Resonance effects in orbits around the Moon

<title>Abstract</title> <p>Resonant orbits arise from specific commensurabilities between the orbital peri- ods of two or more bodies. A proper understanding of these orbital configurations is essential for analyzing long-term dynamic behavior. In this work, we analyze orbits around the Moon by considering the primary perturbing forces, including the effects of the selenopotential, third-body perturbations, and Solar Radiation Pressure (SRP). 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. An analytical approach is conducted to study six cases of resonance. The goal is to determine the initial values of the semi-major axis and inclination that contribute to amplifying the rate of change of orbital eccentricity and inclination, which can accelerate the reentry of space debris onto the lunar surface. Conversely, we also seek values of the semi-major axis and inclination that stabilize the eccentricity and inclination, thus helping to delay the reentry of a spacecraft. Using dynamic maps of the semi- major axis as a function of inclination, obtained via numerical integration of the equations of motion, we show the regions where eccentricity is strongly affected and where resonance zones emerge. These regions of large eccentricity variation may aid in the removal of space debris from lunar orbit. In particular, we show a range of semi-major axis values that exhibit a significant increase in eccentricity for resonant inclinations close to 60 and 120 degrees, corresponding to the critical inclination region in the prograde and retrograde cases. Finally, we identify the regions where artificial satellites in lunar orbit should avoid resonance effects.</p>