Generalized Averaging Principle and the Secular Evolution of Planet Crossing Orbits
Abstract
Planet crossing orbits give rise to mathematical singularities that make it not possible to apply the classical averaging principle to study the qualitative evolution of Near Earth Asteroids (NEAs). Recently this principle has been generalized to deal with crossings in a mathematical model with the planets on circular coplanar orbits. More accuracy is needed to compute the averaged evolution of planet crossing orbits for different purposes: computing reliable crossing times for the averaged motion, writing more precise proper elements and frequencies for NEAs, etc. In this paper we present the generalization of the averaging principle using a model where the eccentricity and the inclination of the planets are taken into account.
 Publication:

Celestial Mechanics and Dynamical Astronomy
 Pub Date:
 May 2002
 Bibcode:
 2002CeMDA..83...97G
 Keywords:

 planet crossing orbits;
 Near Earth asteroids;
 averaging principle