## 2 Materials and Methods
### A Coordinate System, a Map Projection, and a Timeframe  
The LRNTS coordinate frame is based on 10 m Lunar Digital Elevation Model (DEM) [48]. If a more precise and detailed Moon reference frame would be introduced in the future, the LRNTS coordinate frame (and all sites within the crater tied to it) would be easily  
Figure 2: A scheme of interconnection between LRNTS sites. transformed into the new system. Throughout this study case, the LRNTS frame is treated separately from any Lunar reference system. Any such connection would introduce error sources related to global reference frame definition and implementation, which would create a false result on LRNTS performance. If this methodology proves its hypotheses and if other environments like Shackleton are to be investigated, then a tie to a Lunar reference system would be implemented. A possible solution for implementing a Lunar frame would be five Lunar Laser Ranging (LLR) retroreflectors, already placed on the Lunar surface. Their positions are determined with a cm level of accuracy, which makes them a good candidate for the reference frame implementation. Their coordinates are expressed as Cartesian 3D X, Y, Z coordinates, with the coordinate system origin in the Moon's center of mass, with no projection defined. Furthermore, where appropriate, spherical latitude-longitude-height coordinates can be used [49; 50]. Although very simple, Cartesian X, Y, Z coordinates with an origin at the Moon's center of mass are not convenient for practical large-scale and precise applications. Therefore, we suggest here a polar xy stereographic projection, with the origin at the Moon's South Pole, as depicted in Figure 1. All simulated measurements and calculations in this study are done in the polar xy stereographic projection. The LRNTS timeframe is based on the transceivers' atomic clocks. Each transceiver node holds an Atomic Frequency Standard (AFS) onboard (Figure 3), thus providing the same time reference for both transmitting and receiving segments. The benefit of this approach is that clock correction terms coming from different time standards (as with GNSS, for example) are neglected in measurement equations since transmitters and receivers use the same time system. A joint LRNTS timescale is developed from all LRNTS clocks, distributing time system parameters to each transceiver. Performance of one-way GNSS timing is estimated to about 20 ns [51], where a significant share in the error budget is related to ionospheric and tropospheric delays. LRNTS timeframe stability is expected to be better for an order of quantity than GNSS, having in mind theoretical one-way transfer accuracy of 100 ps for code ranges and 1 ps for carrier phase measurements [52]. However, the stability of LRNTS clocks should be checked on regular basis by time series analysis of LRNTS daily solutions (transceivers coordinates). Furthermore, differences in gravity conditions between the Moon and Earth have an impact on the operation of atomic clocks. The differences in gravitational potential between the Moon and Earth can cause a change in the resonant frequency of the atoms, which is known as a gravitational redshift. This redshift can result in a shift in the frequency of the atomic clock, leading to inaccuracies in time measurements. Furthermore, the effects of special and general relativity also need to be considered. Special relativity affects the sticking rate of clocks, whereas general relativity causes a change in the geometry of space-time. Finally, thermal effects are important for precise definition of the Lunar timescale,  
Figure 3: Conceptual diagram of a transceiver. resulting from rather different temperature conditions on the Moon compared to Earth. Changes in temperature can cause changes in the resonant frequency of the atoms, leading to inaccuracies in time measurements. To mitigate these effects, atomic clocks must be designed and tested to withstand the harsh conditions on the Moon and to account for the effects of different gravity conditions.