1 AN ANALYTICAL SOLUTION TO QUICK-RESPONSE COLLISION AVOIDANCE MANEUVERS IN LOW EARTH ORBIT Jason A. Reiter * and David B. Spencer † Collision avoidance maneuvers to prevent orbital collisions between two cata- logued objects are typically planned multiple days in advance. If the warning time is decreased to less than half-an-orbit in advance, the problem becomes more complex. Typically, the burn (assumed to be impulsive) would be placed at perigee or apogee and oriented in the direction that allows for a fuel-optimal maneuver to be performed well before the predicted collision. Instead, for quick- response scenarios, finite burn propagation was applied to determine the thrust duration and direction required to reach a desired minimum collision probabil- ity. Determining the thrust time and direction for a wide range of orbits and spacecraft properties resulted in a semi-analytical solution to the collision avoid- ance problem anywhere in Low Earth Orbit. The speed at which this method can be applied makes it valuable when minimal time is available to perform such a maneuver. INTRODUCTION In typical debris collision avoidance scenarios, the optimal maneuver is first determined by analyzing the encounter region where the two objects are predicted to collide. In situations where both the primary and secondary bodies can be tracked, their positions and velocities are deter- mined to within their associated errors within the corresponding position covariance ellipsoids. Though not necessary for most cases with almost-circular orbits, the covariance ellipsoids may be oriented for which the velocities are not perfectly aligned with their major principal axes. At the predicted time of collision, the covariance data is used to determine a maximum probability of collision and miss distance for the encounter. For any collision avoidance scenario, the goal is to reach a desired separation distance between the two objects at the predicted time of collision by performing a fuel-optimal maneuver. 1,2 One main factor driving the planning of the maneuver is the starting and desired orientation of the primary object. Depending on the current operating conditions, the spacecraft may be pointed in a certain direction to best utilize its solar panels, scientific equipment, or other direc- tional hardware. Time must be allotted to re-orient the spacecraft so that the main thrusters are pointed in the desired thrust direction to perform the maneuver. Additional time will be allotted to ensure that the thrust is applied at apogee or perigee, the most efficient locations in orbit to * Graduate Student, Department of Aerospace Engineering, The Pennsylvania State University, 229 Hammond Build- ing, University Park, PA 16802. † Professor, Department of Aerospace Engineering, The Pennsylvania State University, 229 Hammond Building, Uni- versity Park, PA 16802. AAS 16-366