geostationary orbits was first put up by [PERSON] [6]. He pointed out that satellites with an altitude of 36,000 km above the equator of the Earth would have the same rotation rates as the Earth and stay stationary relative to an observer on the equator. Therefore, geostationary satellites are often used for the sake of communications and navigations. Four equilibrium solutions for geostationary orbits were shown to exist by [PERSON] [7]. Moreover, two of them were stable while the other two were unstable. [PERSON] [8] calculated periodic orbits around equilibrium points in the Earth second degree and order gravity field. For Mars, the stationary orbits, also known as areostationary orbits, and the equilibrium points were studied by [PERSON] et al. [9]. The periodic orbits around the equilibrium points were also calculated by [PERSON] et al. [10]. For orbits at the critical inclination, the eccentricity and argument of perigee are invariant on average. The concept of the Earth critical inclination was first introduced by [PERSON] [11]. [PERSON] [12] used canonical transformations to eliminate short-period terms. [PERSON] et al. gave a geometrical interpretation of the critical inclination for satellites by investigating the averaged Hamilton system [8]. Representatives of orbits at the critical inclination are the Russian Molniya satellites. The combined effects of the critical inclination and the 2:1 mean motion resonance of a Molniya orbit have been intensively studied since then, for example, in [13; 14; 15; 16; 17]. Similarly, frozen orbits are characterized by the invariance of average eccentricity and argument of perigee. Frozen orbits are not limited to specific inclinations. They may exist at any inclination. Usually, the argument of perigee is equal to 90 or 270 deg, depending on the sign of the ratio of the harmonic coefficients \(J_{3}\) and \(J_{2}\). Frozen orbits were first proposed by [PERSON] et al. [18] for orbit analysis of the Earth satellite SEASAT-A. [PERSON] et al. [19] showed that there exist three families of frozen orbits in the averaged zonal problem up to \(J_{9}\) in the gravity field of an Earth-like planet. The frozen orbits around the moon in the full gravity model were considered by [PERSON] [20], and [PERSON] [21]. Some researchers also view orbits at the critical inclination as frozen orbits, for example [19; 22]. Sun-synchronous orbits are defined with a precession rate of the orbital plane equal to the revolution angular velocity around the sun. Generally, remote sensing satellites are placed into these orbits. [PERSON] et al. [23] used an undefined, non-orientation-constrained, low-thrust propulsion system to consider an extension of the sun-synchronous orbits. For repeating ground track orbits, the trajectory ground track repeats after a whole number of revolutions within some days. Orbits of this type are widely used to achieve better coverage properties. [PERSON] showed that orbits repeating their ground track on the surface of the Earth were members of periodic-orbit families of the tesseral problem of the Earth artificial satellite [24]. [PERSON] [25] considered the leading terms of the Earth's oblateness and the luni-solar gravitational perturbations to describe the secular dynamics of navigation satellites moving in the medium Earth orbit and geosynchronous orbit regions. [PERSON] et al. [9] calculated these five types of special orbits around Mars with analytical formulations and numerical simulations. In fact, the gravity field of Mars shares many similarities with that of the Earth. The \(J_{2}\) terms of them are dominant among the harmonic coefficients. However, the \(J_{2}\) term is not as dominant as Earth's \(J_{2}\). The other first few harmonic coefficients are also strong for Mars: about 1-2 orders of magnitude smaller than \(J_{2}\); for the Earth, the other first few harmonic coefficients are about 3-4 orders of magnitude smaller than \(J_{2}\). The situation is rather different for Jupiter compared with the Earth and Mars.