A study of the planetary secular perturbations

We compare the classical method and Gauss' method for deriving secular inequalities and find the latter to be more accurate, especially in cases where the orbital eccentricities and inclination are moderate or large. Based on Gauss' method, we derive some practical algorithms and then Investigate numerically the orbital evolution of the nine major planets over the last 2,100,000 years or so, taking into account all their secular perturbations. The main results are shown in TABLE 3, alongside with Stockwell's results for easy comparison. Detailed variations of the elements are plotted in Figs. 1 and 2.