  We investigate the orbital motions of dwarf spheroidal galaxies (dSphs) in
the halo of the Milky Way (MW) to understand their possible effects on the
diversity of the star formation histories seen in these MW satellites. In this
work, we explicitly consider a time-varying gravitational potential due to the
growth of the MW's dark halo mass to calculate the long-term orbital evolutions
of the dSphs, guided with {\it Gaia} DR2 proper motions, over the past 13.5
billion years. We find that the infall time of a satellite, defined at which
the galaxy first crosses within the growing virial radius of the MW's halo,
coincides well with the time when the star formation rate (SFR) is peaked for
the sample of classical dSphs. On the other hand, ultra-faint dSphs already
finished their SF activity prior to their infall times as already suggested in
previous works, but there is a signature that their earlier SF histories are
affected by interaction with the growing MW's halo to some extent. We also
find, for classical dSphs, that the relative fraction of stars formed after the
peak of the SFR to the current stellar mass is smaller for the smaller
pericentric radius of the galaxy at its first infall. These results suggest
that the infalling properties of the dSphs into the MW and the resultant
environmental effects such as ram-pressure stripping and/or tidal disturbance
in the MW's dark halo containing hot gas play important roles in their star
formation histories.
