  Close-in planets are in jeopardy as their host stars evolve off the main
sequence to the subgiant and red giant phases. In this paper, we explore the
influences of the stellar mass (in the range 1.5--2\Mso ), mass-loss
prescription, planet mass (from Neptune up to 10 Jupiter masses), and
eccentricity, on the orbital evolution of planets as their parent stars evolve
to become subgiants and Red Giants. We find that planet engulfment during the
Red Giant Branch is not very sensitive to the stellar mass or mass-loss rates
adopted in the calculations, but quite sensitive to the planetary mass. The
range of initial separations for planet engulfment increases with decreasing
mass-loss rates or stellar mass and increasing planetary masses. Regarding the
planet's orbital eccentricity, we find that as the star evolves into the red
giant phase, stellar tides start to dominate over planetary tides. As a
consequence, a transient population of moderately eccentric close-in Jovian
planets is created, that otherwise would have been expected to be absent from
main sequence stars. We find that very eccentric and distant planets do not
experience much eccentricity decay, and that planet engulfment is primarily
determined by the pericenter distance and the maximum stellar radius.
