  In his mathematical theory, Milankovic finds a link between the heat received
by the Earth surface per unit time as a function of the solar ephemerids and
derives a model of climate changes at periods longer than a few thousand years
and more. In this paper, we investigate the potential connections of global
temperature and Earth rotation at much shorter periods, in the complementary
range of one to a few hundred years. For temperature, we select the HadCrut05.
For Earth rotation, defined by pole coordinates and length of day, we use the
IERS data sets. Using iterative Singular Spectrum Analysis (iSSA), we extract
the trend and quasi-periodic components of these time series. The first
quasi-periodic components (period ~80-90 years) are expressions of the
Gleissberg cycle and are identical (at the level of uncertainty of the data).
Taken together, the trend and Gleissberg components allow one to reconstruct
87% of the variance of the data for lod and 48% for temperature. The next four
iSSA components, with periods ~40, 22, 15 and 9 years. The Lagrange and Laplace
theories imply that the derivative of pole motion should be identical to lod
variations: this strong check is passed by the trend + Gleissberg
reconstructions. The annual oscillations of pole motion and lod are linked to
annual variations in Sun-Earth distance, in agreement with an astronomical, but
not a climatic origin. The results obtained in this paper for the observed
temperature/rotation couple add to the growing list of evidence of solar and
planetary forcings of gravitational nature on a number of geophysical processes
(including sea-level, sea-level pressure, sea-ice extent, oceanic climate
indices).
