A contribution to a global a priori model of climatic changes for the Quaternary Ice Age is tentatively proposed. Special emphases are put on the astronomical problem and on the insolation available in the assumption of a perfectly transparent atmosphere. It is shown that for these two steps an accurate solution can be obtained, limiting the cumulative effect of computational approximation and allowing input to a climatological model to be of real value. For the earth's orbital elements, the proposed solution includes terms dependent to the second degree on disturbing masses, to third degree on planetary eccentricities and inclinations and, for the obliquity and the annual general precession in longitude, also to the second degree on earth's eccentricity. Improvements introduced by this solution upon the insolation computed through the Milankovitch series are deduced from the differences between Vernekar's results and present ones. The relative agreement between results clearly shows that the new astronomical solution is probably close to the ideal one from a paleoclimatological point of view.