  We propose that detailed data on the star formation history of a dwarf
spheroidal galaxy (dSph) may be used to estimate the evolution of the total
mass M_g(t) for cold gas in its star-forming disk. Using Fornax as an
illustrative example, we estimate its M_g(t) and the corresponding net gas flow
rate Delta F(t) assuming a global star formation rate psi(t) =
lambda_*(t)[M_g(t)/M_sun]^alpha consistent with observations of nearby
galaxies. We identify the onset of the transition in Delta F(t) from a net
inflow to a net outflow as the time t_sat at which the Fornax halo became a
Milky Way satellite and estimate the evolution of its total mass M_h(t) at t <
t_sat using the median halo growth history in the LambdaCDM cosmology and its
present mass within the half-light radius derived from observations. We examine
three different cases of alpha = 1, 1.5, and 2, and justify the corresponding
lambda_*(t) by comparing the gas mass fraction f_g(t) = M_g(t)/M_h(t) at t <
t_sat with results from simulations of gas accretion by halos in a reionized
universe. We find that the Fornax halo grew to M_h(t_sat) ~ 2x10^9 M_sun at
t_sat ~ 5 or 8 Gyr, in broad agreement with previous studies using data on its
stellar kinematics and its orbital motion. We describe qualitatively the
evolution of Fornax as a satellite and discuss potential extension of our
approach to other dSphs.
