What question did this study set out to answer?

This research aims to identify and analyze a periodic signal in lunar laser ranging residuals, investigating its implications for lunar navigation and orbital mechanics.

May 27, 2026Open Access

A 27.55-Day Periodicity in Lunar Laser Ranging O–C Residuals: Empirical Detection, Orbital Projection Analysis, Multi-Satellite Verification, and Forward Predictions

Key Points

This research aims to identify and analyze a periodic signal in lunar laser ranging residuals, investigating its implications for lunar navigation and orbital mechanics.
Analyzed five independent Lunar Laser Ranging datasets with 16,367 measurements from 1979–2001.
Used Monte Carlo permutations to confirm the periodic signal with false alarm probability ≤ 0.024.
Calculated orbital projection predictions for LAGEOS satellites and derived forward predictions for lunar navigation.
Confirmed significant 27.55-day periodic signal accounting for 3.6% of total variance with a best-fit angular frequency of 2.2770 (FAP ≤ 0.024).
Predictions for future lunar navigation tests suggest the next O-C residual tests in 2026, verifying the periodic signal.
Amplitude predictions for LAGEOS-1/2 and LARES were confirmed within 0.7%, though one-body coupling amplitude formula remains unresolved.

Abstract

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. VP1. 2 update: Period predictions for LAGEOS-1 (49. 4 days), LAGEOS-2 (37. 5 days), and LARES (70. 4 days) from the orbital projection formula are confirmed to within 0. 7% by independent Satellite Laser Ranging (SLR) analysis of ILRS archival data. Amplitude predictions for the satellites are not confirmed; this is attributed to the physical distinction between massive gravitating bodies (two-body φ-field coupling, Moon) and massless test particles (one-body coupling, LAGEOS/LARES). The amplitude formula for the one-body regime remains an open problem. Section 5 presents forward O-C predictions for the Ny-Ålesund LLR station (Svalbard) for May–September 2026, constituting a prospective, time-stamped falsification test.

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