  We analyse how drag forces modify the orbits of objects moving through
extended gaseous distributions. We consider how hydrodynamic (surface area)
drag forces and dynamical friction (gravitational) drag forces drive the
evolution of orbital eccentricity. While hydrodynamic drag forces cause
eccentric orbits to become more circular, dynamical friction drag can cause
orbits to become more eccentric. We develop a semi-analytic model that
accurately predicts these changes by comparing the total work and torque
applied to the orbit at periapse and apoapse. We use a toy model of a radial
power-law density profile, $\rho \propto r^{-\gamma}$, to determine that there
is a critical $\gamma = 3$ power index which separates the eccentricity
evolution in dynamical friction: orbits become more eccentric for $\gamma < 3$
and circularize for $\gamma > 3$. We apply these findings to the infall of a
Jupiter-like planet into the envelope of its host star. The hydrostatic
envelopes of stars are defined by steep density gradients near the limb and
shallower gradients in the interior. Under the influence of gaseous dynamical
friction, an infalling object's orbit will first decrease in eccentricity, then
increase. The critical separation that delineates these regimes is predicted by
the local density slope and is linearly dependent on polytropic index. More
broadly, our findings indicate that binary systems may routinely emerge from
common envelope phases with non-zero eccentricities that were excited by the
dynamical friction forces that drove their orbital tightening.
