  We develop a simple analytical criterion to investigate the role of the
environment on the onset of star formation. We will consider the main external
agents that influence the star formation (i.e. ram pressure, tidal interaction,
Rayleigh-Taylor and Kelvin-Helmholtz instabilities) in a spherical galaxy
moving through an external environment. The theoretical framework developed
here has direct applications to the cases of dwarf galaxies in galaxy clusters
and dwarf galaxies orbiting our Milky Way system, as well as any primordial
gas-rich cluster of stars orbiting within its host galaxy. We develop an
analytic formalism to solve the fluid dynamics equations in a non-inertial
reference frame mapped with spherical coordinates. The two-fluids instability
at the interface between a stellar system and its surrounding hotter and less
dense environment is related to the star formation processes through a set of
differential equations. The solution presented here is quite general, allowing
us to investigate most kinds of orbits allowed in a gravitationally bound
system of stars in interaction with a major massive companion. We present an
analytical criterion to elucidate the dependence of star formation in a
spherical stellar system (as a dwarf galaxy or a globular cluster) on its
surrounding environment useful in theoretical interpretations of numerical
results as well as observational applications. We show how spherical
coordinates naturally enlighten the interpretation of the two-fluids
instability in a geometry that directly applies to astrophysical case. This
criterion predicts the threshold value for the onset of star formation in a
mass vs. size space for any orbit of interest. Moreover, we show for the first
time the theoretical dependencies of the different instability phenomena acting
on a system in a fully analytical way.
