Escape dynamics and fractal basins boundaries in the three-dimensional Earth-Moon system

Zotos, Euaggelos E.

doi:10.1007/s10509-016-2683-6

Cited by 20 publications

(13 citation statements)

References 40 publications

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“…For instance, in [62] we detected a considerable amount of trapped chaotic orbits when we investigated the orbital properties of an open tidally limited star cluster, using a three dimensional dynamical model. On the other hand, in the 3D Earth-Moon system which was explored in [69] we did not find any numerical evidence of trapped chaos. The most important changes that occur on the (x, z) plane as the value of the Jacobi constant decreases are the following:…”

Section: Results For the 3d Systemcontrasting

confidence: 65%

“…In [69] the numerical investigation has been expanded into three dimensions thus exploring the orbital structure of the three degrees of freedom Earth-Moon system. Furthermore, very recently the escape and collision dynamics in the Saturn-Titan and in the Pluto-Charon binary planetary systems have been revealed in [67] and [68], respectively, by classifying initial conditions of orbits in the configuration space.…”

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confidence: 99%

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Orbit classification in the Hill problem: I. The classical case

Zotos

2017

Nonlinear Dyn

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The case of the classical Hill problem is numerically investigated by performing a thorough and systematic classification of the initial conditions of the orbits. More precisely, the initial conditions of the orbits are classified into four categories: (i) non-escaping regular orbits; (ii) trapped chaotic orbits; (iii) escaping orbits; and (iv) collision orbits. In order to obtain a more general and complete view of the orbital structure of the dynamical system our exploration takes place in both planar (2D) and the spatial (3D) version of the Hill problem. For the 2D system we numerically integrate large sets of initial conditions in several types of planes, while for the system with three degrees of freedom, three-dimensional distributions of initial conditions of orbits are examined. For distinguishing between ordered and chaotic bounded motion the Smaller ALingment Index (SALI) method is used. We managed to locate the several bounded basins, as well as the basins of escape and collision and also to relate them with the corresponding escape and collision time of the orbits. Our numerical calculations indicate that the overall orbital dynamics of the Hamiltonian system is a complicated but highly interested problem. We hope our contribution to be useful for a further understanding of the orbital properties of the classical Hill problem.

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Section: Results For the 3d Systemcontrasting

confidence: 65%

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confidence: 99%

Orbit classification in the Hill problem: I. The classical case

Zotos

2017

Nonlinear Dyn

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“…In the present section, we use the well‐known multivariate version of the Newton–Raphson method to discuss the convergency of basins of attraction, which is a fast (converges quadratically), simple, and accurate computational tool. In this section, we shall use the computational method applied by Croustalloudi & Kalvouridis (), Douskos et al (), and Zotos (). The Newton–Raphson process starts with the given initial approximation ( x 0 , y 0 ) on the plane and stops when the libration point is found with a predetermined accuracy.…”

Section: The Newton–raphson Basins Of Attractionsmentioning

confidence: 99%

Divulging the effect of small perturbations in the Coriolis and centrifugal forces in the photogravitational version of autonomous restricted four‐body problem with oblate primary

et al. 2019

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In the present problem, we have studied the effect of small perturbations in the Coriolis and centrifugal forces on the locations and stability of libration points by taking the smaller primary as radiating oblate spheroid in the restricted four‐body problem. We have supposed that all the primaries are set in an equilateral triangle configuration, moving in circular orbit around their common center of mass. We have observed that the oblateness and radiation of the third primary, and the effect of the small perturbation in centrifugal force have substantial influences on the locations of libration points but the effect of the small perturbation in the Coriolis force has no impact on their locations. However, the stability of the libration points is highly influenced by the effect of the small perturbation in the Coriolis force. Furthermore, it is obtained that the effect of the small perturbation in the centrifugal force has a substantial influence on the regions of possible motion. In addition, we have also discussed how the oblateness and radiation pressure of the third primary, and the small perturbations in the Coriolis and centrifugal forces influence geometry of the basins of convergence by using multivariate version of the Newton–Raphson iterative scheme.

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“…We shall follow the procedure given in Zotos () to draw the Newton–Raphson basins of attraction in the R4BP with variable mass under the effect of small perturbations in the Coriolis and centrifugal forces. This method is a fast, simple, and accurate computational tool.…”

Section: The Newton–raphson Basins Of Attractionmentioning

confidence: 99%

The effect of small perturbations in the Coriolis and centrifugal forces on the existence of libration points in the restricted four‐body problem with variable mass

et al. 2018

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This paper shows the effect of small perturbations in the Coriolis and centrifugal forces in the restricted four‐body problem (R4BP) with variable mass. The existence, location, and stability of the libration points are investigated numerically and graphically under these perturbations. In the present problem, a fourth body with infinitesimal mass is moving under the Newtonian gravitational attraction of three primaries which are moving in a circular orbit around their common center of mass fixed at the origin of the coordinate system. Moreover, according to the solution of Lagrange, the primaries are fixed at the vertices of an equilateral triangle. The fourth body does not affect the motion of three primaries. Furthermore, the fourth body's mass varies according to Jeans' law. The equations of motion of the test particle, i.e., fourth body moving under the gravitational influence of the primaries, are derived. Throughout the paper, we consider the case where the primary body placed along the x‐axis is dominant while the other two small primaries are equal. Further, it is shown that there exist either 8 or 10 libration points out of which 2 or 4 are collinear with the dominating primary and the rest are non‐collinear for fixed values of the parameters. The linear stability of all the libration points under consideration is investigated, and these libration points are found to be unstable. The allowed regions of motion are determined by using the zero‐velocity surface, and the positions of the libration points on the orbital plane are presented. Moreover, by using the Newton–Raphson iterative scheme, we unveiled the effects of the Coriolis and centrifugal forces on the topology of the basins of convergence associated with the libration points.

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Escape dynamics and fractal basins boundaries in the three-dimensional Earth-Moon system

Cited by 20 publications

References 40 publications

Orbit classification in the Hill problem: I. The classical case

Orbit classification in the Hill problem: I. The classical case

Divulging the effect of small perturbations in the Coriolis and centrifugal forces in the photogravitational version of autonomous restricted four‐body problem with oblate primary

The effect of small perturbations in the Coriolis and centrifugal forces on the existence of libration points in the restricted four‐body problem with variable mass

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