A survey of the dynamics of main belt asteroids. II.

Details A survey of the dynamics of main belt asteroids. II. A survey of the dynamics of main belt asteroids. II.

Aug 1995

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995a%26a...300..289m&link_type=abstract

Astronomy and Astrophysics, v.300, p.289

Astronomy and Astrophysics

Astrophysics

5

Celestial Mechanics, Stellar Dynamics, Minor Planets, Asteroids

Scientific paper

We present the second part of a survey of the dynamical structure of the asteroid belt. The model used for this purpose is extended to a dynamical system consisting of the Sun, Jupiter and Saturn (model II). Comparing now to the results of part I of the survey, where we treated only the elliptic restricted problem (model I: Sun + Jupiter + fictitious massless asteroid) we can determine Saturn's direct, respectively indirect influence on the structure of the main belt. The results are again displayed as 3-dimensional plots showing the dynamical evolution of the fictitious asteroids. The initial semimajor axis ranges from 0.3 to 0.8 (in units of the semimajor axis of Jupiter's orbit); the initial eccentricities of these bodies were fixed between 0.0 and 0.30; the mesh has a grid width in initial semimajor axis {DELTA}a=0.002 and {DELTA}e=0.025 in initial eccentricity. The orbits of about 4000 fictitious asteroids were integrated numerically over 5x10^4^ Jupiter periods corresponding to approximately 5x10^5^ years, which is an extension of factor 5 in time with respect to paper I. We take the standard deviations σ of the semimajor axis a, eccentricity e and inclination i, as parameters characterizing the orbital perturbations due to Jupiter and Saturn. The σ(a), σ(e), σ(i) are plotted as functions of the initial conditions a and e in the new model. We also discuss in detail the differences between the integrations in the old (restricted) model and the new one including Saturn. From our results we can conclude that the main features of the inner part of of the belt (up to the 2:1 resonance) change according to the presence of secular resonances in the new model. In the outer main belt the asteroids suffer from very strong perturbations in model I and model II, which may throw most of the asteroids out of that region. In model II we recognize also, that strong perturbations are acting for small initial eccentricities as well. We also check the Lyapunov exponents which indicate that in the resonances chaos is present; this allows the asteroids to undergo sudden significant changes in eccentricities, which then may lead to close approaches to the planets and subsequent escapes. Finally we compared our results in the two models with the real asteroid distribution and found a relatively good agreement of model II with reality.

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