  We assess the ability of a solid ring to model a global perturbation induced
by several thousands of main-belt asteroids. The ring is first studied in an
analytical framework that provides an estimate of all the ring's parameters
excepting mass. In the second part, numerically estimated perturbations on the
Earth-Mars, Earth-Venus, and Earth-Mercury distances induced by various subsets
of the main-belt population are compared with perturbations induced by a ring.
To account for large uncertainties in the asteroid masses, we obtain results
from Monte Carlo experiments based on asteroid masses randomly generated
according to available data and the statistical asteroid model. The radius of
the ring is analytically estimated at 2.8 AU. A systematic comparison of the
ring with subsets of the main belt shows that, after removing the 300 most
perturbing asteroids, the total main-belt perturbation of the Earth-Mars
distance reaches on average 246 m on the 1969-2010 time interval. A ring with
appropriate mass is able to reduce this effect to 38 m. We show that, by
removing from the main belt ~240 asteroids that are not necessarily the most
perturbing ones, the corresponding total perturbation reaches on average 472 m,
but the ring is able to reduce it down to a few meters, thus accounting for
more than 99% of the total effect.
