  We preliminarily investigate the impact of the Kuiper Belt Objects (KBOs) and
of the asteroid ring on some proposed high-precision tests of Newtonian and
post-Newtonian gravity to be performed in the Solar System by means of
spacecraft in heliocentric \approx 1 AU orbits and accurate orbit determination
of some of the inner planets. It turns out that the Classical KBOSs (CKBOS),
which amount to \approx 70% of the observed population of Trans-Neptunian
bodies, induce a systematic secular error of about 1 m after one year in the
transverse direction T of the orbit of a test particle orbiting at 1 AU from
the Sun. For Mercury the ratios of the secular perihelion precessions induced
by CKBOs to the ones induced by the general relativity and the solar oblateness
J_2 amount to 6 10^-7 and 8 10^-4, respectively. The secular transverse
perturbation induced on a \approx 1 AU orbit by the asteroid ring, which
globally accounts for the action of the minor asteroids whose mass is about 5
10^-10 solar masses, is 10 m yr^-1; the bias on the relativistic and J_2
Mercury perihelion precessions is 6.1 10^-6 and 1 10^-2, respectively. Given
the very ambitious goals of many expensive and complex missions aimed to
testing gravitational theories to unprecedented levels of accuracy, these notes
may suggest further and more accurate investigations of such sources of
potentially insidious systematic bias.
