Asteroid-type orbit evolution near the 5:2 resonance

In this case of the 5:2 commensurability with the motion of Jupiter, an asteroid can reach the orbits of Mars, Earth, and Venus when eccentricity e is greater than 0.41, 0.65, and 0.74, respectively. For individual fictitious asteroids, Ipatov and Yoshikawa obtained a growth in e from 0.15 to 074-0.76. Rates of changes in orbital orientations are different for Mars, Earth, Venus, and the asteroid. Therefore, for corresponding values of e, the asteroid could encounter these planets and leave the gap at those encounters. In order to investigate this hypothesis of the 5:2 Kirkwood gap formation, Ipatov studied the regions of initial data for which the eccentricities of asteroids located near the 5:2 commensurability exceeded 0.41 during evolution. The orbit evolution for 500 fictitious asteroids was investigated by numerical integration of the complete (unaveraged) equations of motion for the three-body problem (Sun-Jupiter-asteroid). The equations of motion were integrated in the time intervals T is greater than or equal to 5(10)(exp 3)t(sub J) (t(sub J) is the heliocentric orbital period of Jupiter) in the planar model, T is greater than or equal to 10(exp 4)t(sub J) at initial inclination 5 deg is less than or equal to i(sub 0) is less than or equal to 20 deg and T = 10(exp 5)t(sub J) at i(sub 0) = 40 deg. The larger interval T was taken at i(sub 0) = 40 deg because in this case for the majority of runs maximum values of e and i were reached in the time delta(t) is greater than 2(10)(exp 4)t(sub J).