How does the oblateness coefficient influence the nature of orbits in the restricted three-body problem?

Abstract

We numerically investigate the case of the planar circular restricted three-body problem where the more massive primary is an oblate spheroid. A thorough numerical analysis takes place in the configuration (x, y) and the (x, E) space in which we classify initial conditions of orbits into three categories: (i) bounded, (ii) escaping and (iii) collisional. Our results reveal that the oblateness coefficient has a huge impact on the character of orbits. Interpreting the collisional motion as leaking in the phase space we related our results to both chaotic scattering and the theory of leaking Hamiltonian systems. We successfully located the escape as well as the collisional basins and we managed to correlate them with the corresponding escape and collision times. We hope our contribution to be useful for a further understanding of the escape and collision properties of motion in this interesting version of the restricted three-body problem.

On the classification of orbits in the three-dimensional Copenhagen problem with oblate primaries

“…Strikingly enough similar behavior, regarding the influence of the oblateness coefficient on the character of the orbits, has also been reported in [69] and [71]. Therefore we may conclude that the oblateness of the primaries affects, in a very similar way, the nature of the orbits in both 2dof and 3-dof versions of the circular restricted three-body problem.…”

“…Our study complements previous works, where bounded, escape and collision motion was studied in a series of papers for the 2-dof RTBP (e.g. [69][70][71]).…”

“…Moreover, a collision occurs if the test particle crosses the sphere with radius R col around the primaries, where R col = 10 −4 . For both the parameters R d and R col we adopted the values also used in [38,39,69,71].…”

Fractal basins of convergence of libration points in the planar Copenhagen problem with a repulsive quasi-homogeneous Manev-type potential

“…In addition, the two exotic bugs with many legs and antennas still exist, corresponding to libration points L 1,7 and for other libration points the butterfly wings shaped region occur. It is observed that the geometry of the basins of convergence in the present case highly resembles to that of the classical case (see [22]).…”

Investigating the planar circular restricted three-body problem with strong gravitational field

“…Throughand it will never come back [6]. Our previous numerical experience (e.g., [53,54,55]) strongly suggests that the total orbital energy of the test-particle in the inertial frame becomes positive much sooner than it takes for the massless particle to cross the disk with radius R d = 10. Thus we may claim that our escape criterion used in the previous series of papers, and also in the present one, is both correct and safe.…”