This paper discusses the dynamics of a tether-based mobile robot in space. The tether-based mobile robot is constrained geometrically using several tethers and can move within an area bounded by the tethers' anchors by changing the tethers' lengths. This robot is equipped with an extendable and retractable arm that approaches the tethers' anchor and reposition it to another point for changing the accessible area and covering a wider area. The Japan Aerospace Exploration Agency conducted an experiment called Robot Experiment on Japanese Experimental Module (REX-J) on the International Space Station for demonstrating such a system's fundamental capabilities. In this paper, the flexibilities of the extendable arm and tethers used in the REX-J are evaluated through image analysis of flight data. This analysis provides the robot's dynamics in three dimensions, which can not be verified experimentally on the ground. In addition, we propose dynamic models for the extendable arm and the tethers. The proposed models are validated by comparing the flight data and the simulation results obtained using the proposed model.