Theory of the Trojan asteroids. Part I.
Abstract
The motion of the Trojan asteroids is treated as a case of 1:1 resonance in the restricted threebody problem with a mass parameter much less than unity. An analytical longperiod solution of the first order in the mass parameter is constructed which provides the polar coordinates of a oneparameter family of orbits in terms of the mean synodic longitude, the angular frequencies associated with the long and short periods, a complex Fourier coefficient of a certain periodic function, and a family parameter related to the Jacobi constant. It is found that the solution has singularities at zero values of the second critical divisor and mean synodic longitude, that the range of validity embraces the regime of libration with its tadpole and horseshoeshaped orbits except those that make a close approach to Jupiter, and that the internal resonant term which carries the second critical divisor imparts an epicyclic character to the orbit.
 Publication:

The Astronomical Journal
 Pub Date:
 May 1977
 DOI:
 10.1086/112060
 Bibcode:
 1977AJ.....82..368G
 Keywords:

 Asteroids;
 Celestial Mechanics;
 Orbital Mechanics;
 Three Body Problem;
 Trojan Orbits;
 Disturbing Functions;
 Hamiltonian Functions;
 Jordan Form;
 Resonance;
 Astronomy