Structures of the phase space near Lagrange's triangular equilibrium points.

Details Structures of the phase space near Lagrange's triangular equilibrium points. Structures of the phase space near Lagrange's triangular equilibrium points.

Aug 1999

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999acasn..40..286z&link_type=abstract

Acta Astron. Sin., Vol. 40, No. 3, p. 286 - 293

Astronomy and Astrophysics

Astronomy

1

Three-Body Problem: Restricted, Minor Planets: Orbital Evolution

Scientific paper

In the framework of the restricted circular 3-body problem (Sun-Jupiter-asteroid), the stability of Lagrange's triangular equilibrium points is studied. From the Hamiltonian equations, which describe the evolution of the asteroid, a symplectic mapping is constructed near Lagrange's triangular equilibrium points. By using this mapping method, both the structure of phase space near Lagrange's triangular equilibrium points in the restricted circular 3-body problem and the stability of this solution are discussed. Numerical results indicate that the triangular equilibrium points are stable, provided the mass-ratio of the two primaries, μ, is smaller than 0.02165, only except the case μ = 0.01440. This matches the theoretical results. When applied in the Sun-Jupiter-asteroid system, this result can be used to explain the stability of asteroids in the Trojan Group and the Greek Group.

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