A Model for the Study of Very-High-Eccentricity Asteroidal Motion: The 3:1 Resonance
Recent work by one of the authors (Ferraz-Mello, 1989, 1990 a,b) and by Mor- bidelli and Giorgilli (1990) has shown the existence of very-high-eccentricity stable and unstable equilibrium solutions (corotation centers) in the averaged Sun-Jupiter- asteroid planar problem, when a secular resonance and a resonance of periods occur simultaneously. They correspond to stationary motions in which the orbits of the asteroid and Jupiter share the same apsidal hne. In the case of a 3:1 resonance of periods, two of these corotation centers form a stable-unstable pair at e = 0.812 and e = 0.788, respectively. The stable corotation center corresponds to a maximum of the energy (Es = −1.775728 in astronomical units). For values close to this maximum the motions are regular oscillations in the neighbourhood of the corotation center (as those shown in the left-hand side of fig. 2).
KeywordsCritical Angle Astronomical Unit Level Curf Regular Oscillation Homoclinic Point
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