Fig. 3

Effects of the small variations of the force model to the ridge structure of close encounters and to individual orbits. In the top panels we represent the value of the FLI computed for many initial conditions with |T| = 400 yrs by numerically integrating the model of the solar system including the four most massive asteroids (model (A), black line), and another model including seven additional asteroids (model (B), blue line). All the initial conditions have x0 = x∗,y0 = y∗,z0 = z∗, ẋ0 = ẋ∗,ẏ0 = ẏ∗, and different ż0 ~ ż∗. From the top-left panel we can see that the FLI profiles obtained with both models (A) and (B) are very similar, and to appreciate the differences we represent a sample zoom-in in the top-right panel. We clearly appreciate that for both models a peak of the FLI is detected, and the effect of the additional asteroids moves the peak by only 50 centimeters/day. In the bottom panels we represent instead the effect of the additional asteroids on the orbit with initial conditions corresponding to the top of the left-peak (marked with an arrow). In the bottom-left panel the FLI evolution for a time interval ranging from 0 to 450 years ago is represented: the impulsive variations of the FLI occur at the close encounters: the very small difference between the two models changes the time of some close encounters, and this is amplified at the other close encounters. The close encounter occurring at 400 yrs ago determines the strong divergence of the two orbits, whose projection on the x-y plane is represented in the bottom-right panel. Up to 400 years the two orbits are almost identical, but between 400 and 450 years ago the two orbits are well separated.
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