Computer Science
Scientific paper
Aug 1978
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1978cemec..18..141e&link_type=abstract
Celestial Mechanics, vol. 18, Aug. 1978, p. 141-161.
Computer Science
17
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
Scientific paper
The problem is considered within the framework of the elliptic restricted three-body problem. The asymptotic solution is derived by a three-variable expansion procedure. The variables of the expansion represent three time scales of the asteroids: the revolution around the sun, the libration around the triangular Lagrangian points L4 and L5, 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 of 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.
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