A ring model of the main asteroid belt for planetary ephemerides

Perturbations in the Main Belt Asteroids (MBAs) are the major obstacle for achieving increased prediction accuracy in planetary ephemerides, especially for Mars, as the large quantities of asteroids make ephemeris calculations computationally difficult and complex. In this study, a multiple-ring model of the main asteroid belt is proposed according to the distribution of MBAs proper elements. A new algorithm is adopted for the highly-accurate perturbation calculation from ring model, without the limitation for outer belt planets. This solution can account for more than 98% of the total effect induced by MBAs. A strategy to select representative asteroids is provided, based on a comparative analysis of the perturbation from the main-belt population and the multiple-ring model. The perturbation error on the Mars–Earth distances induced by the difference between the main-belt population and the ring model was estimated numerically. The error is below 0.5 meters over 10 years. This accuracy meets the range measurement accuracy requirements for current Mars missions and makes possible further improvements in the Mars ephemerides estimation.