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We assess the ability of a solid ring to model a global perturbation inducedby several thousands of main-belt asteroids. The ring is first studied in ananalytical framework that provides an estimate of all the ring's parametersexcepting mass. In the second part, numerically estimated perturbations on theEarth-Mars, Earth-Venus, and Earth-Mercury distances induced by various subsetsof the main-belt population are compared with perturbations induced by a ring.To account for large uncertainties in the asteroid masses, we obtain resultsfrom Monte Carlo experiments based on asteroid masses randomly generatedaccording to available data and the statistical asteroid model. The radius ofthe ring is analytically estimated at 2.8 AU. A systematic comparison of thering with subsets of the main belt shows that, after removing the 300 mostperturbing asteroids, the total main-belt perturbation of the Earth-Marsdistance reaches on average 246 m on the 1969-2010 time interval. A ring withappropriate mass is able to reduce this effect to 38 m. We show that, byremoving from the main belt ~240 asteroids that are not necessarily the mostperturbing 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 formore than 99% of the total effect.

A ring as a model of the main belt in planetary ephemerides