Astronomy and Astrophysics – Astronomy
Scientific paper
Oct 1993
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993cemda..57...59m&link_type=abstract
Celestial Mechanics and Dynamical Astronomy (ISSN 0923-2958), vol. 57, no. 1-2, p. 59-94
Astronomy and Astrophysics
Astronomy
61
Asteroid Belts, Asteroids, Chaos, Orbit Calculation, Orbit Perturbation, Orbital Elements, Orbital Resonances (Celestial Mechanics), Systems Stability, Eccentricity, Fourier Transformation, Inclination, Jupiter (Planet), Libration, Numerical Integration, Perihelions
Scientific paper
I have computed proper elements for 174 asteroids in the 1:1 resonance with Jupiter, that is for all the reliable orbits available (numbered and multi-opposition). The procedure requires numerical integration, under the perturbations by the four major planets, for 1,000,000 years; the output is digitally filtered and compressed into a 'synthetic theory' (as defined within the LONGSTOP project). The proper modes of oscillation of the variables related to eccentricity, perihelion, inclination and node define proper elements. A third proper element is defined as the amplitude of the oscillation of the semimajor axis associated with the libration period; because of the strong nonlinearity of the problem, this component cannot be determined by a simple Fourier transform to the frequency domain. I therefore give another definition, which results in very good stability with time.
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