Spectral analysis of asteroidal trajectories in the 2:1 resonance.

Details Spectral analysis of asteroidal trajectories in the 2:1 resonance. Spectral analysis of asteroidal trajectories in the 2:1 resonance.

Aug 1995

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995a%26a...300..591v&link_type=abstract

Astronomy and Astrophysics, v.300, p.591

Astronomy and Astrophysics

Astrophysics

1

Chaotic Phenomena, Celestial Mechanics, Stellar Dynamics, Minor Planets

Scientific paper

The evolution of the eccentricity of particular asteroidal trajectories in the 2:1 resonance is analysed by a spectral scheme. This analysis is an alternative to the well known analysis based on the computation of Liapunov exponents. The method can be used to estimate the long time evolution of a trajectory from a segment considerably shorter than the one needed for a Liapunov exponent calculation. The particular trajectories analysed by our method may be divided into two classes: (a) those appearing to be unstable, in the sense that their eccentricities become overcritical within the time interval of our numerical integrations, which, in turn, implies close encounters with a planet (Mars, the Earth or Jupiter) and (b) those appearing, in the above sense, to be stable. Trajectories are computed in the frame of four models: (i) the elliptic restricted three body problem (ERTBP) model with a fixed value of 0.048 for Jupiter's eccentricity, e_J_, (ii) the ERTBP model with a fixed e_J_>=0.055, (iii) the ERTBP model with an artificially oscillating e_J_ with amplitudes corresponding to the full problem, including all outer planets, but with a frequency not corresponding to the real problem, and (iv) the six-body problem Sun - outer planets - asteroid. The main results are: (a) There are trajectories which are stable in model (i) and which are chaotic as well as unstable in models (ii)-(iv). This suggests that chaos sets on when Jupiter's eccentricity exceeds a certain threshold value. This is not universal all over the 2:1 resonance region. (b) Trajectories which are stable in all four models are chaotic in models (ii)-(iv) according to our spectral analysis.

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