  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.
