Ejection velocities and stability among the Trojan L4 asteroids

Abstract

I have made long-term integrations over 100Myr of 6 asteroids, with 150 fictitious collision fragments originating from them in perihelion and aphelion. From the 53 by the program ejected fragment within the time period I have fitted a formula log(t)=14.371-30.409|a_0-5.2039|-2.6944e_0+0.055575i_0-0.0023921i^2_0 in the a, e, i space where t is in days. The formula is not a perfect real representation due to the presence of resonances in the libration volume and the fact that the orbital elements are oscillating. However the formula predicts no ejection of real Trojan asteroids from the L4 swarm within a few 100Myr. I have also used simplified formulas in order to get the libration elements, without loosing to much accuracy.

(I have spotted a few small errors but I am to lasy to correct them. I am currently working on a paper on stability of the L4 swarm partly inspired by some results from this paper.)

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