  This paper discusses new Fundamental physics experiment that will test
relativistic gravity at the accuracy better than the effects of the second
order in the gravitational field strength, ~G^2. The Laser Astrometric Test Of
Relativity (LATOR) mission uses laser interferometry between two
micro-spacecraft whose lines of sight pass close by the Sun to accurately
measure deflection of light in the solar gravity. The key element of the
experimental design is a redundant geometry optical truss provided by a
long-baseline (100 m) multi-channel stellar optical interferometer placed on
the International Space Station (ISS). The spatial interferometer is used for
measuring the angles between the two spacecraft and for orbit determination
purposes. LATOR will not only improve the value of the parameterized
post-Newtonian (PPN) $\gamma$ to unprecedented levels of accuracy of 1 part in
10e8, it will also reach ability to measure effects of the next post-Newtonian
order (1/c^4) of light deflection resulting from gravity's intrinsic
non-linearity. The solar quadrupole moment parameter, J2, will be measured with
high precision, as well as a variety of other relativistic effects including
Lense-Thirring precession. 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.
