Motions of asteroids at the Kirkwood gaps I. On the 3:1 resonance with Jupiter
Abstract
The behavior of asteroids at the 3:1 resonance is studied in a large parameter region, and the various motions that these asteroids show are summarized. First, the motions of asteroids are investigated qualitatively using a semianalytical method, and the variations of ( a, σ) and (e, overlineω) are obtained graphically for various values of the parameters (a = semimajor axis, σ = critical argument, e = eccentricity, overlineω = longitude of perihelion) . Next, to know the motions of asteroids more quantitatively, the orbital changes in asteroids are calculated by numerical integrations in the scheme of a planar elliptical restricted threebody problem. The main results are as follows: (1) The variations in a and σ are rather complicated, and the variations in e and overlineω depend strictly on the behavior of these elements. (2) The region where the resonance occurs is obtained on the a e plane, and almost all numbered asteroids avoid this region. (3) The eccentricities of most asteroids in the resonance region change markedly ( ∆e ⪆ 0.2 or much larger), and these changes take place in a period of 10 ^{4}10 ^{5} years. (4) In terms of the orbital changes of asteroids, the resonance region shows a complicated structure.
 Publication:

Icarus
 Pub Date:
 September 1990
 DOI:
 10.1016/00191035(90)900222
 Bibcode:
 1990Icar...87...78Y
 Keywords:

 Asteroids;
 Equations Of Motion;
 Orbit Calculation;
 Orbital Mechanics;
 Orbital Resonances (Celestial Mechanics);
 Numerical Integration;
 Orbital Elements;
 Perturbation Theory;
 Three Body Problem;
 Lunar and Planetary Exploration