Variations of the Milankovitch frequencies in time

The sensitivity of the amplitudes and frequencies in the development of the Earth's orbital and rotational elements involved in the astronomical theory of paleoclimates (eccentricity, obliquity, and climate precession), to the Earth-Moon distance and consequently to the length of the day and to the dynamical ellipticity of the Earth has been discussed for the last billions of years. The shortening of the Earth-Moon distance and of the length of the day, as well as the lengthening of the dynamical ellipticity of the Earth back in time induce a shortening of the fundamental astronomical periods for precession and obliquity. At the same time, the amplitudes of the different terms in the development of the obliquity are undergoing a relative enlargement of about 50 percent at 2 x 10(exp 9) yr BP but the independent term is increasing very weakly (less than 0.1 percent). In other words, the value of the obliquity, which lies within a range of 21.7 to 24.9 deg over the Quarternary was restricted to a range of 22.5 to 24.1 deg at 2 x 10(exp 9) yr BP. On the other hand, the amplitudes in the development of the climatic precession do not change. Moreover, these changes in the frequencies and amplitudes for both obliquity and climatic precession are larger for longer period terms. Finally, the periods in the eccentricity development are not influenced by the variation of the lunar distance. But the motion of the solar system, especially of the inner planets, was shown to be chaotic. It means that it is impossible to compute the exact motion of the planets over more than about 100 Myr, and the fundamental frequencies of the systems are not fixed quantities, but are slowly varying with time. As long as we consider the most important terms, the maximum deviation from the present-day value of the 19-kyr precessional period due to the chaotic motion of the solar system only does not reach more than a few tens of years around 80 Myr BP. Therefore the shortening of the obliquity and climatic precession periods is mostly driven by the change in the lunar distance and the consequent variations in the dynamical ellipticity of the Earth's angular speed. At first sight, the deviation in the period for the eccentricity can be neglected, as the chaotic behavior of the solar system implies a relative change of the main periods by less than 0.2 percent, 1.4 percent, and 1.9 percent respectively, this maximum change being achieved around 80 Myr BP. This implies, in particular, that the eccentricity periods for Quarternary climate studies may be considered more or less constant for pre-Quaternay times and equal to their Quaternary values.