## 5 Evaluation for Lunar NHRO Orbiters for NAV/COM Applications  
One of the next missions that will be deployed in a Moon Halo orbit is the Lunar Gateway. The Lunar Gateway will be a science laboratory, a test bed for innovative technologies, and represents a stepping stone to deep space exploration, especially toward Mars [9]. The current baseline orbit for the Gateway is an NRHO with a period of approximately 6.56 days. It exhibits a 9:2 resonance with the lunar synodic period, completing nine revolutions around the Moon every two synodic months. The mean radius at perilune is approximately 3400 km, while the orbit extends to a radius of approximately 71,000 km at apolune [35]. The case study proposed and evaluated here is a system of three spacecraft: the main one, which can be the Gateway, and two additional anchor orbiters for a totally autonomous and precise OD&T and for providing Navigation and Telecommunication services on the Moon's surface, and in particular on the Moon South Pole, where the future Artemis missions are planned [36]. The idea is to test the possibility to add a reduced number of small and inexpensive spacecraft in the same orbit as the Lunar Gateway to be used as relays for communication with the Moon's Surface and for the transmission of ranging signals (as in the case of terrestrial GNSS system) to provide a navigation service. The additional orbiters can be equipped only with a telecommunication payload for communication with the Moon's surface (and for transmitting ranging signals) and with ISLs able to perform the TOA and FOA measurements with the Gateway and, in principle, can be deployed from the same vector used for the Gateway components or from the Gateway itself. All of the OD&T operations are performed on the Gateway. The constellation for the test is composed of the Gateway and two additional spacecraft and is represented in Figure 5; all the details about the constellation are reported in Table 1.  
As can be seen from Figure 5, the spacecraft are not equally distributed in the orbit; this configuration was chosen because it has good performance in terms of Navigation and Telecommunication service availability on the South Pole of the Moon. Figure 6 reports the elevation angle for each spacecraft for all the orbiting period, for different epochs, as seen from the South Pole. It is possible to note that there is always at least one satellite in the view from the South Pole that can be used for telecommunication purposes with an elevation angle higher than 40 degrees. Figure 5: Constellation of spacecraft in the NRHO, composed of the Lunar Gateway and two additional floating anchors. Moreover, three satellites are in view for more than 95% of the time with an elevation angle higher than 10 degrees and can be used as ranging sources for navigation purposes. Having three synchronized satellites in view, it is possible to have an estimation of the user position if it is imposed to be on the Moon surface exploiting a Digital Elevation Model (DEM) or, for flying users, exploiting the DEM together with an altimeter as shown, for example, in [37]. Simulations of the OD&T process are performed using the previously introduced orbit determination algorithm and considering the errors reported in Table 2, exploding different time spans (between one and two orbital periods) and measuring intervals (between 15 and 60 min) for two system conditions: with (RR) and without (NORR) range-rate measurements. These two different configurations are compared to understand if the simpler configuration exploiting anchors without the ability to perform PLL-based range-rate measurements is also able to allow OD&T performances compatible with the stringent requirements to provide a navigation service. Regarding the measurement errors reported in Table 2, they are the typical measurement performances that can be obtained using a receiver implementing DLL and PLL and referring to Equations (11) and (12) with the previously mentioned parameters.