Abstract
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:
-
(a)
further improvement in planetary masses will not have significant influence:
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(b)
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;
-
(c)
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.
Résumé
L'analyse critique de théories des variations à longues périodes des éléments de l'orbite terrestre conduit aux conclusions suivantes en ce qui concerne l'influence des différents termes sur la précision même des développements utilisés:
-
(a)
l'amélioration ultérieure de la connaissance des masses planétaires n'aura plus d'incidence notable sur la précision de la variation temporelle des divers éléments de l'écliptique.
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(b)
pour le système (e, π), les termes au second ordre des masses ont une influence beaucoup plus grande que ceux au troisième degré des excentricités et des inclinaisons.
-
(c)
pour le système (i, Ω), ces derniers termes jouent, au contraire, un rôle prépondérant. Ceci est aussi valable pour le système (ε,Ψ g ).
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Berger, A. Long-term variations of the Earth's orbital elements. Celestial Mechanics 15, 53–74 (1977). https://doi.org/10.1007/BF01229048
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DOI: https://doi.org/10.1007/BF01229048