Long-term variations of the Earth's orbital elements

Critical analysis of theories of the long-term variations of the ecliptical elements of the Earth leads to the following conclusions, regarding the influence of different terms on the accuracy of the expansions used:

1. further improvement in planetary masses will not have significant influence:
2. for the (e, π) system, terms depending upon the second order as to the disturbing masses are more important than ones coming from the third degree with respect to the planetary eccentricities and inclinations;
3. for the (i, Ω) system, the latter terms have highly significant influence, whereas additional terms in masses are negligible. The same conclusion can be drawn for (ε,Ψ _g ). Using these results, a new solution for the long-term variations of the Earth's orbital elements is obtained. The results fore, π,i, Ω include terms depending upon the second power as to the disturbing masses and to the third degree with respect to the planetarye's andi's. For the obliquity ε and the annual general precession in longitudeΨ _g , a Laplace series is proposed where amplitudes, mean rates and phases are computed from those of the (i, Ω) system.