Constructing a refined model of small bodies in the solar system - I. The Jovian Trojans

Aim. We construct a new arc model to represent the global perturbation induced by the Jupiter Trojans for the development of the modern planetary ephemerides. Methods. The Jupiter Trojans are divided into two groups: (1) the 226 biggest ones with absolute magnitudes $H<11$, have well determined masses and are treated as individual bodies; (2) the remaining small ones with $H\geqslant11$, are modeled by two discrete arcs centered at Jupiter's L4 and L5 points, respectively. Then we derived the parameters characterizing the arcs, such as the total mass, the mass ratio, and the spatial distributions. Uncertainties on the fitted parameters have also been taken into account. Results. We find that the total mass of all the Jupiter Trojans, including the undiscovered ones, is most likely about $1.861\times 10^{-5}$ Earth mass. Then the global perturbation of the trojan population induced on the Earth-Mars distance is numerically estimated to be about 70 m during the 2014-2114 time interval. We also give a simple analytic expression. For the satellites of Mars and Jupiter, however, the change of the distance between the Earth and a satellite can be much more significant, reaching on tens of thousands of meters over one century, due to perturbations of the Jupiter Trojans.

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