We report the detection of a statistically significant 27. 55-day periodic signal in the Observation minus Calculation (O–C) residuals of five independent Lunar Laser Ranging (LLR) datasets from the POLAC archive (N = 16, 367 measurements, 1979–2001). The signal is confirmed with false alarm probability FAP <= 0. 024 at all five stations via 1000 Monte Carlo permutations, accounts for approximately 3. 6% of total residual variance, and is temporally stable over both chronological halves of each dataset. The anomaly period of 27. 55 days does not correspond to any known instrumental, atmospheric, or tidal systematic effect in standard LLR error models. We further show that the observed best-fit angular frequency omegabest = 2. 2770 can be explained analytically by the orbital projection formula: omegaₑff = omega₀ * sqrt (1 - e² - sin² (iₑff) ) = 2. 276972 where e = 0. 0549 is the lunar orbital eccentricity, iₑff = 5. 088 deg is the dataset-epoch-averaged orbital inclination, and omega₀ is a reference frequency. The formula yields omegaₑff with 0. 000% residual against the MC best-fit. We derive three parameter-free falsification predictions for LAGEOS-1/2 Satellite Laser Ranging data and future lunar navigation missions, and invite independent replication of the spectral analysis.
Per Loeining (2026) studied this question.