Abstract
This research explores the existence of some new families of frozen orbits for satellites orbiting the triaxial Moon. The Hamiltonian of the problem incorporates the Moon's gravitational zonal harmonic coefficients up to \({J_6}\), along with the most significant triaxiality terms \({J_{22}}\), \({J_{31}}\),\({J_{32}}\), \({J_{33}}\), and the third-body perturbation due to Earth. By applying canonical Lie transforms, the short periodic terms are eliminated from the Hamiltonian, retaining the long periodic terms up to the second order. This study uncovers new families of critical inclination roots, with one set close to polar orbits and another near the typical critical inclination. It examines the dynamical variations in critical inclination due to changes in eccentricity, semi-major axis, and argument of periapsis. A family of frozen orbits with a fixed apsidal line is derived and graphically represented. To ensure the stability of these orbits, the periapsis argument solution imposes specific restrictions on selecting the inclination that satisfies the frozen argument of periapsis condition. Perturbations in the critical inclination become notably significant for high lunar orbits due to 3rd body perturbation from Earth.