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P. Michel (O.C.A.), G.F. Gronchi (U. Pisa)
In this work, we test the accuracy of proper elements and proper frequencies for NEAs computed by a semianalytic method with the planets on circular and coplanar orbits; we compare them with the ones computed by pure numerical integrations in the same reference frame and in a more realistic planetary system.
Proper elements are quasi--integrals of the motion, i.e. quantities that change very slowly with the time and that can be considered approximately constant over time spans not too long. They are the maximum and minimum values of the eccentricity and inclination that result from secular perturbations.
Proper frequencies of perihelion argument and longitude of node are useful to draw a map of the NEAs affected by the secular resonances.
Given the required accuracy, this comparison between theory and numerical integrations appears satisfaying, apart from a few cases for which the theory is not valid a priori.
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