  This paper discusses experimental design for the Laser Astrometric Test Of
Relativity (LATOR) mission. LATOR is designed to reach unprecedented accuracy
of 1 part in 10^8 in measuring the curvature of the solar gravitational field
as given by the value of the key Eddington post-Newtonian parameter \gamma.
This mission will demonstrate the accuracy needed to measure effects of the
next post-Newtonian order (~G^2) of light deflection resulting from gravity's
intrinsic non-linearity. LATOR will provide the first precise measurement of
the solar quadrupole moment parameter, J2, and will improve determination of a
variety of relativistic effects including Lense-Thirring precession. The
mission will benefit from the recent progress in the optical communication
technologies -- the immediate and natural step above the standard radio-metric
techniques. The key element of LATOR is a geometric redundancy provided by the
laser ranging and long-baseline optical interferometry. We discuss the mission
and optical designs, as well as the expected performance of this proposed
mission. LATOR will lead to very robust advances in the tests of Fundamental
physics: this mission could discover a violation or extension of general
relativity, or reveal the presence of an additional long range interaction in
the physical law. There are no analogs to the LATOR experiment; it is unique
and is a natural culmination of solar system gravity experiments.
