Astronomical Forcing through Geological Time

  1. P. L. de Boer2 and
  2. D. G. Smith3
  1. A. Berger and
  2. M. F. Loutre

Published Online: 29 APR 2009

DOI: 10.1002/9781444304039.ch2

Orbital Forcing and Cyclic Sequences

Orbital Forcing and Cyclic Sequences

How to Cite

Berger, A. and Loutre, M. F. (1994) Astronomical Forcing through Geological Time, in Orbital Forcing and Cyclic Sequences (eds P. L. de Boer and D. G. Smith), Blackwell Publishing Ltd., Oxford, UK. doi: 10.1002/9781444304039.ch2

Editor Information

  1. 2

    Utrecht, The Netherlands

  2. 3

    London, UK

Author Information

  1. Institut d'Astronomie et de Géophysique G. Lemaître, 2 Chemin du Cyclotron, 1348 Louvain-la-Neuve, Belgium

Publication History

  1. Published Online: 29 APR 2009
  2. Published Print: 28 JAN 1994

ISBN Information

Print ISBN: 9780632037360

Online ISBN: 9781444304039



  • astronomical forcing through geological time;
  • precessional frequency k to the ‘ slow’ and ‘fast’ varying parameters;
  • independent term of obliquity;
  • angular rotational speed;
  • fundamental frequencies


The sensitivity of the amplitudes and frequencies in the development of the Earth's orbital elements involved in the astronomical theory of palaeoclimates (obliquity and climatic precession) to the Earth–Moon distance and consequently to the length of the day and to the dynamical ellipticity of the Earth is investigated for the last few billions of years. The influence of the stability of the fundamental frequencies of planetary motion is also discussed.

The value of the amplitudes and frequencies for the most important terms of obliquity and climatic precession, as well as the value of the independent term for obliquity, have been computed for the last 2500 Ma with the assumption that the chaotic behaviour of the solar system may be disregarded, which is realistic for the last 200 Ma, and that the general solution of the planetary system has kept its general form over the last billion years. Moreover the time scale presented here assumes only two different lunar recession rates, while it could have varied more continuously.

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 (the 19-ka and 23-ka quasi-periods becoming respectively 11.3 and 12.7 ka at 2500 Ma BP) and for obliquity (the 41-ka and 54-ka quasi-periods becoming respectively 16.7 and 18.5 ka at 2500 Ma BP). At the same time, one observes for obliquity at 2500 Ma BP a relative enlargement of about 60% of the amplitudes, but a very weak increase (less than 0.1%) of the independent term. On the other hand, the amplitudes of precession change very little. These changes in the frequencies and amplitudes for both obliquity and climatic precession are larger for longer period terms.

The periods in eccentricity development are not influenced by variation of the lunar distance. Only the long-term changes of the fundamental planetary frequencies seem to induce very small variations in these periods, of the order of 1.5% over the last 200 Ma, although the chaotic behaviour of the planetary system complicates the problem particularly before 100 Ma BP.