Mathematical Foundations of the Lunar Logistics System

Abstract: This paper presents the second draft of mathematical foundations for a prospective lunar transportation system based on ion propulsion. The architecture features multiple interacting modules with distinct operational cycles and functional roles. The work encompasses ballistic trajectory calculations, mass-fuel characteristics analysis, and economic efficiency assessment. Research focuses on orbital maneuver optimization, inclination correction, and synchronization with lunar windows. System performance calculations and compatibility with existing launch vehicles are presented. The mathematical model incorporates the Tsiolkovsky rocket equation, numerical integration methods, and iterative optimization algorithms. Compatibility with various launch vehicle types and system scalability potential are analyzed. Note: This work represents the second version of a conceptual study. Calculations require further refinement and experimental validation.