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The necessity to take into account the perturbations caused by a large number of asteroids on the terrestrial planets is fundamental in the construction of modern numerical ephemeris on the solar system. Therefore about 300 of the largest asteroids were taken into account in recent ephemeris. Yet, the uncertainty on the mass values of the great majority of these asteroids constitutes a crucial and the main limit of accuracy of this ephemeris. Consequently, it is important to conduct a specific and detailed study of their individual effects especially on the terrestrial planets, which are far more affected than the giant planets. This was already done explicitly, but only for Mars and for only two orbital elements (a and λ). We aim both to confirm these previous results and to extend the study to all orbital elements and to the other three terrestrial planets (Mercury, Venus and the Earth), which are priori less affected by asteroid perturbations. Our methodology consists in several steps: we carried out precise computations of the orbital motions of the planets at short (100 y) and longer (1000 y) time scales with numerical integration. For that purpose we included the eight planets and also considered 43 of the most powerful asteroids. These were added to the numerical integrations once separately and once combined to determine their specific effects on the orbital elements of the Earth and the three other terrestrial planets. This procedure also allowed us to assess the spatial geocentric coordinates of the three terrestrial planets. We determined the signal that represents the effects by simple subtraction. Then we systematically analyzed this signal by FFT (fast Fourier transform), and finally we adjusted the signal with a set of sinusoidal components. We analyzed in detail the variations of the six orbital elements a, e, i, Ω, ω̃ and λ of Mercury, Venus, the Earth-Moon barycenter (EMB) and Mars that are caused by the individual influences of the set of our 43 selected asteroids. We compared our results for Mars with the analytical ones on the semi-major axis and the longitude. The tow studies agree very well. All our results, consisting of 1032 different curves (43 asteroids × 4 planets × 6 orbital elements) and the related tables that provide the fitted Fourier and Poisson components are gathered the ASETEP database (asteroid effect on the terrestrial planets). Moreover, we include in this database the influence of our sample of 43 asteroids on three fundamental parameters: the distance and the bidimensional orientation vector (α, δ) from the EMB to each of the other terrestrial planets. This database, which will be regularly updated by taking into account more asteroids with improved mass determinations, constitutes a precious tool for understanding specifically the influence of the large asteroids on the orbital motion of the terrestrial planets, and also for better understanding how modern ephemeris can be improved.

Specific effects of large asteroids on the orbits of terrestrial planets and the ASETEP database