Astronomy and Astrophysics – Astronomy
Scientific paper
May 1976
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1976cemec..13..313v&link_type=abstract
Celestial Mechanics, vol. 13, May 1976, p. 313-324.
Astronomy and Astrophysics
Astronomy
1
Asteroids, Circular Orbits, Motion Stability, Orbital Mechanics, Planetary Systems, Solar Orbits, Astronomical Models, Eccentricity, Equations Of Motion, Orbit Perturbation
Scientific paper
The restricted problem of the motion of a point of negligible mass ('asteroid') in an N-planetary system is considered. It is assumed that all the planets move about the central body ('sun') along circular orbits in the same plane and the mean motions of the asteroid and the planets are incommensurable. The asteroid orbit evolution is described as a first approximation by secular equations with the perturbing function averaged by the mean longitudes of the asteroid and the planets. For small values of the asteroid orbit eccentricity an expression for the secular part of the perturbing function has been obtained. This expression holds for the arbitrary values of the asteroid orbit semi-axis which are different from those of the planet orbit radii. The stability of the asteroid circular orbits in a linear approximation with respect to the eccentricity is studied. The critical inclinations for a solar system model are calculated.
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