On the long-period lunar and solar effects on the motion of an artificial satellite: 2.

Abstract

The disturbing function for the long-period lunisolar effects is developed into a series of polynomials in the components of the vectorial elements in the direction to the disturbing body. This development is convergent for all eccentricities and all inclinations. The equations are established for the variation of elements in a form suitable for the use of numerical integration and for the development of the perturbations into trigonometric series with numerical coefficients. An application of Milankovich's theory of perturbations leads to the equations for perturbed elements in which the small numerical divisors, the sine of the inclination and the eccentricity, are not present. These new equations, like the equations for canonical elements, have a symmetrical form and a wider range of applicability than the equations for elliptic elements.