Abstract
An enlarged averaged Hamiltonian is introduced to compute several families of periodic orbits of the planar elliptic 3-body problem, in the Sun–Jupiter–Asteroid system, near the 4:1 resonance. Four resonant critical point families are found and their stability is studied. The families of symmetric periodic orbits of the elliptic problem appear near the corresponding fixed points computed in this model. There is a good agreement for moderate eccentricity of the asteroid for three of these families, whereas the remaining family cannot be considered as a family of periodic orbits of the real model.
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