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

TL;DR

This paper evaluates the effectiveness of a solid ring model to represent the gravitational perturbations caused by main-belt asteroids on planetary distances, demonstrating the model's accuracy after removing the most perturbing asteroids.

Contribution

It introduces a ring model for main-belt asteroid perturbations and validates its accuracy through analytical and numerical comparisons, including Monte Carlo simulations.

Findings

A ring at 2.8 AU can approximate asteroid perturbations.

Removing ~240 asteroids reduces perturbations significantly.

The ring accounts for over 99% of the total perturbation after removal.

Abstract

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.