An analytical solution to quick-response collision avoidance maneuvers in Low Earth Orbit

Collision avoidance maneuvers to prevent orbital collisions between two catalogued 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 probability. Determining the thrust time and direction for a wide range of orbits and spacecraft properties resulted in a semi-analytical solution to the collision avoidance 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.