ESCAPE DYNAMICS FOR THE COPENHAGEN PROBLEM

Sheila Crisley de Assis¹; Maisa de Oliveira Terra¹

¹ Instituto Tecnológico de Aeronáutica - ITA

doi:10.20906/CPS/COB-2015-2563

Resumo

In this contribution we investigate the escape dynamics in the planar circular restricted three-body problem for the Copenhagen case. This mathematical model describes the planar dynamics of a particle subject to the gravitational potential of two bodies P1 and P2, named primaries, that performs coplanar circular orbits around their center of mass. The mass of the third body is much smaller than that of the primaries, thus the movement of P1 and P2 is not disturbed by the third body. The primaries present equal masses, so the parameter mass of the mathematical model is equal ½ and the necks around L2 e L3 open simultaneously. In this work, we are considering the initial conditions between the collinear Lagrangian points L2 and L3. The analysis is divided into two important cases, which are defined from different energy levels, revealing different possibilities for exits of the forbidden regions in the phase space. In the first case, just the neck around L1 is open, then we analyzed trajectories which collide with P1 or with P2 and and trajectories which do not collide until the maximum integration time (limited trajectories); the second case, the necks around L2 e L3 are open, then we have to consider trajectories which collide with P1 or with P2, trajectories that escape through L2 or L3 channels and trajectories which not collide or escape from the scattering region after completing the integration time (limited trajectories). The spatial distribution of escape time values are also investigated and associated with the fractality of the boundaries. This analysis is valuable both in the context of investigation of natural systems and for design of trajectories of modern space missions.

Palavras-chave: Escape Basin; Fractal Basin Boundaries ; Chaotic Scattering ; Restricted Three-Body Problem; Copenhagen Case