The Orbital Duration/Gravitational Field-Density Equivalence

A new structural relation is introduced that predicts planetary orbital periods using planetary mean density, total satellitic mass, and orbital radius scaling. The relation reproduces the solar system’s planetary orbital periods within ±10 days, providing a compact and falsifiable law. An exoplanetary application indicates predictive perfor- mance beyond the Solar System. Theoretical construction, data sets, and graphical visualizations are presented, mathematically supporting the empiricism of the relation as an emergent orbital invariant.