Theory of Secular Perturbations of Asteroids Including Terms of Higher Orders and Higher Degrees

Abstract A theory of the secular perturbations of asteroids including terms of higher orders and higher degrees is constructed. After the short-periodic terms are eliminated, terms of up to the fourth degree are retained when factored by the disturbing mass, and terms of up to the second degree are retained when factored by the square of the mass of the disturbing planets. The solution is obtained by HORI’s (1966) perturbation theory. The difference between the new solution and existing solutions (retaining only second degree terms in the first order with respect to the disturbing mass) appears in the longitudes of the proper perihelion π1 and the proper node θ1. The new solution together with existing solutions are compared with the numerical integrations. The result shows that the new solution is superior to the existing ones.