Orateur
Description
In the three-body problem, for all values of the masses, the vertical eigenvectors of the Lagrange relative equilibrium give rise to a family of spatial quasi-periodic orbits; these orbits are periodic in a rotating frame.
For the equal masses' cases, this is the P12 family with its order-12 symmetry group, which ends at the figure Eight solution (studied in Chenciner-Fejoz-Montgomery (2005), Chenciner-Fejoz (2008) and Calleja, Garcia-Azpeitia, Hénot, Lessard and Mireles (2024)).
In 2009, Christian Marchal studied this family in the special case of the average restricted secular problem.
We propose a numerical study to follow this family in the general case. We show that the family discovered by Marchal exists in the full three-body problem (neither restricted nor secular) for a wide range of masses, and that the stability of its orbits evolves along the family, sometimes leading to stable systems for masses exceeding the Gascheau's value.
We also link this family to P12: in the equal masses case, they are identical up to a bifurcation, where P12 continues towards the Eight and the Marchal branch goes to collisions.
