We explore the use of grippers with gecko-inspired adhesives for spacecraft docking and acquisition of tumbling objects in microgravity. Towards the goal of autonomous object manipulation in space, adhesive grippers mounted on planar free-floating platforms are shown to be tolerant of a broad range of incoming linear and angular velocities. Through modeling, simulations, and experiments, we characterize the dynamic “grasping envelope” for successful acquisition and derive insights to inform future gripper designs and grasping strategies for motion planning.