  We calculate the degree of linear polarization of radiation from stars having
planets that may not be resolved spatially. We assume single scattering by
water and silicate particulates in the planetary atmosphere. The dilution of
the reflected polarized radiation of the planet by the unpolarized stellar
radiation and the effect of oblateness of the planet as well as its elliptical
orbit are included. We employ a chemical equilibrium model to estimate the
number density of water and silicate condensates and calculate the degree of
linear polarization at R band of starlight as a function of (1) mean size of
condensates, (2) planetary oblateness, (3) inclination angle, (4) phase angle,
(5) orbital eccentricity e and (6) the epoch of periastron passage. We show
that the polarization profile alters significantly at all inclination angles
when elliptical orbit is considered and the degree of polarization peaks at the
epoch of periastron passage. We predict that detectable amount of linear
polarization may arise if the planetary atmosphere is optically thin, the mean
size of the condensates is not greater than a few microns and the oblateness of
the planet is as high as that of Jupiter.
