The rapid growth of satellite constellations and the increasing congestion of low Earth orbit are intensifying the need for reliable and fuel-efficient collision avoidance strategies. When a potential conjunction is detected, spacecraft operators must rapidly determine corrective maneuvers capable of guaranteeing a safe miss distance while minimizing propellant consumption and operational impact. In this context, optimal control theory provides a powerful framework for computing efficient avoidance maneuvers under strict dynamical and operational constraints. This work presents an optimal-control approach for the design of minimum-propellant collision avoidance maneuvers in low Earth orbit. The proposed methodology combines collision risk assessment with indirect optimal control techniques.