Phase trajectories of asteroids in the case of third-order commensurabilities

Details Phase trajectories of asteroids in the case of third-order commensurabilities Phase trajectories of asteroids in the case of third-order commensurabilities

Apr 1991

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1991azh....68..437g&link_type=abstract

Astronomicheskii Zhurnal (ISSN 0004-6299), vol. 68, Mar.-Apr. 1991, p. 437-439. In Russian.

Statistics

Computation

Asteroids, Jupiter (Planet), Orbital Mechanics, Three Body Problem, Trajectory Analysis, Computational Astrophysics, Orbital Resonances (Celestial Mechanics)

Scientific paper

Orbits of asteroids for which the ratio of their mean motions to the one of Jupiter is close to (k+3)/k, where k is an integer, are discussed. The internal variant of the restricted three-body (the sun, Jupiter and an asteroid of negligibly small mass) problem is examined. The solution of equations for phase trajectories describing the evolution of the orbits is obtained in terms of Weierstrass' functions. The solution of the entire problem of the evolution of the orbits of resonance asteroids for the commensurabilities under consideration is facilitated, classification of phase trajectories becomes identical to the classification developed for first-order commensurabilities, and analysis of the motion of apsidal lines is simplified.

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