Moon's influence on the plane variation of circular orbits

The long-term orbital plane motion of a satellite in circular orbit has been investigated, taking into account the influence of the Earth's oblateness and luni-solar perturbations, to determine solutions characterised by initial conditions (in terms of Right Ascension of the Ascending Node and orbit inclination) which guarantee quasi-frozen orbital planes. The Moon's influence has been investigated considering the real motion of the lunar pole around the ecliptic pole, also evaluating the differences with respect to the simplified case in which these poles are considered as coincident at 23.445 deg of inclination. After having studied in detail the case of geosynchronous orbits, where at low inclination differences in the order of ±1.5 deg have been found for the optimal initial inclination with respect to the above-mentioned simplified case, the analysis has been extended to the range of altitude 20,000-60,000 km. The study has highlighted how the optimal initial conditions are strictly correlated to the launch date and how the differences between the real and the simplified cases increase with satellite altitude.