Evolution of mass-less test particles (i.e., exomoons) around GJ 1148 b, under the gravitational perturbation of the outer planet. Each panel tracks the evolution of the test particles with a step of 9000 yr to match the snap-shot evolution of the massive bodies in the GJ 1148 system shown in Fig. 9. Shown are the position of GJ 1148 b (blue dot), the planetary Roche limit (gray dashed line), and the planetary 0.5 R_Hill (blue dashedline), which scales with (1–e_b) due to the dynamical perturbations of GJ 1148 c. See text for details.