Space robots will play a crucial role in on-orbit operations like refuelling, servicing, and capture of debris. This paper focuses on capturing a non-cooperative target using a multi-arm space robot and its post-capture control. In the post-capture phase, a target object gets rigidly attached to end-effectors, and arms get into a closed-loop configuration, resulting in added constraints. Further, due to a target object’s unknown inertial parameters, system behaviour becomes unpredictable and poses difficulty in achieving reactionless manipulation to minimize base attitude disturbance. We present acceleration-based adaptive reactionless manipulation in the post-capture phase considering the unknown inertial parameter of a target. The regressor form required for adapting the joint states is derived using the acceleration-based approach. To update unknown parameters recursively immediately after impact, three methods, namely, recursive least square (RLS), weighted recursive least square (WRLS), and Kalman filter (KF), are used and compared. The efficacy of these methods has been demonstrated by using numerical studies of a dual-arm space robot that captures a non-cooperative target. Further, the acceleration-based and the velocity-based approaches are individually compared with RLS, WRLS and KF methods. Investigations have also been carried out to study the effects of change in ratios of base-to-target and base-to-robot masses, as well as angular velocities of a target.