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Migration of asteroids from the 3/1 and 5/2 resonances with Jupiter to the Earth

By S. I. Ipatov

Abstract

Last years many scientists used symplectic integrators [1], which are much faster than usual integrators. For asteroids, a step of integration for a symplectic integrator usually was taken in a range between 7 and 30 days. Some scientists compared the results obtained with different integration steps, but usually they did not compare these results with those obtained with a usual integrator. We have made series of computer runs of the orbital evolution of asteroids for the 3/1 and 5/2 resonances with Jupiter using both the symplectic integrator RMVS3 [1] and the Bulirsh-Stoer method [2] (BULSTO). The results obtained with different integrators and different integration steps ds were compared in order to understand what error we usually make if we use a symplectic method for investigations of orbital evolution of resonant main-belt asteroids. For BULSTO the error ε per integration step was taken to be less than 10 −8 or 10 −9. For RMVS3, we have made integrations with ds equal to 3, 10, and 30 days. In each run we considered the Sun, 7 planets (except Mercury and Pluto) and N asteroids moving in the 3/1 or 5/2 resonances with Jupiter (a◦=2.5 or a◦=2.823 AU). Initial eccentricities and inclinations were the same in all runs: e◦=0.15 and i◦=10 ◦. Initial values of the mean anomaly and the longitude of the ascending node were different. The considered time interval TS equaled severa

Year: 2002
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