# A Single-Launch Deployment Strategy for Lunar Constellations
## 1 Introduction  
Lunar exploration has seen renewed interest in recent years, with the Artemis-1 mission validating the new NASA Space Launch System and Orion spacecraft, designed to take humans back to the Moon, and deploying the first CubeSat missions to the cislunar and translunar space [1; 2; 3; 4]. The infrastructure that could support the forthcoming missions, either manned or autonomous, often relies on distributed satellite systems, such as constellations, that can provide navigation, telecommunication, and data relay services to both in-orbit and on-ground facilities [5; 6; 7; 8; 9; 10]. This deployment represents one of the most critical phases in the implementation of a satellite constellation, and its complexity is due to the need to distribute the satellites on different orbital planes, a task that is usually accomplished with dedicated launches. For constellations operating in low-Earth orbit (LEO), this issue is mitigated by the large number of launch opportunities available on the market. Unfortunately, this is not an option yet for lunar constellations, since the number of launches to the Moon is still limited to no more than a few per year. It should be observed that, when dealing with a small satellite constellation, limitations on the propellant (mass) budget and on the propulsion systems characterizing this class of spacecraft further complicate this issue, since traditional plane change maneuvers are not possible [11; 12]. A strategy is proposed here to deploy multiple satellites in different orbital planes based on a single-launch opportunity equivalent to that of the Artemis-1 mission. This result is achieved by taking advantage of low-energy trajectories associated with the Earth-Moon libration point \(L_{1}\)[13]. Libration points and their associated trajectories have been studied for decades [13; 14; 15; 16; 17; 18; 19; 20; 21; 22]. In 1978, the International Sun-Earth Explorer (ISEE)-3 was the first spacecraft to be deployed to a libration point orbit (LPO) [23], followed in 1991 by the Hiten mission [24], the first succeeding in an Earth-Moon transfer using a low-energy trajectory. In the late 1960s, [PERSON] was a pioneer in proposing constellations of satellites located in the neighborhood of Earth-Moon collinear libration points \(L_{1}\) and \(L_{2}\)[25], devoted to communication operations. A few decades later, [PERSON] et al. extended this design to Earth communication constellations [26] and, more recently, the use of LPO constellations has been investigated for lunar navigation services [27; 28; 29]. It should be noted that, when compared to LEO ones, LPO constellations allow the reduction of the fueling effort for station-keeping and the eclipse period but, by virtue of their larger distance from the ground, they are characterized by larger communication delay times and higher power consumption. Therefore, LEO constellations could be preferred for some applications [30; 31]. In 2004, [PERSON] et al. observed that a satellite can be transferred from a Lissajous orbit around the Earth-Moon libration point \(L_{1}\) to an Earth orbit whose inclination and right ascension of the ascending node (RAAN) depend only on the epoch at the beginning of the transfer [32]. Based on this fact, they proposed a constellation deployment strategy in which all the satellites are transferred from the same launch trajectory to the same Lissajous orbit where station-keeping is performed independently by each satellite waiting for the right epoch to transfer back to an Earth orbit with the desired inclination and RAAN values. Operating in the dynamic framework of the circular restricted 3-body problem (CR3 BP), [PERSON] and [PERSON] proposed a similar solution, in which the satellites are first transferred to the same halo orbit about the Earth-Moon \(L_{1}\) and are transferred back to LEO at different times, taking advantage of nodal precession to target the arrival orbital plane [33].