Secular resonances from 2 to 50 AU

Abstract By means of a new algorithm which generalizes the second-order and fourth-degree secular perturbation theory of Milani and Kneževic (1990, Celest. Mech. 49, 347–411), we find in the a-e-I proper elements space the location of secular resonances between the precession rates of the longitudes of perihelion and node of a minor body and the corresponding eigenfrequencies of the secular perturbations of the four outer planets. Among the most interesting implications of our findings, we can quote: (i) the fact that the g = g6 (or ν6) resonance in the inner asteroid belt lies closer than previously assumed to the densely populated Flora region, providing a plausible dynamical route to inject asteroid fragments into planet-crossing orbits; (ii) the existence of another possible meteorite source near 2.4 AU at moderate inclinations, again through g = g6; (iii) the existence, confirmed by numerical experiments, of a region affected in a chaotic way by the s = s6 (or ν16) resonance at semimajor axis ⋍ 2.2 AU and moderate inclination, where no asteroid is observed; (iv) the possible presence of some low-inclination “rings” between the orbits of the outer planets where no major mean motion or secular resonance lies very near, allowing minor bodies to survive long times without close encounters; (v) the fact that none of the secular resonances considered in this work exists beyond 50 AU, so that these resonances cannot be effective for transporting inward comets belonging to a possible Kuiper flattened disk.

[1]  G. Hahn,et al.  Dynamics of planet-crossing asteroids: Classes of orbital behavior: Project SPACEGUARD , 1989 .

[2]  W. Ward.  Solar nebula dispersal and the stability of the planetary system: I. Scanning secular resonance theory , 1981 .

[3]  R. Smoluchowski,et al.  Chaotic motion in a primordial comet disk beyond Neptune and comet influx to the Solar System , 1990, Nature.

[4]  M. Yoshikawa.  A simple analytical model for the secular resonance ν6 in the asteroidal belt , 1987 .

[5]  M. Bailey,et al.  Stochastic capture of short-period comets , 1989 .

[6]  George W. Wetherill,et al.  Where do the Apollo objects come from , 1988 .

[7]  Dirk Brouwer,et al.  The secular variations of the orbital elements of the principal planets , 1950 .

[8]  Zoran Knežević.  Asteroid long-periodic perturbations: The second order Hamiltonian , 1989 .

[9]  J. Laskar.  Secular evolution of the solar system over 10 million years , 1988 .

[10]  B. Gladman,et al.  On the Fates of Minor Bodies in the Outer Solar System , 1990 .

[11]  S. Tremaine,et al.  Planetary perturbations and the origins of short-period comets , 1990 .

[12]  T. Heppenheimer.  Reduction to proper elements for the entire solar system , 1979 .

[13]  Andrea Milani,et al.  Secular perturbation theory and computation of asteroid proper elements , 1990 .

[14]  H. Scholl,et al.  The nu6 Secular Resonance Region Near 2 AU: A Possible Source of Meteorites , 1991 .

[15]  H. Scholl,et al.  The effects of the secular resonances v16 and V5 on asteroidal orbits , 1986 .

[16]  G. Colombo,et al.  Secular resonance, solar spin down, and the orbit of Mercury , 1976 .

[17]  M. Lecar,et al.  On the original distribution of the asteroids II. Do stable orbits exists between Jupiter and Saturn , 1989 .

[18]  James G. Williams,et al.  The positions of secular resonance surfaces , 1981 .

[19]  J. Laskar.  A numerical experiment on the chaotic behaviour of the Solar System , 1989, Nature.

[20]  J. Laskar.  Théorie Générale Planétaire. Eléments orbitaux des planètes sur 1 million d'années , 1984 .

[21]  G. Wetherill.  Dynamical relations between asteroids, meteorites and Apollo-Amor objects , 1987, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[22]  M. Carpino,et al.  Dynamics of Pluto , 1989 .

[23]  H. Scholl,et al.  The secular resonance ν6 in the asteroidal belt , 1986 .

[24]  Yoshihide Kozai,et al.  Secular perturbations of asteroids with high inclination and eccentricity , 1962 .

[25]  A. Milani,et al.  Fundamental frequencies and small divisors in the orbits of the outer planets , 1989 .

[26]  H. Nakai,et al.  Secular perturbations of asteroids in secular resonance , 1985 .

[27]  A. Morbidelli,et al.  The main secular resonances ν6, vs and ν16 in the asteroid belt , 1991 .

[28]  J. Henrard,et al.  Secular resonances in the asteroid belt: Theoretical perturbation approach and the problem of their location , 1991 .

[29]  W. M. Kaula,et al.  A computer search for stable orbits between Jupiter and Saturn , 1990 .

[30]  G. Wetherill.  Steady state populations of Apollo-Amor objects , 1979 .

[31]  James Gerard Williams,et al.  Secular Perturbations in the Solar System. , 1969 .

[32]  H. Scholl,et al.  Secular resonances: New results , 1987 .

[33]  R. Abbot,et al.  Surfaces of section in the elliptic restricted problem for the Sun-Jupiter system. , 1973 .

[34]  T. Heppenheimer.  Secular resonances and the origin of eccentricities of Mars and the asteroids , 1979 .

[35]  G. M. Clemence,et al.  Methods of Celestial Mechanics , 1962 .

[36]  C. F. Yoder.  Notes on the origin of the Trojan asteroids , 1979 .

[37]  R. Bien,et al.  Trojan orbits in secular resonances , 1984 .