Quasi Satellite Orbits to observe a possible small moon of Pallas

The purpose of this paper is to make a numerical search for natural orbits that can be used for a spacecraft to study a possible small moon of Pallas. There are many speculations about the existence of a small companion around this large asteroid, so finding and classifying orbits around this possible celestial body is an interesting problem in astrodynamics and that can be used for a spacecraft to observe this body. It is assumed that this moon has a radius that can vary from 0.125 to 1 km and that is located 750 or 500 km away from the center of Pallas. The idea is to show the effects of this parameter in the orbits around this moon. It means that the moon is much smaller than Pallas, so Keplerian orbits are not possible around it. To solve this problem, it is possible to find some special orbits that are called Quasi Satellite Orbits (QSO). They are orbits dominated by the gravity of Pallas, but that use the smaller perturbation from the moon to keep the spacecraft close to it. The present work searches for orbits that make the spacecraft to remain at given limits in its distance from the moon, like in the range from 3 to 50 km, the values used as an example in the present paper. This value is used because it is a good range to observe the body without getting to close to it, so reducing the risks of collisions. Each trajectory can be identified by the initial conditions of the spacecraft with respect to the moon, which means its initial position and velocity. The dynamics considers the restricted three-body problem and the influence of the solar radiation pressure, because some spacecraft may have higher values for the area-to-mass ratio, which gives a non-negligible effect in the trajectory of the spacecraft.