On　the　basis　of　the　momentum　conservation　equations　and　recursive　least　squares　with　forgetting　factor,　a　new　adaptive　reactionless　planning　algorithm　is　proposed　for　the　reaction　null-space　motion　of　the　free-floating　space　manipulator　after　capturing　an　unknown　rotating　target.　First,　the　Lagrange　dynamic　model　of　the　manipulator　is　established.　Second,　the　adaptive　reactionless　planning　algorithm　is　designed　to　update　the　null-space　solutions　for　joint　rates　in　online　manner.　To　go　to　a　step　further,　the　desired　motion　generated　by　adaptive　reactionless　planning　is　produced　by　driving　joints　with　the　PID　controller.　Finally,　on　the　basis　of　Lyapunov　method,　the　stability　of　the　proposed　scheme　is　proved　theoretically,　and　the　effectiveness　of　the　designed　scheme　is　verified　by　computer　simulation.　©　2023,　The　Author(s),　under　exclusive　license　to　Springer　Nature　Singapore　Pte　Ltd.