# Solar Sail-Based Mars-Synchronous Displaced Orbits for Remote Sensing Applications
## 1 Introduction  
Solar radiation pressure is the physical phenomenon that enables the operation of solar sails, a class of advanced propulsion systems for space navigation that convert sunlight into propulsive acceleration without the need for propellant expenditure [1, 2, 3]. In particular, photonic solar sails reflect photons coming from the Sun thanks to a large and thin membrane coated with a highly reflective material (e.g., aluminum), while refractive [4, 5] and diffractive [6, 7, 8] sails exploit other optical phenomena such as refraction and diffraction of light. Thanks to their intrinsic nature as propellants' propulsion systems, solar sails are particularly suitable for carrying out long-term missions or covering trajectories that require the continuous application of a steerable (but usually of small magnitude) thrust [9]. A category of heliocentric missions to which solar sails would be well suited is that constituted by the generation and maintenance of displaced non-Keplerian orbits (DNKOs) around the Sun [10]. They are two-dimensional, closed heliocentric trajectories that do not contain the center of mass of the primary attractor of the solar sail itself [11, 12] (i.e., the Sun) and, for this reason, require a continuous propulsive acceleration to balance both the (apparent) centrifugal and gravitational forces acting on the spacecraft. In this context, it is interesting to recall that an approximation of a circular or an elliptical DNKO may also be obtained by considering a sequence of Keplerian arcs patched by a set of suitable (high-thrust-induced) impulsive maneuvers, as proposed first by [PERSON] [13] for a circular orbit and then generalized by [PERSON] et al. [14] for a generic, elliptic trajectory. The employment of a heliocentric DNKO is useful for monitoring high-latitude regions of planets [15] (or generic celestial bodies) and it is an interesting potential option formany other mission applications, as discussed by [PERSON] at p. 25 of Ref. [16] and by [PERSON] et al. [10] in their useful and interesting survey paper published in 2011. Among all the possible scientific applications, it is interesting to mention, for example, continuous solar wind monitoring [17; 18], real-time polar imaging and stereographic investigations of a planetary surface [19; 20; 21], continuous communications with high-latitude regions, and in situ observations of the planetary rings. That is the reason why so many studies have dealt with the problem of reaching and maintaining DNKOs by means of a solar sail-propelled spacecraft. In this context, [PERSON] and [PERSON] [12] proposed exploiting solar sails to generate families of artificial libration points and displaced (periodic) orbits around the Earth, while [PERSON] et al. [19; 22] analyzed the possibility of maintaining elliptical DNKOs by means of a solar sail for planetary polar observation. In particular, [PERSON]. [19; 22] investigated the relative orbit design and control methods for formation flight around an assigned displaced orbit maintained by a spacecraft equipped with a classical (photonic) solar sail. About ten years ago, [PERSON] et al. [21] analyzed solar sail displaced orbits in [PERSON]'s restricted three-body problem, while [PERSON] et al. [23; 24] investigated the interesting concept of a pole-sitter mission, in which the spacecraft is always above one of Earth's geographic poles to obtain the continuous observation of planetary high-latitude regions. Finally, [PERSON] et al. [25] analyzed the possibility of using a classical solar sail to generate artificial equilibrium points and displaced periodic orbits around small bodies in the solar system such as asteroids or binary asteroid systems. More recently, [PERSON] et al. [26; 27] studied the performance of [PERSON]'s magnetic sails [28; 29; 30] and [PERSON]'s diffractive sails [6; 7; 8] in maintaining circular DNKOs of assigned characteristics, with applications in a typical Earth-based mission scenario.