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Using numerical simulations, we have studied the escape of globular clusters(GCs) from the satellite dwarf spheroidal galaxies (dSphs) of the Milky Way(MW). We start by following the orbits of a large sample of GCs around dSphs inthe presence of the MW potential field. We then obtain the fraction of GCsleaving their host dSphs within a Hubble Time. We model dSphs by a Hernquistdensity profile with masses between $10^7\,\mathrm{M}_{\odot}$ and $7\times10^9\,\mathrm{M}_{\odot}$. All dSphs lie on the Galactic disc plane, but theyhave different orbital eccentricities and apogalactic distances. We compute theescape fraction of GCs from 13 of the most massive dSphs of the MW, using theirrealistic orbits around the MW (as determined by Gaia). The escape fraction ofGCs from 13 dSphs is in the range $12\%$ to $93\%$. The average escape time ofGCs from these dSphs was less than 8 $\,\mathrm{Gyrs}$, indicating that theescape process of GCs from dSphs was over. We then adopt a set ofobservationally-constrained density profiles for specific case of the FornaxdSph. According to our results, the escape fraction of GCs shows a negativecorrelation with both the mass and the apogalactic distance of the dSphs, aswell as a positive correlation with the orbital eccentricity of dSphs. Inparticular, we find that the escape fraction of GCs from the Fornax dSph isbetween $13\%$ and $38\%$. Finally, we observe that when GCs leave their hostdSphs, their final orbit around the MW does not differ much from their hostdSphs.

The Escape of Globular Clusters from the Satellite Dwarf Galaxies of the Milky Way