On the influence of geometric intuition in the development of celestial mechanics

Abstract

The connections between geometric intuition and the analytic statement of a problem are briefly investigated. It is especially emphasized the implications involved by Lagrange's classical method of the variation of the parameters when applied to perturbation theories. To avoid some difficulties which arise in classical methods, a new guide is proposed, that essentially implies the classification of the orbital variables according to the role they play. We shall have according to this statement, variables that change explicitly with time (dynamic variables), and variables that change implicitly with time (geometric variables). Appropriate statement of the problem gives rise to an interesting equation already quoted in previous papers, published in other numbers of this Bulletin. The new statement opens an interesting field of research which seeks for a closer connection between the geometry implied by mechanic problems and the corresponding analytic statement of the same. The main result will be such that, in the particular case of Celestial Mechanics, it is possible to approach the desideratum of having series for the coordinates, convergent for every value of the independent variable.