Determination of motion extrema in multi-satellite system

Spacecraft, or satellite formation flight has been a topic of interest dating back to the Gemini program of the 1960s. Traditionally space missions have been designed around large monolithic assets. Recent interest in low cost, rapid call up mission architectures structured around fractionated systems, small satellites, and constellations has spurred renewed efforts in spacecraft relative motion problems. While such fractionated, or multi-body systems may provide benefits in terms of risk mitigation and cost savings, they introduce new technical challenges in terms of satellite coordination. Characterization of satellite formations is a vital requirement for them to have utility to industry and government entities.;Satellite formations introduce challenges in the form of constellation maintenance, inter-satellite communications, and the demand for more sophisticated guidance, navigation, and control systems. At the core of these challenges is the orbital mechanics which govern the resulting motion. New applications of algebraic techniques are applied to the formation flight problem, specifically Grobner basis tools, as a means of determining extrema of certain quantities pertaining to formation flight.;Specifically, bounds are calculated for the relative position components, relative speed, relative velocity components, and range rate. The position based metrics are relevant for planning formation geometry, particularly in constellation or Earth observation applications. The velocity metrics are relevant in the design of end game interactions for rendezvous and proximity operations. The range rate of one satellite to another is essential in the design of radio frequency hardware for inter-satellite communications so that the doppler shift can be calculated a priori. Range rate may also have utility in space based surveillance and space situational awareness concerns, such as cross tagging. The results presented constitute a geometric perspective and have utility to mission designers, particularly for missions involving rendezvous and proximity operations.