Searching sequences of resonant orbits between a spacecraft and Jupiter

This research shows a study of the dynamical behavior of a spacecraft that performs a series of close approaches with the planet Jupiter. The main idea is to find a sequence of resonant orbits that allows the spacecraft to stay in the region of the space near the orbit of Jupiter around the Sun gaining energy from each passage by the planet. The dynamical model considers the existence of only two massive bodies in the systems, which are the Sun and Jupiter. They are assumed to be in circular orbits around their center of mass. Analytical equations are used to obtain the values of the parameters required to get this sequence of close approaches. Those equations are useful, because they show which orbits are physically possible when taking into account that the periapsis distances have to be above the surface of the Sun and that the closest approach distances during the passage by Jupiter have to be above its surface