Abstract |
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The analytical expressions of the `secular' variations of the orbital elements of the Earth are derived in a vectorial form for the two basic systems (/b e/, pi ) and (/b i/, Omega ). The accuracy of the solution when expanded in series of trigonometrical terms is discussed. Successive improvements lead to a solution including terms depending on the second power of the masses and the third degree with respect to the eccentricities and inclinations of the planets. Then the Laplace solution for the obliquity and precession is revised to obtain an accuracy consistent with the basic systems. The analysis of the expansion including terms depending on the second degree to the eccentricity it is concluded that, for a period up to 10/sup 6/ years from present, a solution where Laplace expansion includes terms of the second power to the masses and third degree to the (/b e/,/b i/) coming from the basic system (/b i/, Omega ) may be accepted. |