On the Slow Drift of Solstices: Milankovic Cycles and Mean Global Temperature

Abstract

The Earth's revolution is modified by changes in inclination of its rotation axis. Despite the fact that the gravity field is central, the Earth's trajectory is not closed and the equinoxes drift. Changes in polar motion and revolution are coupled through the Liouville-Euler equations. Milankovic (1920) argued that the shortest precession period of solstices is 20,700 years: the Summer solstice in one hemisphere takes place alternately every 11 kyr at perihelion and at aphelion. Milanković assumed that the planetary distances to the Sun and the solar ephemerids are constant. There are now observations that allow one to drop these assumptions. We have submitted the time series for the Earth's pole of rotation, global mean surface temperature and ephemeris to iterative Singular Spectrum Analysis. iSSA extracts from each a trend, a 1yr and a 60yr component. Both the apparent drift of solstices of Earth around the Sun and the global mean temperature exhibit a strong 60yr oscillation. We monitor the precession of the Earth's elliptical orbit using the positions of the solstices as a function of Sun-Earth distance. The "fixed dates" of solstices actually drift. Comparing the time evolution of the Winter and Summer solstices positions of the rotation pole and the first iSSA component (trend) of the temperature allows one to recognize some common features. A basic equation from Milankovic links the derivative of heat received at a given location on Earth to solar insolation, known functions of the location coordinates, solar declination and hour angle, with an inverse square dependence on the Sun-Earth distance. We have translated the drift of solstices as a function of distance to the Sun into the geometrical insolation theory of Milankovic. Shifting the inverse square of the 60yr iSSA drift of solstices by 15 years with respect to the first derivative of the 60yr iSSA trend of temperature, that is exactly a quadrature in time, puts the two curves in quasi-exact superimposition. The probability of a chance coincidence appears very low. Correlation does not imply causality when there is no accompanying model. Here Milankovic's equation can be considered as a model that is widely accepted. This paper identifies a case of agreement between observations and a mathematical formulation, a case in which an element of global surface temperature could be caused by changes in the Earth's rotation axis .