Analysing orbits around the Moon for the Garatéa-L Mission

Recently, we have seen a series of space missions to the Moon and asteroids, whether for exploratory or scientific purposes, with possibilities of a lot of profitability in a sustainable way. Given this scenario, the Garatéa-L Mission (from the Brazilian original people language Tupi-Guarani, “Search for Life”) stands out, a genuinely Brazilian mission, whose main objective is to place a 6U brazilian cubeSat in orbit around the Moon, in 2024 or 2025, with the aim of carrying out experiments in astrobiology and studying the Aitken Basin, a basin located at the lunar south pole. In this context, the main goal of the present work is to study the orbits that meet the needs of the mission, obeying the necessary parameters of 300 km of periselene and 3000 km of aposelene. The system is formed by the Moon (the central body) and its gravitational coefficients, $J_2$ $J_{2}$ , $J_3$ $J_{3}$ and $C_{22}$ $C_{22}$ , the Earth as the perturbing body and a particle (cubesat). As a result, we obtained a sample of orbits that meets the requirements of the mission, their lifetimes in the region of interest and the evolution of the semi-major axis and eccentricity for each value of the inclination analysed. The results showed that the largest number of orbits with the longest lifetime have inclinations of 60° and 65°, with a semi-major axis of 3460 km and an eccentricity of approximately 0.38, remaining in the mission’s region of interest for an approximate period of 180 days.