The Main Problem of Lunar Orbit Revisited

A novel algorithm based on the Lindstedt–Poincaré method is proposed to construct an analytical solution of the lunar orbit. Based on the analytical solution, a numerical fitting algorithm is proposed to improve the coefficients of the analytical solution so that its accuracy can reach the level of a few kilometers within 20 yr. By fitting our solution to the long-term JPL ephemerides, we are able to recover the receding speed of the Moon from the Earth due to tidal effects. The proposed algorithm also provides a general way to treat the third-body perturbation in rectangular coordinates.