Optimal solution of orbital facility location problem utilizing optimum rocket staging and Q-Law orbit transfer

Abstract

The rapid growth of satellite constellations has made satellite servicing a crucial aspect of sustaining and enhancing their functionality over extended periods. This thesis focuses on developing an optimization framework to address the Orbital Facility Location Problem (OFLP), which involves determining the optimal placement of service facilities in orbit to minimize the combined costs of launching and servicing satellite constellations. The research emphasizes the importance of aligning servicing strategies with cost efficiency while adhering to operational and logistical constraints. A comprehensive methodology is adopted to tackle the OFLP, combining advanced techniques such as rocket staging optimization and low-thrust orbit transfer analysis. The launch cost is modeled based on the maximum payload capacity of launch vehicles and the characteristics of candidate orbits. Service costs, on the other hand, are determined by calculating the fuel consumption and payload requirements for servicing trips between service facilities and client satellites. These costs are integrated into an optimization model formulated using Binary Linear Programming (BLP), which enables the identification of cost-efficient orbital configurations. The study explores multiple scenarios defined by varying numbers of launch vehicles and servicing trips. For each scenario, the model identifies the optimal orbits for deploying service facilities, ensuring that the launch vehicles operate within payload capacity limits and that client satellites are serviced efficiently. The results reveal critical insights into the interplay between launch and servicing costs, highlighting the significance of parameters such as semi-major axis, eccentricity, and right ascension of ascending node in achieving cost-effective solutions. The thesis also presents detailed numerical analyses and visualizations that illustrate the spatial distribution of service facilities, the alignment between service orbits and client satellite constellations, and the trade-offs between resource allocation and operational efficiency. These findings underline the importance of precise orbit selection and resource management in reducing mission costs. In conclusion, this research provides a robust framework for solving the OFLP and offers practical guidelines for designing satellite servicing missions. The insights gained from this work contribute to the field of aerospace engineering by promoting cost-effective strategies for managing satellite constellations. This framework can serve as a foundation for future research and operational planning in orbital servicing and satellite maintenance.