The impact of the Kuiper Belt Objects and of the asteroid ring on future high-precision relativistic Solar System tests

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 ≈1≈1 AU orbits and accurate orbit determination of some of the inner planets. It turns out that the classical KBOs (CKBOs), which amount to ≈70%≈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 J2J2 amount to 6×10-76×10-7 and 8×10-48×10-4, respectively. The secular transverse perturbation induced on a≈1a≈1  AU orbit by the asteroid ring, which globally accounts for the action of the minor asteroids whose mass is about 5×10-105×10-10 solar masses, is 10myr-1; the bias on the relativistic and J2J2 Mercury perihelion precessions is 6.1×10-66.1×10-6 and 1×10-21×10-2, 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.