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Investigation of the effect of albedo and oblateness on the circular restricted four variable bodies problem

Abdullah A. Ansari

Abdullah A. Ansari

Department of Mathematics, College of Science Al-Zulfi, Majmaah UniversityAl Majma'ah, Kingdom of Saudi Arabia
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Ansari, Abdullah A.
  
12 dic 2017
Investigation of the effect of albedo and oblateness on the circular restricted four variable bodies problem's Cover Image
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Pubblicato online: 12 dic 2017
Pagine: 529 - 542
Ricevuto: 09 feb 2017
Accettato: 12 dic 2017
DOI: https://doi.org/10.21042/AMNS.2017.2.00044
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© 2017 Abdullah A. Ansari, published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Fig. 1

Configuration of the problem in CRFVBP with the effect of oblateness and Albedo.
Configuration of the problem in CRFVBP with the effect of oblateness and Albedo.

Fig. 2

The locations of lagrangian points during in-plane motion (i.e. ξ≠0, η≠0, ζ = 0) in five cases: (a). Third primary is placed at one of the lagrangian points of the classical circular restricted three-body problem (points with blue color), (b). Variation of masses (points with green color), (c). Solar radiation pressure (points with red color), (d). Albedo effect (points with black color), (e). Oblateness effect (points with magenta color).
The locations of lagrangian points during in-plane motion (i.e. ξ≠0, η≠0, ζ = 0) in five cases: (a). Third primary is placed at one of the lagrangian points of the classical circular restricted three-body problem (points with blue color), (b). Variation of masses (points with green color), (c). Solar radiation pressure (points with red color), (d). Albedo effect (points with black color), (e). Oblateness effect (points with magenta color).

Fig. 3

The locations of lagrangian points during out of plane motion (i.e. ξ ≠ 0, η = 0, ζ ≠ 0) in five cases: (a). Third primary is placed at one of the lagrangian points of the classical circular restricted three-body problem (points with blue color), (b). Variation of masses (points with green color), (c). Solar radiation pressure (points with red color), (d). Albedo effect (points with black color), (e). Oblateness effect (points with magenta color).
The locations of lagrangian points during out of plane motion (i.e. ξ ≠ 0, η = 0, ζ ≠ 0) in five cases: (a). Third primary is placed at one of the lagrangian points of the classical circular restricted three-body problem (points with blue color), (b). Variation of masses (points with green color), (c). Solar radiation pressure (points with red color), (d). Albedo effect (points with black color), (e). Oblateness effect (points with magenta color).

Fig. 4

The locations of lagrangian points during out of plane motion (i.e.ξ = 0, η ≠ 0, ζ ≠ 0) in five cases: (a). Third primary is placed at one of the lagrangian points of the classical circular restricted three-body problem (points with blue color), (b). Variation of masses (points with green color), (c). Solar radiation pressure (points with red color), (d). Albedo effect (points with black color), (e). Oblateness effect (points with magenta color).
The locations of lagrangian points during out of plane motion (i.e.ξ = 0, η ≠ 0, ζ ≠ 0) in five cases: (a). Third primary is placed at one of the lagrangian points of the classical circular restricted three-body problem (points with blue color), (b). Variation of masses (points with green color), (c). Solar radiation pressure (points with red color), (d). Albedo effect (points with black color), (e). Oblateness effect (points with magenta color).

Fig. 5

Poincaré surface of sections for five cases: (a). Third primary is placed at one of the lagrangian points of the classical circular restricted three-body problem (with blue color), (b). Variation of masses (with green color), (c). Solar radiation pressure (with red color), (d). Albedo effect (with black color), (e). Oblateness effect (with magenta color). (i) Poincaré surface of sections in ξ−ξ′-plane, (ii) Poincaré surface of sections in η−η′-plane, (iii) Zoomed part of figure (ii) near the origin.
Poincaré surface of sections for five cases: (a). Third primary is placed at one of the lagrangian points of the classical circular restricted three-body problem (with blue color), (b). Variation of masses (with green color), (c). Solar radiation pressure (with red color), (d). Albedo effect (with black color), (e). Oblateness effect (with magenta color). (i) Poincaré surface of sections in ξ−ξ′-plane, (ii) Poincaré surface of sections in η−η′-plane, (iii) Zoomed part of figure (ii) near the origin.

Fig. 6

(a): The basin of attraction for the case when third primary is placed at one of the lagrangian points of the classical circular restricted three- body problem. (b): Zoomed image of (a) near the lagrangian configuration.
(a): The basin of attraction for the case when third primary is placed at one of the lagrangian points of the classical circular restricted three- body problem. (b): Zoomed image of (a) near the lagrangian configuration.

Fig. 7

(a): The basin of attraction for the variable mass case. (b): Zoomed image of (a) near the lagrangian configuration.
(a): The basin of attraction for the variable mass case. (b): Zoomed image of (a) near the lagrangian configuration.

Fig. 8

(a): The basin of attraction for the solar radiation pressure case. (b): Zoomed image of (a) near the lagrangian configuration.
(a): The basin of attraction for the solar radiation pressure case. (b): Zoomed image of (a) near the lagrangian configuration.

Fig. 9

(a): The basin of attraction for the Albedo case. (b): Zoomed image of (a) near the lagrangian configuration.
(a): The basin of attraction for the Albedo case. (b): Zoomed image of (a) near the lagrangian configuration.

Fig. 10

(a): The basin of attraction for the oblateness case. (b): Zoomed image of (a) near the lagrangian configuration.
(a): The basin of attraction for the oblateness case. (b): Zoomed image of (a) near the lagrangian configuration.
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