On the Relation of the Lunar Recession and the Length-of-the-Day

TL;DR

This paper examines the consistency between lunar recession rates and the increase in Earth's length-of-the-day, highlighting discrepancies and discussing potential geophysical and cosmological implications.

Contribution

It provides a comprehensive review of observational data on lunar recession and Earth's rotation, analyzing their relationship and discussing possible explanations for discrepancies.

Findings

Observed LOD variation rate is 1.09 ms/cy from 1680 to 2020.

Lunar recession appears too large compared to Earth's tidal slowing.

Discrepancies may relate to geophysical effects or cosmological factors.

Abstract

We review the problem of the consistency between the observed values of the lunar recession from Lunar Laser Ranging (LLR) and of the increase of the length-of-the-day (LOD). From observations of lunar occultations completed by recent IERS data, we derive a variation rate of the LOD equal to 1.09 ms/cy from 1680 to 2020, which compares well with McCarthy and Babcock (1986) and Sidorenkov (2005). This rate is lower than the mean rate of 1.78 ms/cy derived by Stephenson et al. (2016) on the basis of eclipses in the Antiquity and Middle Age. The difference in the two observed rates starts at the epoch of a major change in the data accuracy with telescopic observations. The observed lunar recession appears too large when compared to the tidal slowing down of the Earth determined from eclipses in the Antiquity and Middle Age and even much more when determined from lunar occultations and IERS data from 1680 to 2020. With a proper account of the tidal effects and of the detailed studies on the atmospheric effects, the melting from icefields, the changes of the sea level, the glacial isostatic adjustment, and the core-mantle coupling, we conclude that the long-standing problem of the presence or absence of a local cosmological expansion is still an open question.