Secular variations of major planets' orbital elements

Abstract

The secular variations of the orbital elements of principal planets are calculated by means of classical Lagrange's method. The terms of the second order with respect to mass, introduced by Hill (1897) and Brouwer and van Woerkom (1950), have been taken into account as well. The best contemporary values of planetary masses and mean elements (Bretagnon, 1982) served as the starting data set for this calculation. Considerable differences with respect to previous solutions of the same type (Brouwer and van Woerkom, 1950: Sharaf and Boudnikova, 1967) were found in the coefficientsA55,A56, andA66 of the system of equations of variation of elements and in the roots (frequencies)r5 andr6. Results are compared with some higher order/higher degree solutions and their accuracy discussed. It is confirmed that the solutions like that of Brouwer and van Woerkom, although not being completely inferior to all higher order/higher degree ones, can be considered as the first approximation only. Hence, they should be replaced by more accurate ones (Duriez, 1979: Bretagnon, 1984: Laskar, 1984) in the future applications.