  We present results from a covariance study for the proposed Laser Astrometric
Test of Relativity (LATOR) mission. This mission would send two
laser-transmitter spacecraft behind the Sun and measure the relative
gravitational light bending of their signals using a hundred-meter-baseline
optical interferometer to be constructed on the International Space Station. We
assume that each spacecraft is equipped with a $ < 1.9 \times 10^{-13}
\mathrm{m} \mathrm{s}^2 \mathrm{Hz}^{-1/2} $ drag-free system and assume
approximately one year of data. We conclude that the observations allow a
simultaneous determination of the orbit parameters of the spacecraft and of the
Parametrized Post-Newtonian (PPN) parameter $\gamma$ with an uncertainty of
$2.4 \times 10^{-9}$. We also find a $6 \times 10^{-9}$ determination of the
solar quadrupole moment, $J_2$, as well as the first measurement of the
second-order post-PPN parameter $\delta$ to an accuracy of about $10^{-3}$.
