Analysis of Orbit Perturbation and Atmospheric Effects for Advanced ODTS Services in Elliptical Lunar Frozen Orbits

The renewed interest in Moon exploration has led to the need for infrastructures that reduce the cost and complexity of future lunar missions. This paper studies the Orbit Determination and Time Synchronization (ODTS) for a small radio navigation constellation around the Moon, providing pseudorange services through a one-way navigation message containing satellite ephemeris and onboard clock information. Accurate Position, Velocity, and Timing (PVT) computations for users depend on high-quality constellation observables and precise dynamical models. The study considers three Earth ground stations tracking the satellites using Multi Spacecraft Per Aperture (MSPA) antennas to generate Range and Doppler data. The quality of these observables is influenced by atmospheric delays, both ionospheric and tropospheric. Ground station locations are chosen to minimize outage due to atmospheric phenomena, which can degrade radio frequency link availability and thus orbit determination performance. The study estimates outages using rain, cloud, gas and scintillation event statistics and analyzes their possible effects on ODTS performance to optimize the system design. The core of the study is to extensively model the main non-gravitational accelerations acting on the constellation orbital dynamics: Solar Radiation Pressure, Thermal Recoil Pressure, lunar Albedo, and lunar InfraRed radiation. The modelling and the ODTS problem are implemented with the support of GODOT, the European Space Agency (ESA) astrodynamics library for mission analysis, OD and operations. The main goal is to understand the impacts of neglecting or mismodelling these nongravitational perturbations on the ephemeris accuracy and forward estimation errors of a lunar radio navigation constellation. Finally, the evolution of the Signal In-Space Error (SISE) is evaluated, considering both satellite timing and ephemeris contributions. SISE directly impacts user PVT computations, and this metric is crucial for assessing the study's results. In conclusion, this comprehensive examination of the ODTS problem through detailed assessments of observables and precise dynamical models lays the groundwork for accurate PVT computations, supporting lunar missions and addressing the main challenges faced by a lunar navigation constellation.