Robust Detection of a Persistent 206-Day Spectral Mode in Lunar Distance and Velocity Envelope Dynamics

Long-period modulations in lunar orbital dynamics may provide insight into the mechanisms governing multi-scale orbital variability. Using daily lunar distance and radial velocitydata spanning approximately 56 years (1970–2026), we investigate the existence and stabilityof a recurrent ∼ 206.8-day spectral mode in envelope-derived signals.Fourier analysis independently identifies a pronounced spectral peak near 206.8 daysin both distance and velocity envelopes. Band-pass filtering and cross-correlation analysesreveal a persistent lead-lag relationship, with lunar distance variations leading velocity variations by approximately 22–27 days. Bootstrap resampling demonstrates the robustness ofthe detected periodicity, yielding a mean peak period of 203.3 days with a standard deviationof 13.4 days.To evaluate whether this mode reflects direct lunar–solar phase synchronization, phaselocking values (PLVs) were compared against phase-randomized surrogate datasets. Theobserved PLV did not exceed surrogate expectations (p = 0.761), indicating that statisticallysignificant phase locking cannot be established.These results demonstrate that a persistent ∼ 206-day spectral mode is a robust featureof lunar envelope dynamics, although its physical origin and potential connection to broaderEarth–Moon–Sun interactions remain unresolved.