Sets of Collision Periodic Orbits in the Restricted Problem

Analytical and numerical results on families of n-ejection-collision orbits in the RTBP

“…On the numerical side, we first mention Hénon's paper [9], where the computation of EC orbits is done along the continuation of some families of symmetric periodic, non collision, orbits in the Copenhagen problem (that is µ = 0.5), in Hill's problem (see [10]) and similarly in [2] the computation of 16 particular collision periodic orbits of the RTBP is done for various values of µ ∈ (0, 0.5].…”

Regularisation in Ejection-Collision Orbits of the RTBP

“…Focussing on numerical results, there are some isolated computations published: we mention Henon's paper (see [8]) about the computation of EC orbits obtained along the continuation of some families of symmetric periodic -non-collision-orbits in the Copenhagen problem (that is µ = 0.5) and also for Hill's problem (see [9]). Finally, the evolution of 16 particular collision periodic orbits obtained from the µ = 0.5 case was numerically studied for various values of the mass ratio µ in [4].…”

Ejection-collision orbits in the RTBP

“…• The other two (which do not intersect the x-axis when they cross the Poincaré section Σ n ) are non symmetric with respect to the x-axis (taking the (x, y) projection), but one can be obtained from the other one applying symmetry (4). Following again the notation previously introduced we will call the corresponding families β n and δ n , respectively.…”

“…Referring to numerical results, we mention Henon's paper about the compu-tation of EC orbits obtained along the continuation of some families of symmetric periodic -non-collision-orbits in the Copenhagen problem (that is µ = 0.5, see [7]) and also for Hill's problem (see [8]). Finally, the evolution of 16 particular collision periodic orbits obtained from the µ = 0.5 case was numerically studied for various values of the mass ratio µ in [4].…”