Searching for orbits to observe the poles of celestial bodies
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The objective of the present paper is to show a method to find orbits near artificial equilibrium points for a satellite equipped with a continuous thrust that allows it to stay near the poles of a celestial body. The physical system includes the presence of a moon of the celestial body under observation, and the perturbation caused by this moon is counteracted by an algorithm to help the satellite to stay close to its original position, instead of escape from it. The equations of motion are changed under some approximations, and analytical solutions for these equations are obtained and analyzed. Initial conditions are used such that their secular terms are nullified. These solutions are restricted to a short period of time, but we propose a method in which there are periodic updates in the thrust. Thus, the solutions can be extended for the duration of the mission. A numerical simulation is obtained, whose results are required to be in agreement with the analytical solution using these periodic adjustments of the thrust. This agreement means that the motion of the spacecraft remains bounded close to its initial position for longer times. Several systems with different sizes and mass parameters are used to show the results of the research, like Sun-Earth-Moon, Sun-Ida-Dactyl, Sun-Saturn-Titan and Sun-Mars-Phobos systems. The results also indicate the locations of points that require minimum magnitude of the thrust.