On the relation of the lunar recession and the length-of-the-day

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 (Phys. Earth Planet. Inter. 44: 281, 1986) and Sidorenkov (Astron. Astrophys. Trans. 24: 425, 2005). This rate is lower than the mean rate of 1.78 ms/cy derived by Stephenson et al. (Proc. R. Soc. A 472: 20160404, 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.

Local Dynamical Effects of Scale Invariance: the Lunar Recession

“…The LOD is defined as the excess of the length of the day with respect to 86'400 SI seconds. We note that the value of 2.395 ms/yr for the change of the LOD over centuries is consistent with the calculation of the tidal coupling under the assumption of conservation of the global angular momentum of the Earth-Moon system [14,31]. This theoretical value of the increase of the LOD has also been very well confirmed recently by [2].…”

“…The most uncertain contribution is that of the core coupling which seems responsible for the 1500 yr undulation. Over the long term, the various negative and positive effects appear to balance each other before the year 1990, see data by [36,37] and our recent detailed review of the problem [31], (since 1990, the fast melting of even the polar ice fields contribute to an increase of the Earth momentum of inertia). The reality of the difference between the above observed mean value of the LOD (1.78 ms/cy) and the value due to the tidal interaction (2.395 ms/cy) has recently been further emphasized by [41].…”

“…The question whether astrophysical systems, such as the solar system and galaxies, follow the Hubble-Lemaître expansion has stimulated a vast literature since the pioneer work of McVittie [33,34] and the Einstein-Straus theorem [16]. The presence of an expansion at smaller scales has been considered as an open question by Bonnor [5] and recently revisited by us [31]. The fact that the dark-energy dominates the matter-energy content of the Universe and that this energy appears as driving the acceleration of expansion is reviving the interest in the question: If dark energy is uniformly distributed in space would it not imply effects that may be present at small scales?…”

An alternative explanation of the orbital expansion of Titan and other bodies in the Solar system

“…If the Earth's rotation slows down on average about 1 ms per century [40], then by the angular momentum conservation law of the Earth-Moon system the average distance d increases about 1.25 cm/yr using the advance of [29, pp. 184-187].…”

“…Since this system is completely locked into the 1:1:1 resonance, tidal forces are negligible and its large orbital momentum can again be due to the fictitious repulsive force. For more information about the local Hubble expansion we refer to [12,14,25,26,27,28,30,36,37,38,39,40].…”