This paper presents strategies for point-to-point reactionless manipulation of a satellite mounted dual-arm robotic system for capture of tumbling orbiting objects, such as out-of-commission satellites and space debris. Use of the dual-arm robot could be more effective than the single-arm when there is no provision for a grapple fixture or the object is tumbling. The dual arms can also provide dexterous manipulation. As the main objective in capture of orbital objects is to move the end-effector from initial position to the grapple point with desired velocity, the task-level reactionless constraints in terms of end-effector velocities are derived. The trajectory planned using these constraints, however, results in several singular points within the robot's workspace. In order to overcome this shortcoming, three point-to-point path planning strategies are presented, which improve the reactionless operation of the dual-arm robot. The strategies are illustrated by carrying out simulations for a 6-degree-of-freedom (DOF) dual-arm robotic system mounted on a satellite.