## 2 Multi-Body Constellation Design
### Possible Cislunar Orbits  
There are several solutions for orbiting the Moon which will be presented below to provide an initial comparative assessment [8]: a visual representation is also provided in Figure 1.  
* **Low Lunar Orbits** (LLOs) are typically circular orbits or slightly elliptical with an average altitude of around 100 km and any possible inclination; these orbits turn out to be the perfect candidate for surface access. * **Elliptical Lunar Orbits** (ELOs) are equatorial orbits with a low perilune distance providing favourable access to the surface, but compared to the previous one they reduce access costs from Earth. * **Prograde Circular Orbits** (PCOs) have a radius up to 5000 km; they are highly stable and require almost zero corrections to be maintained. * **Frozen Lunar Orbits** are orbits with constant average eccentricity and an argument of periapsis values; this kind of orbit was discovered by analysing gravitational potential and looking for regions, corresponding to defined orbital parameters, in which effects due to perturbations are cancelled out or minimised. Those orbits exist for only certain combinations of energy, eccentricity, and inclination, and although they can provide high stability over time, research into them is not trivial. An in-depth study of this kind of orbit may be found in [9]. * **Earth-Moon Liberation Point Halo Orbits** are periodic orbits around the collinear liberation points which remain relatively fixed in the Earth-Moon plane, rotating at the same rate as that of the Moon around the Earth and that of the Moon around its own axis. [PERSON] coined the term halo in 1966, noting how these orbits create a halo about the Moon by observing them from Earth [10]. Within a full ephemeris model, they may be slightly unstable, but their strengths include continuous Earth visibility, relatively easy access from Earth, and in certain cases predictable behaviour. * **Distant Retrograde Orbits*** The [PERSON]/Mozhaev constellation consisting of evenly distributed satellites in evenly distributed planes in circular orbits. * Identical orbit shape: anomalistic period, argument of perigee, height of perigee, and inclination:
- Compatibility: the orbital period is evaluated in such a way as to yield a perfectly repeated ground track;
- An equally displaced node line along the equatorial plane for each satellite in a complete FC. Compared to the Walker constellation design, an FC design demonstrates higher performance given the higher number of possible design parameters [15]: furthermore, with the Flower Constellation the design process is generalised to include elliptical orbits allowing a greater focus on particular areas. Architectures for Lunar South Pole Coverage  
Useful guidelines to design a local coverage constellation are proposed in [16]: to provide redundant, continuous, and focused coverage minimising the number of satellites, orbits should have the following characteristics:  
* Sufficiently large semi-major axis values to produce continuous single and double coverage with a minimal number of satellites;
* Large eccentricity values to focus coverage near apoapsis for longer contact durations;
* Inclination values to orient the coverage swaths over the poles (rather than the equator):
* The argument of periapsis values set to either \(90^{\circ}\) or \(270^{\circ}\) depending on whether apoapsis should be over the south pole or north pole, respectively. Having understood the necessary characteristics for a coverage constellation, the choice of the ideal orbit is the result of a thorough trade-off between the constellation stability, i.e., its lifetime, and the deploying and maintenance cost of the entire multi-body architecture, which is extremely tied to the number and size of the single spacecraft. For example, because of the Moon's anisotropic gravitational field, the authors of ref.