THE ROLE OF APPLIED MATHEMATICS IN OPTIMIZING SATELLITE CONSTELLATION DEPLOYMENT - Joydeb Debnath (IJRDO -JOURNAL OF MATHEMATICS, 2025)
The surge in demand for global satellite coverage in communication, navigation, and Earth observation has amplified the necessity for optimized satellite constellation deployment strategies. This study explores how applied mathematics underpins these complex optimization challenges, including maximizing coverage, minimizing collision risks, reducing latency, and enhancing fuel efficiency. A hybrid optimization framework is developed, combining Genetic Algorithms (GA), Sequential Quadratic Programming (SQP), and surrogate modeling to address multi-objective optimization in both small and large constellations. The mathematical modeling employs Keplerian dynamics, constraint-based coverage formulations, and algorithmic phasing to ensure optimal satellite placement. Simulation using MATLAB and the SGP4 propagator compares three strategies—baseline manual deployment, GA-only optimization, and the hybrid approach across metrics such as coverage percentage, collision risk, latency, and delta-v requirements. The hybrid model achieves up to 99.6% global coverage, reduces collision risks by 85%, decreases latency by 58%, and cuts fuel consumption by 25% relative to baseline models. Sensitivity and Monte Carlo analyses confirm its robustness under uncertainties, validating the indispensable role of applied mathematics in achieving sustainable, resilient, and efficient constellation deployments. This research contributes a computationally efficient and scalable optimization methodology that bridges mathematical theory and aerospace engineering, offering strategic insights for future satellite network design and space sustainability.