Quasi-frozen polar orbits around the Moon

<title>Abstract</title> <p>In this work, we analyze orbits around the Moon by considering the primary perturbing forces, including the effects of the selenopotential and third-body perturbations. We adopt a simplified model with zonal truncation up to order eighteen, incorporating sectoral and tesseral terms of order and degree three, named Model 18 × 3. Additionally, we develop an analytical model that includes zonal harmonics up to the J18 term, named Model 18 × 0. Using this analytical model, we analyze the conditions for frozen orbits when the perilune argument is 90 and 270 degrees. The results are presented in eccentricity versus inclina- tion graphs, from which the initial conditions of frozen orbits are obtained. By numerically integrating the equations of motion using these initial conditions, we identify quasi-frozen polar orbits. To validate the results, we used the GMAT soft- ware, considering a 50 × 50 order and degree selenopotential model and Earth’s gravitational perturbation.</p>