Nonresonant tesseral coupling. Shape matters

Abstract Long-term effects induced by the coupling of gravitational harmonics can be significant in nonresonant orbits about bodies whose shape clearly departs from an Earth-like mass distribution. Based on a perturbation arrangement that assumes a mild dominance of the zonal harmonic of the second degree, the transformation that removes the short-period terms is derived for a degree and order 3 truncation of the expansion of the gravitational potential. Particularization of the ensuing mean dynamics for the gravity coefficients of the Moon illustrates the important differences that the coupling of non-zonal terms may introduce with respect to typical perturbed Kepler motions.