The ThreeDimensional Motion of Trojan Asteroids
Abstract
The problem is considered within the framework of the elliptic restricted threebody problem. The asymptotic solution is derived by a threevariable expansion procedure. The variables of the expansion represent three timescales of the asteroids: the revolution around the Sun, the libration around the triangular Lagrangian pointsL _{4},L _{5}, and the motion of the perihelion. The solution is obtained completely in the first order and partly in the second order. The results are given in explicit form for the coordinates as functions of the true anomaly of Jupiter. As an example for the perturbations of the orbital elements the main perturbations of the eccentricity, the perihelion longitude and the longitude of the ascending node are given. Conditions for the libration of the perihelion are also discussed.
 Publication:

Celestial Mechanics
 Pub Date:
 August 1978
 DOI:
 10.1007/BF01228712
 Bibcode:
 1978CeMec..18..141E
 Keywords:

 Asteroids;
 Celestial Mechanics;
 Orbital Mechanics;
 Three Body Problem;
 Three Dimensional Motion;
 Trojan Orbits;
 Equations Of Motion;
 Jupiter (Planet);
 Lagrangian Equilibrium Points;
 Libration;
 Orbit Perturbation;
 Orbital Elements;
 THREE BODY PROBLEM;
 ASTEROIDS;
 TROJAN ASTEROIDS;
 REVOLUTION;
 SUN;
 PERTURBATIONS;
 MOTION;
 PERIHELION;
 JUPITER;
 ANOMALIES;
 ECCENTRICITY;
 LONGITUDE;
 ORBITS;
 LIBRATIONS;
 GRAVITATIONAL FIELDS;
 Astronomy; Asteroids