The high-eccentricity libration of the Hildas

Details The high-eccentricity libration of the Hildas The high-eccentricity libration of the Hildas

Jul 1988

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1988aj.....96..400f&link_type=abstract

Astronomical Journal (ISSN 0004-6256), vol. 96, July 1988, p. 400-408. Research supported by the Fundacao de Amparo a Pesquisa d

Astronomy and Astrophysics

Astronomy

33

Asteroids, Celestial Mechanics, Eccentric Orbits, Libration, Elliptical Orbits, Jupiter (Planet), Numerical Integration, Stellar Orbits

Scientific paper

The analytical modeling of the planar motion of high-eccentricity asteroids near first-order resonances leads to three approximative laws: the law of structure relating the semimajor axis and the eccentricity at the libration centers, the law of periods giving the proper periods about the libration centers, and the law of the second forced mode giving the amplitude of the oscillation induced by the eccentricity of Jupiter. The law of structure shows the existence of a forbidden interval in the distribution of the mean semimajor axes at 0.763-0.773 (3.97-4.02 AU). However, the existence of asteroids whose osculating semimajor axis is in that interval is not excluded. The law of structure just prevents the asteroids from remaining there stationarily. This structural gap can be crossed and at any time some 15 of the presently known Hildas will be incursioning in it, some of them crossing it completely. The group appearance of the Hildas is due to the nonexistence of apocentric librators or inner circulators among them. In the case of the resonance 2:1, both groups exist, one on each side of the forbidden interval.

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