## 1 Introduction  
In recent years, the lunar south pole has attracted growing attention due to its remarkable scientific and strategic potential. With more than 140 missions planned between 2023 and 2033, the exploration of this region has become a priority for major space agencies worldwide [1, 2]. This interest stems from both its unique geomorphological characteristics and the presence of permanently shadowed regions (PSRs), which are believed to contain significant deposits of water ice. These ice reservoirs, if confirmed, could serve as a crucial resource for future long-term lunar missions, providing essential support for a human presence by enabling in situ resource utilisation (ISRU) for drinking water, oxygen production, and fuel generation. Furthermore, certain elevated regions within the south pole receive near-continuous sunlight, making them ideal candidates for solar power installations that could sustain a permanent lunar base and other critical infrastructure [3].  
The biggest effort arrives from NASA's Artemis mission which aims to return humans to the Moon more than fifty years later. A key component of this effort is the Lunar Gateway,a space station planned to orbit the Moon, facilitating exploration missions and serving as a hub for scientific research and technology development. However, one of the primary challenges in establishing a sustainable lunar presence is ensuring continuous communication coverage over the south polar region. To address this, the European Space Agency (ESA) has introduced the Moonlight Initiative, a programme dedicated to developing a reliable lunar communication and navigation network that would provide uninterrupted connectivity between Earth, orbiting spacecraft, and surface missions [4]. To achieve continuous coverage of the lunar south pole, a multi-body constellation is essential. Various orbit options must be carefully analysed to determine the most effective configuration that balances coverage, stability, and operational cost. Various studies propose different orbital architectures that optimise communication and navigation for lunar exploration, pointing out that the stability of some elliptical orbits makes them highly cost-effective [5, 6]; furthermore, ref. [6] evidences the excellent scalability of circular polar orbits united with their potential for global coverage even if they require a larger number of satellites. The study of cislunar dynamics, particularly leveraging orbits around Earth-Moon Lagrange points L1 and L2, presents a promising solution [7]. These orbits offer unique advantages in maintaining continuous communication with Earth due to their specific geometric properties. The first part of this work is aimed at selecting a family of orbits that would best verify the requirements for local continuous coverage of the lunar polar regions. Thereafter, the analysis provides new insights into the residence time of different satellite constellations over a specific Artemis' landing site provided with different antenna minimum elevation angles; the constellations are propagated around Lagrangian points L1 and L2 exploiting high-fidelity simulations considering gravitational perturbations.