Operator-Based Optimal Transfers and Debris Collision Assessment in LEO

The NASA Standard Breakup Model models collisions and explosions in space, which identifies the future distribution of debris. Given a possible breakup event, this work analyzes the risk posed by the generated debris in the orbit of an asset spacecraft. Using the Koopman operator (KO) solution of the [Formula: see text] perturbed two-body dynamics, the family of all possible orbits that cross the asset’s pathway is identified and parameterized according to their velocity. The KO provides the family of velocities that connect two points in space, which can be used to obtain minimum energy, minimum fuel, and minimum time-of-flight orbit transfers. Such representation is exploited to evaluate the threat that a collision poses to the asset, considering the intersection between the velocities of the breakup model and the Koopman transfer solutions.