Theory of the Trojan asteroids. I

Details Theory of the Trojan asteroids. I Theory of the Trojan asteroids. I

May 1977

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977aj.....82..368g&link_type=abstract

Astronomical Journal, vol. 82, May 1977, p. 368-379.

Astronomy and Astrophysics

Astronomy

36

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

Scientific paper

The motion of the Trojan asteroids is treated as a case of 1:1 resonance in the restricted three-body problem with a mass parameter much less than unity. An analytical long-period solution of the first order in the mass parameter is constructed which provides the polar coordinates of a one-parameter 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 horseshoe-shaped 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.

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