Eccentric orbits bring about the problem of close encounters. One can, in principle, switch to a new dominating central body whenever necessary and choose a suitable near-integrable Keplerian configuration. For an asteroid approaching Jupiter, this zone is roughly between 0.02 AU and 1 AU from the planet. Proper'' close encounters are thus very rare, and even in them the time spent in the transition zone dominates the computational effort. A further problem is that the object may wander in and out of the transition zone several times during the encounter.
Close encounters are thus clearly easiest to handle in conventional integration variables.
Frequent close encounters undermine the efficiency of near-integrability, so only an object not engaged in continuous interplay with Jupiter can be integrated well in this scheme. To summarize, our numerical tests show that the near-integrable approach is efficient whenever the perturbations do not considerably exceed about a hundredth part of the force caused by the dominating body. Occasional close encounters are no obstacle, but they must be handled with a separate method. Orbits with high eccentricities can be efficiently integrated if their inclinations are suitable.