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tokens: by an analytic MW potential, as well as to resolve analytically the interaction between the dwarf gas and the MW halo gas. The gas removal from dwarf galaxies is analytically calculated using the Close et al. ( 2013 ) model, for which two physical processes are considered, i.e., the balance between the gravitational force of the dwarf galaxy and the external ram pressure (i.e., from the Gunn Gott 1972 formula), and the mass loss introduced by Kelvin–Helmholtz instabilities (e.g., Nulsen 1982 ). We have verified that the above technique of “pure N -body for stars plus analytical ram pressure for gas” is able to reproduce the gas removal process resolved by hydrodynamics simulations done in Yang et al. ( 2014 ) and in Hammer et al. ( 2018 , 2019 ). The above allows us to probe the interaction of dSph stars with the MW gravitational field in a full Newtonian scheme. By adopting a gravitational force softening of 0.005 pc, it implies that there should be no stellar particles that can be affected by the undesirable effects due to the softening in media with central stellar density ∼500 times smaller than at the Sun neighborhood (see H19 ). From left to right, Figure 4 shows three different steps in evolution of such a stellar system after the gas removal, i.e., when it may resemble a dSph. It includes (1) when the gas has just been fully removed, (2) just after pericenter at the peak of tidal shock effects, and (3) well after pericenter, when the system almost vanishes owing to the heavy tidal stripping process that unavoidably follows tidal shocks. Figure 4. Summary of two N -body simulations of a DM-free and gas-rich dSph progenitor, with three columns on the left (right) for model C (model Q), respectively. They are shown at steps 1, 2, and (3), from left to right, respectively (see text). The first line shows the appearance of the simulated galaxies in gray colors. For other lines, green, red, black, and gray symbols represent stars in step 1, from very low velocity and very near the center to very high velocity and very far from the center (gray symbols with extremely low density); see left panels of the (d)–(f) rows. From top to bottom: (a) projected view on sky; (b) V los vs. sky projected radius, with the vertical blue dashed line showing r half that includes the selected stars; (c) the evolution of σ los with time showing a peak very near the pericenter passage (see point in middle panel), and with the gray curve indicating the theoretical expectation from Equation ( 5 ) for f MW shocks = 0.25 (0.08) for model C (model Q), which also includes self-gravity from gas and stars; (d) the velocity distribution projected in gal-( Y , Z ) plane in Galactocentric coordinates, and with the arrow showing the MW direction; (e) the phase diagram indicating that many stars are leaving the system after gas removal (left panel); and (f) V los vs. showing that near pericenter (middle panel) most stars have their motions only on the line of sight. In Figure