducing mass.