Geometry of transit orbits in the periodically-perturbed restricted three-body problem. Issue 1 (1st July 2022)

• Record Type: Journal Article
• Authors: Fitzgerald, Joshua; Ross, Shane D.
• Is Part Of: Advances in space research. Volume 70:Issue 1(2022)
• Page Start: 144
• Page End: 156
• Publication Date: 2022-07-01
• Subjects: Astrodynamics -- Three-body problem -- Low energy transfer -- Tube dynamics -- Lagrange points -- Perturbations; Space sciences -- Periodicals; Astronautics -- Periodicals; Geophysics -- Periodicals; 500.505
• DOI: 10.1016/j.asr.2022.04.029
• Languages: English
• ISSNs: 0273-1177

Abstract

Abstract: In the circular restricted three-body problem, low energy transit orbits are revealed by linearizing the governing differential equations about the collinear Lagrange points. This procedure fails when time-periodic perturbations are considered, such as perturbation due to the sun (i.e., the bicircular problem) or orbital eccentricity of the primaries. For the case of a time-periodic perturbation, the Lagrange point is replaced by a periodic orbit, equivalently viewed as a hyperbolic-elliptic fixed point of a symplectic map (the stroboscopic Poincaré map). Transit and non-transit orbits can be identified in the discrete map about the fixed point, in analogy with the geometric construction of Conley and McGehee about the index-1 saddle equilibrium point in the continuous dynamical system. Furthermore, though the continuous time system does not conserve the Hamiltonian energy (which is time-varying), the linearized map locally conserves a time-independent effective Hamiltonian function. We demonstrate that the phase space geometry of transit and non-transit orbits is preserved in going from the unperturbed to a periodically-perturbed situation, which carries over to the full nonlinear equations.