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Astron. Astrophys. 328, L5-L8

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Letter to the Editor

Overlapping of secular resonances in a Venus horseshoe orbit

Patrick Michel

Observatoire de la Côte d'Azur, Dept. Cassini, UMR 6529, B.P. 4229, F-06304 Nice Cédex 4, France

Received 21 August 1997 / Accepted 16 September 1997


A numerical N-body integration of the asteroid (4660) Nereus over 3.5 Myr shows the presence of the Kozai resonance and two secular resonances inside a horseshoe orbit with Venus. This 1/1 mean motion resonance with Venus remains stable during the whole time span though a secular increase of the orbital inclination of the small body occurs due to the overlapping of two secular resonances, namely $\nu_{13}$ and $\nu_{14}$. This result shows that the dynamics of horseshoe orbits can be very complex since an interplay with some secular mechanisms is possible. Whether such interplay can occur frequently with Venus or the Earth and does not either affect or increase the long-term stability of this kind of orbits is still not clear and needs further investigations.

Key words: Minor planets, asteroids - Celestial mechanics

Send offprint requests to: P. Michel

© European Southern Observatory (ESO) 1997

Online publication: October 30, 1997
Last change: March 24, 1998