# Low-Thrust Transfer to Quasi-Synchronous Martian Elliptic Orbit via Nonlinear Feedback Control
## 1 Introduction  
Mars represents a primary objective in the forthcoming space exploration programs. Several scientific missions are planned or currently ongoing, with the prospect of carrying out the first human mission in the next two decades. A satellite constellation capable of supplying continuous, global coverage over the great majority of Mars would represent a precious asset as a communications infrastructure useful to orbiters, probes, and instruments located on the surface while extending the existing capabilities of NASA's Deep Space Network. Several goals were defined [1] for a satellite constellation about Mars, including the global coverage over a specified time span and the maximization of the communication and navigation performance across all latitudes. [PERSON] et al. [2] designed a constellation of eight satellites mainly devoted to carrying out radio occultation measurements, with reconfiguration capabilities aimed at providing navigation services. [PERSON] et al. [3] proposed four configurations of microsatellite constellations using low-altitude, inclined orbits. Each configuration is composed of six satellites and ensures satisfactory navigation and communication performance, with special regard to the equatorial region. However, continuous coverage is not guaranteed, and the maximum revisit even reaches 8 h while exceeding 2 h over the great majority of the Martian surface. [PERSON] and [PERSON] [4] proposed a constellation of 15 satellites that ensures global and continuous coverage of the entire Martian surface, using 5 equally spaced, inclined orbit planes. Most recently, [PERSON] et al. [5] designed a constellation composed of 12 satellitesreleased in 4 distinct orbit planes. While three satellites travel an areostationary orbit, the remaining nine satellites are released in three repeating, circular, quasi-synchronous, inclined orbits. This configuration was proven to guarantee global and continuous coverage while ensuring repetition and predictability of the visible passes as well as the visibility of multiple satellites. While the preceding contributions deal with the constellation of satellites that travel circular orbits, the scientific literature also includes relevant contributions that consider eccentric-orbit constellations. Tundra and Molniya (2016); Tundra and Molniya (2016) inclined orbits are especially suitable for the coverage of high-latitude regions. [PERSON] and [PERSON] (2018) propose highly elliptical polar orbits for global-coverage constellations, whereas [PERSON] (2019) introduced the polyhedral elliptic-orbit constellation. The same author also designed the Ellipso configuration Tundra and Molniya (2019), composed of elliptic orbits and a single circular, equatorial, medium-altitude orbit. [PERSON] and [PERSON] [PERSON] and [PERSON] (2018) used a correlation-based approach to design elliptic-orbit constellations composed of a reduced number of satellites and tailored to continuous regional coverage. To ensure repetition and predictability of the visible passes, this study considers repeating-ground-track, quasi-synchronous orbits at the critical inclination as a convenient option for Martian constellations. Moreover, the low-thrust transfer to this orbit is investigated, with the use of nonlinear orbit control, starting from the ESA 4-sol orbit [PERSON] and Teofilatto (2018), which is entered after planetary capture. Orbit dynamics about Mars is modeled with the inclusion of the most relevant perturbations, i.e., several harmonics of the areopotential, together with the gravitational pull due to the Sun as a third body and solar radiation pressure. Low-thrust propulsion has recently gained increased relevance in space mission design because it allows substantial propellant savings at the price of increasing (even considerably) the time of flight.