The pursuit/evasion game for two spacecraft is significantly simplified by being described with a linearized system of equations of motion. A pursuit/evasion game is also known as a "minimax" problem, because the object of the pursuer is to minimize the time to capture, while the evader's goal is to maximize the time to capture. In this work, the minimax problem is solved in the Hill-Clohessy-Wiltshire (HCW) reference frame with Earth as the central body. The thrust-pointing direction is the control for each spacecraft. Each vehicle has a finite specific impulse and therefore the mass of each vehicle decreases as propellant is consumed. Each spacecraft uses continuous low-thrust propulsion. Due to the nature of the minimax problem, creating a traditional closed-loop feedback control is difficult. A closed-loop controller has been developed using a method called kriging. Results for both open and closed-loop trajectories are reported for a significant range of initial conditions and for different thrust accelerations of the two spacecraft.

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While there has been extensive theoretical and analytical research regarding the characterization of spacecraft propellant slosh and structural frequencies, there have been limited studies to compare the analytical predictions with measured flight data. This paper uses flight telemetry from the Cassini spacecraft to get estimates of high-g propellant slosh frequencies and the magnetometer boom frequency characteristics, and compares these values with those predicted by theoretical works. Most Cassini attitude control data are available at a telemetry frequency of 0.5 Hz. Moreover, liquid sloshing is attenuated by propellant management device and attitude controllers. Identification of slosh and structural frequency are made on a best-effort basis. This paper reviews the analytical approaches that were used to predict the Cassini propellant slosh frequencies. The predicted frequencies are then compared with those estimated using telemetry from selected Cassini burns where propellant sloshing was observed (such as the Saturn Orbit Insertion burn). Determination of the magnetometer boom structural frequency is also discussed.