This paper presents energy optimum capture of orbiting objects using a dual-arm robot mounted on a service satellite. An attempt has been made to formulate energy efficient trajectories for the dual-arm robot such that the reaction moments acting on the base satellite are minimum. To achieve this, first a local optimization problem is formulated exploiting redundancy associated with the constraints for reactionless manipulation. This method, however, fails to provide optimal trajectories. In order to overcome this disadvantage, an optimal control problem is formulated which not only helps in achieving energy efficient trajectories but also ensures zero reaction moments to the base satellite. The proposed method is validated using a 6-link planar dual-arm robot mounted on a service satellite.