High-eccentricity non-secular Three-Period Resonances inside Two-period Resonances (Kirkwood Gaps)

Details High-eccentricity non-secular Three-Period Resonances inside Two-period Resonances (Kirkwood Gaps) High-eccentricity non-secular Three-Period Resonances inside Two-period Resonances (Kirkwood Gaps)

Sep 1998

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998dps....30.1001f&link_type=abstract

American Astronomical Society, DPS meeting #30, #10.01; Bulletin of the American Astronomical Society, Vol. 30, p.1028

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Recent investigations (Nesvorny and Morbidelli, AJ, in press; Murray et al., AJ, in press) are emphasizing the important role played by high-order two-period and three-period resonances in the generation of chaos all over the asteroidal belt. Inside the 2/1 asteroidal resonance (Hecuba gap), the role of these three-period resonances was also shown to be determinant (Ferraz-Mello, CMDA, 1997; Ferraz-Mello et al., AJ, 1998; Roig and Ferraz-Mello, PSS, in press). Indeed, due to the almost commensurability between the periods of Jupiter and Saturn, important low-order three-period resonances occur inside the Kirkwood gaps. For instance, we have the (4, -5, -1), (6, -5, -2) and (8, -5, -3) resonances, of orders, respectively, 2, 1 and 0, accumulating in the interval 3.31 to 3.32 AU, in the middle of the 2/1 resonance. At variance with other three-period resonances, those inside a Kirkwood gap will strongly depend on the proper oscillation of the main critical argument and, in fact, they will work as an (1, 1) resonance between the frequency of the Jupiter-Saturn Great Inequality and the libration frequency. In the case of the Hecuba gap, experiments using different values of the Great Inequality's frequency showed the effects due to the overlap of the Great Inequality with multiplets generated by linear combinations of the asteroid libration and perihelion frequencies. The main effect of this overlap is an increase in the diffusion of orbits initially located in the central region of the resonance, allowing them to escape from the resonance in some hundreds of Myrs. On the other hand, similar overlaps do not affect the asteroids of the Hilda group (inside the 3/2 resonance). An analogous effect was conjectured to exist in the case of the 2/3 resonance in the Kuiper belt because of the (1, -2) near-comemnsurability between the motions of Neptune and Uranus. However, in this case, those effects are important only for eccentricities higher than 0.5 (Milani, PSS, 1997), in a region where the dynamics is strongly determined by close approaches to Uranus. (Gallardo and Ferraz-Mello, PSS, in press).

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