# Dynamics and Control of Typical Orbits around Saturn
## 1 Introduction  
Interplanetary exploration is one of the most important methods to seek the origin and evolution of the universe, suitable living planets for human beings, and the existence of other intelligent life. Over the last few decades, with the development of science and technology, we have launched numerous spaceships to explore the planets of our solar system. Saturn, since its discovery, is absolutely one of the most attractive planets in the solar system. The tremendous thin ring consisting of many ringlets has become the famous characteristic of Saturn. Saturn is the second biggest planet in the solar system with a volume about 755 times larger than Earth. It is made predominantly of hydrogen and helium, which causes its density to be smaller than water. Saturn rotates so fast that its rotation period is only 10.656 h [1]. However, its orbital period is tremendously longer than its rotation period, at 29.4 Earth years [1]. The gravitational field of the Saturn system is extremely complicated, as Saturn is the planet with the largest amount of moons in the solar system. There are 53 known moons and 29 moons waiting to be formally confirmed [2]. The largest moon in the Saturn system, named Titan, was found to have a nitrogen-rich atmosphere similar to that of ancient Earth. Therefore, the exploration of the Saturnian system could promote the process of searching for habitable planets and researching the evolution of planets in the solar system. However, few spacecraft had investigated Saturn. Pioneer11 is the first spacecraft to reach the Saturn system. It reached Saturn in 1979, and discovered a narrow ring, which is named the F-ring, outside the A-ring for the first time [3]. It also first discovered the existence of the magnetosphere of Saturn. After two years, Voyager 2, the third spacecraft to visit Saturn, gained a glimpse of Saturn on its way to Uranus. Using photopolarimeter,Voyager 2 provided more detail about the ringlets and shepherding moons around the F-ring [4]. The most famous and longest exploration around Saturn is the Cassini-Huygens mission. Cassini-Huygens was the first mission to orbit Saturn [5]. It completed 294 orbits and sent total 453,048 images back to Earth in 13 years of discovery. These missions provided a precious opportunity for planetary scientists to observe Saturn closely. [PERSON] [6] and [PERSON] et al. [7] presented Saturnian gravitational zonal harmonic coefficients using spacecraft tracking data. [PERSON] et al. [8] observed the infalling material flux, which was calculated to be between 4800 and 45,000 kg/s, could affect the carbon content of Saturnian ionosphere and atmosphere. [PERSON] et al. [9] emphasized the importance of thermospheric temperatures when examining the state of Saturnian magnetosphere. The formation and evolution of the Saturnian interior structure [10], the magnetosphere [11], rings [12], and moons [13] around Saturn are always at the centre of the research [14]. Nevertheless, few researchers study the dynamics around Saturn. On the contrary, the studies of dynamics around terrestrial planets had already enriched the theories of [PERSON] [15] and [PERSON] [16]. The applications of these theories had been widely used when scientists and engineers analyzed the dynamics of artificial satellites around Earth. The design of frozen orbits was first proposed by [PERSON] et al. [17]. The existence of four equilibrium points of geostationary orbits was shown by [PERSON] et al. [18]. Moreover, the periodic orbits around these equilibrium points are investigated by [PERSON] et al. [19]. [PERSON] [20] considered secular perturbations, combining Earth's aspheric gravitation with the luni-solar gravitation to analyze the dynamics of the medium Earth orbit navigation satellites. At the same time, some feasible research aimed to offset the effect caused by perturbations. [PERSON] [21] studied predicting the local time of the ascending node of sun-synchronous orbits around Earth. [PERSON] et al.