Empirical Scaling Between Electromagnetic Spectral Break Frequency and the Square of Circular Orbital Velocity

This study examines an empirical relationship between electromagnetic spectral break frequency and the square of circular orbital velocity in the heliosphere. Using eight published spectral break-frequency measurements obtained at heliocentric distances from 0.42 to 5.3 AU, a strong positive relationship is identified between break frequency and v². The analysis yields Pearson r = 0.983, R² = 0.965, and p = 1.30 × 10⁻⁵. A log-log analysis gives a scaling exponent of approximately 1.023, consistent with an approximately linear proportionality between spectral break frequency and v² over the examined range. Because circular orbital velocity squared is itself related to heliocentric distance, the present result is interpreted as an empirical scaling rather than proof of an independent physical law. The proposed relationship is therefore presented as a falsifiable hypothesis that can be tested independently using electromagnetic spectral measurements at different radial distances within planetary magnetospheres, particularly the Jovian system.