A remotely controlled apparatus for grasping an object such as a satellite in space includes a free-flying grasper unit connected by a selectively extendable cable to an orbital platform. The orbital platform and the grasper unit are preferably each independently propelled by respective propulsion systems including multi-axis maneuvering nozzles respectively provided on the orbital platform and on the grasper unit. The grasper unit preferably includes a grasper unit body and a grasper-arm mechanism having a controllable grasping claw articulately mounted on the end of a controllable telescoping arm that extends from the grasper unit body. The grasper unit preferably further includes a camera and a distance measuring sensor to provide visual and distance feedback data for assisting the remotely controlled maneuvering of the grasper unit and actuation of the grasper-arm mechanism.