H. Scholl

The three principal secular resonances ?5, ?6, and ?16 in the asteroidal belt

We review theoretical and numerical results obtained for secular resonant motion in the asteroidal belt. Williams theory (1969) yields the locations of the principal secular resonances ν5, ν6, and ν16 in the asteroidal belt. Theories by Nakai and Kinoshita (1985) and by Yoshikawa (1987) allow us to model the basic features of orbital evolution at the secular resonances ν16 and ν6, respectively. No theory is available for the secular resonance v5. Numerical experiments by Froeschlé and Scholl yield quantitative and new qualitative results for orbital evolutions at the three principal secular resonances ν5, ν6, and ν16. These experiments indicate possible chaotic motion due to overlapping resonances. A secular resonance may overlap with another secular resonance or with a mean motion resonance. The role of the secular resonances as possible sources of meteorites is discussed.

Numerical experiments in the 3/1 andv 6 overlapping resonance region

Numerical experiments of fictitious small bodies with initial eccentricities e=0.1 have been performed in the overlapping region of the 3/1mean motion resonance and of the v 6 secular resonance 2.48 ≤ a ≤ 2.52AU for different values of the initial inclination 16° ≤ i ≤ 20°. An analysis for the v 6 secular resonance shows that the topology is different from the one found outside the overlapping region: the critical argument for the v 6 resonance in the overlapping region rotates in opposite direction as compared to the pure v 6 region. In the 3/1 resonance region the secular resonance v 5 is dominant, and some secondary secular resonances as v 6 — v 16 and v 5 + v 6 are present.

Delivery of Meteorites from the v 6 Secular Resonance Region Near 2 AU

Numerical integrations in the frame of Sun-Mars-Jupiter-Saturn model over 1Myr have been performed in order to investigate the orbital evolution of asteroid fragments produced in the innermost asteroid belt (2.07–2.13AU). Fragments injected in the vicinity of the V6 secular resonance enhance their eccentricities and become Mars-crossers. Close encounters to Mars will then lead to a random walk in semi- major axes. Two different mechanisms may occur to produce Earth-crossers. In the first case, the fragment enters the 4/1 mean motion resonance and becomes an Earth-crosser within at least 2.6 * 105 years. In the second case, which involves only the secular resonance V6 the shortest timescale for deriving meteorites is of the order of 5.6 * 105years.

Evolution of Asteroidal Orbits Located in the Main Secular Resonances v5,v6 and v16

We investigated the orbital evolution of fictitious asteroids located in and near the three main secular resonances v5, v6 and v16. Our results confirm a suggestion by Wetherill (1979) concerning the delivery of Apollo asteroids: asteroids located in the secular resonances v5 and v6 may increase strongly their eccentricities and therefore may become Mars-crossers, Earth-crossers and even Venus-crossers. For the secular resonance v16, large increases in inclination are obtained. In case of the v16 resonance, three different regions for secular resonant motion are found similar to the case of mean motion resonances: transitions between these three regions occur. According to our numerical results, secular resonances should be considered as sources of meteorites as conjectured by Wetherill and Williams (1979).

A Possible Source for Highly Inclined Apollo-Armor Asteroids: The Secular Resonance ν 16

In order to find a mechanism to explain highly inclined Apollo-Armor asteroids, we integrated over some Myrs the orbital evolutions of asteroids located in the secular resonance ν 16. When the resonant argument Ω - Ω J librates around 180°, the inclination of model asteroids increases from 4° to 24° only. Also, additional passages through the ν 16 secular resonance do not increase the inclinations furthermore. On the other hand, after a temporary passage through the ν 5 resonance, the ν 16 resonance argument Ω - Ω J may librate around 0°. Libration about this new libration center causes further increase of inclination. It appears that the overlapping resonances, ν 5 and ν 16, may produce highly inclined orbits. A backwards integration of the asteroid 2335 James located at present in the ν 16 resonance illustrates the mechanism we propose to produce highly inclined Apollo-Armor asteroids.