On Higher Order Resonant Periodic Orbits in the Photo–Gravitational Planar Restricted Three–Body Problem with Oblateness

Pathak, Niraj; Abouelmagd, Elbaz I.; Thomas, V. O.

doi:10.1007/s40295-019-00178-z

Cited by 47 publications

(12 citation statements)

References 32 publications

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“…There are many authors devoted their research to investigate the aforementioned properties within frame work of the "perturbed restricted three-body problem" [3,5,6,10,11,15,17,33]. Furthermore, the analysis of lower or higher order of resonant periodic orbits with in frame of the photogravitational "restricted three-body problem" are studied by [28,29].…”

Section: Introductionmentioning

confidence: 99%

Periodic orbit in the frame work of restricted three bodies under the asteroids belt effect

Abozaid

Selim

Gadallah

et al. 2020

Applied Mathematics and Nonlinear Sciences

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In this paper, we present a comprehensive analytical study on the perturbed restricted three bodies problem. We formulate the equations of motion of this problem, in the event of the asteroids belt perturbation. We find the locations of equilibrium points (collinear and triangular points) and analysis their linear stability. Furthermore the periodic orbits around both collinear and triangular points are found.

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Section: Introductionmentioning

confidence: 99%

Periodic orbit in the frame work of restricted three bodies under the asteroids belt effect

Abozaid

Selim

Gadallah

et al. 2020

Applied Mathematics and Nonlinear Sciences

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“…He stated that "what makes these solutions so precious to us, is that they are, so to say, the only opening through which we can try to enter a place." There is too much literature in this area, mainly involving three aspects-qualitative analysis, approximate quantitative solution, and computer-aided numerical simulation (see References [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32], and the references therein).…”

Section: Introductionmentioning

confidence: 99%

Approximate Analytical Periodic Solutions to the Restricted Three-Body Problem with Perturbation, Oblateness, Radiation and Varying Mass

Gao

Wang

2020

Universe

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Against the background of a restricted three-body problem consisting of a supergiant eclipsing binary system, the two primaries are composed of a pair of bright oblate stars whose mass changes with time. The zero-velocity surface and curve of the problem are numerically studied to describe the third body’s motion area, and the corresponding five libration points are obtained. Moreover, the effect of small perturbations, Coriolis and centrifugal forces, radiative pressure, and the oblateness and mass parameters of the two primaries on the third body’s dynamic behavior is discussed through the bifurcation diagram. Furthermore, the second- and third-order approximate analytical periodic solutions around the collinear solution point L3 in two-dimensional plane and three-dimensional spaces are presented by using the Lindstedt-Poincaré perturbation method.

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“…Indeed, there are many cases in the solar system and the binary stars system or in outer space in which the lacks of sphericity or the arbitrary mass material distribution and unequal density layers have serious and considerable effects on the dynamical motion of bodies. The motion of bodies under the mutual gravitation of irregular bodies or the lack of nonspherical bodies, suffer from extra disturbing forces, see Abouelmagd et al (2015b); Pathak et al (2019a); Pathak et al (2019b).…”

Section: Introductionmentioning

confidence: 99%

Gravitational potential formulae between two bodies with finite dimensions

Ansari¹,

Abouelmagd

2020

Astron Nachr

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The aim of this paper is to analyze and shed light on the potential relations between two bodies of finite dimensions and different shapes. After explaining the properties of different shaped bodies, we analyze the gravitational potential between an irregular body and a point mass, followed by the potential relation between two irregular bodies with discussion of its different properties. We also explore the potential relation between two solid cylinders, which can be degraded to 16 potential relations; one of these relations is the potential relation between two finite straight segments. With a new development for the potential relation, we evaluate the gravitational potential between a heterogeneous irregular body and a point mass followed by the potential between two heterogeneous irregular bodies with N−layers, which also can be reduced to the potential between two oblate or prolate heterogeneous bodies. We demonstrate that this relation can be degraded to many potential relations between two bodies, because it depends on the moments of inertia of the body's shape. Finally, we emphasize that this relation is considered a golden relation, which can be developed to generate the potential relation between different shaped bodies, either natural celestial bodies or between celestial and artificial bodies.

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On Higher Order Resonant Periodic Orbits in the Photo–Gravitational Planar Restricted Three–Body Problem with Oblateness

Cited by 47 publications

References 32 publications

Periodic orbit in the frame work of restricted three bodies under the asteroids belt effect

Periodic orbit in the frame work of restricted three bodies under the asteroids belt effect

Approximate Analytical Periodic Solutions to the Restricted Three-Body Problem with Perturbation, Oblateness, Radiation and Varying Mass

Gravitational potential formulae between two bodies with finite dimensions

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