The first part of this note provides all trigonometrical formulas which allow the direct spectral analysis and the computation of those long-term variations of the earth's orbital elements which are of primary interest for the computation of the insolation. The elements are the eccentricity, the longitude of the perihelion, the processional parameter and the obliquity. This new formulary is much more simple to use than the ones previously designed and still provides excellent accuracy, mainly because it takes into account the influence of the most important higher order terms in the series expansions. The second part is devoted to the computation of the daily insolation both for calendar and solar dates.