Comparison between the outcomes of N-body simulations and our semi-analytical model in systems with DF. Left panels: comparison between the evolution of the satellite’s CoM in both N-body simulations and semi-analytical models, each using the best value for α. The different panels correspond to the three different initial satellite’s velocities, v_i = 0.75v_c, v_i = 0.50v_c and v_i = 0.25v_c from top to bottom. The thick dotted orange line refers to the semi-analytical model, while the thick solid black line shows the result of the N-body simulations. Right panel: relative error in the evaluation of the satellite mass for the same values of the initial velocities as a function of time. Different line colours indicate different initial satellite velocities. The dashed vertical lines represent the initial time of the semi-analytical models, which corresponds to the first apocentre, and are coloured using the same colour code employed for the solid lines.