HALO: A High-Precision Orbit Propagation Tool for Mission Design in the Cis-Lunar Domain

The paper’s data-driven recommendations are: adopt 150×150 for the lunar gravity field (LGF) to reduce the cumulative remainder to O(1e-11) with acceptable runtime, cap the Earth gravity field (EGF) at 3×3 because the 3×3 increment falls below the smallest considered perturbation (Earth albedo ~1e-16 km/s²), and use ODE113 with RT=1e-8 for complex LLO/ELFO cases. These are supported by Table 1 (LGF improvements and 27.0 s vs 66.5 s timing for 70×70 vs 150×150), Table 2 (EGF increments: 1.6227e-14 from 0×0→2×2, then 3e-18 from 2×2→3×3), and the integration-section experiments selecting ODE113 with RT=1e-8 for stability on complex orbits . The candidate model answers a slightly sharper optimization question (“smallest M such that any further increase is < 1e-16 km/s²”), which yields M=(2,2) because the next increment (to 3,3) is 3e-18, i.e., below the 1e-16 albedo floor, while still agreeing with the paper on N=(150,150) and ODE113/RT=1e-8. Hence both are consistent with the evidence; they differ only in the selection criterion for EGF truncation (paper: ‘no need beyond 3×3’; model: ‘minimal M for which all subsequent increments are sub-floor’), not in the underlying numbers or conclusions .