The list of asteroids perturbing the Mars orbit to be seen during future space missions

Context. Over the last decade, the positional observations of Mars have reached such an accuracy that the uncertainty of the asteroid masses has become the main cause of uncertainty in its ephemeris. Currently, only about 36 masses are estimated by direct measurements with a formal accuracy better than 10%. However, the true errors are probably larger due to unaccounted systematic effects. Thus, asteroid masses are still a limitation in the accurate modeling of the perturbations on Mars. Nevertheless, two future space missions, Gaia and Dawn, could improve the situation by combining their results. Aims. The main objective of this paper is to identify and provide a list of major perturbers of Mars which could bring significant disturbances over the next 50 years, having in perspective the expected contribution of Gaia to asteroid mass determination. It will also point out the asteroids whose mass only could be improved from ground-based observations - by direct measurements or size and shape derivation. Methods. The selection procedure of Mars' perturbers includes analytical and numerical treatments. The analytical analysis is based on harmonic decomposition of the perturbations on the longitude and semi-major axis of Mars as a function of the mean longitude of the planet and the perturbing asteroid to the first order in asteroid mass. Regarding the numerical treatments, the first consists in selecting the potential perturbers, filtering them out with the cumulative deviations of Mars' path over the next 50 years. The second one uses the accumulation of the perturbations on the semi-major axis, eccentricity, and inclination of Mars due to each asteroid over the same period of time. Thus, a list of perturbers of Mars is derived from the number of selections by each method. Results. 62 asteroids have been selected as the most perturbing - or potentially so - for the orbit of Mars, among which 32 were already listed by Williams in 1984, and all are in the list of 300 perturbing asteroids derived by the same author in about 1995. More interestingly, 53 belong to the list of asteroids for which Gaia could give their mass with a relative precision better than 50% and 27 less than 10%, a further indication of the importance of Gaia to contribute to improving Mars' ephemeris. Nevertheless, 7 of them will have a mass poorly estimated - with a relative error greater than 30% - and 9 without estimates at all. Therefore, ground-based observations may be useful to overcome these limitations.