Evolution of the orbits of resonant asteroids in the case of thirdorder commensurabilities.
Abstract
The orbits of asteroids for which the ratio of their mean motions to Jupiter's one is close to (m+3)/m, where m is integer, are under discussion in the case of the restricted circular threebody problem. Time dependences of the resonant asteroids orbital elements are derived in terms of the Weierstrass functions. Formulae for computing the periods of variation of elements and limits of varitions of the eccentricity and of the semimajor axis are obtained. The method described in the first part of the paper for solving the problem of the evolution of resonant asteroids orbits is considered with regard to Minervatype asteroids moving close to commensurability 5:2 to Jupiter. An algorithm for computing the evolutionary characteristics of these asteroids is suggested. A statistical analysis of resonant group 5:2 was carried out.
 Publication:

Astronomicheskii Vestnik
 Pub Date:
 July 1993
 Bibcode:
 1993AVest..27...87V
 Keywords:

 Asteroids;
 Evolution (Development);
 Jupiter (Planet);
 Numerical Analysis;
 Orbital Resonances (Celestial Mechanics);
 Three Body Problem;
 Algorithms;
 Orbit Calculation;
 Orbital Elements;
 Ratios;
 Statistical Analysis;
 Time Dependence;
 Astrophysics