On the Stability of the Triangular Equilibrium Points in the Photogravitational R3BP with an Oblate Infinitesimal and Triaxial Primaries for the Binary Lalande 21258 System

Gyegwe, Jessica Mrumun; Vincent, Aguda Ekele; Perdiou, A. E.

doi:10.1007/978-3-030-84122-5_21

Cited by 5 publications

(15 citation statements)

References 35 publications

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“…If we consider a third dimension that counts the Jacobian constant C, then we obtain the so-called zero-velocity surface (ZVS). Here, we note that the aforementioned model reduces to Gyegwe et al (2022) when M b = 0, while for M b = 0 and A 3 = 0 some of the results can be found in Singh (2013).…”

Section: Equations and Integral Of Motionmentioning

confidence: 64%

“…Then, the coordinates of the bigger and smaller primaries are (−μ, 0) and (1 − μ, 0), respectively, while the coordinates of the third body of negligible mass are (x, y, z). Following Gyegwe et al (2022) and Singh and Leke (2014), the equations of motion of the massless body under the influence of its shape, forces of radiation pressure, and triaxiality coupled with gravitational potential from a belt around the stars are:…”

Section: Equations and Integral Of Motionmentioning

confidence: 99%

“…So, the triangular equilibrium points come in pairs. Using the perturbation technique as that in Gyegwe et al (2022), Eqs 8, 9 yield:…”

Section: Equilibrium Points and Zero-velocity Surfacesmentioning

confidence: 99%

“…They also showed that the equilibria are always linearly unstable for all possible values of the parameters of the primary body. Recently, Gyegwe et al (2022) have studied the positions and stability of the triangular equilibrium points in the framework of the R3BP when the primaries are triaxialradiating rigid bodies, while the third body of infinitesimal mass is an oblate spheroid. They found that the parameters of the problem play a significant role on the regions of stability and in particular that the comprehensive effects of the perturbations have destabilizing tendencies.…”

Section: Introductionmentioning

confidence: 99%

“…In the present work, we aim to extend the work of Gyegwe et al (2022) by considering not only the radiation pressure and asphericity of the primaries but also the gravitational potential of the belt. Moreover, taking into account these perturbing forces, we investigate the existence, location, and stability of both the collinear and triangular equilibrium points of this system.…”

Section: Introductionmentioning

confidence: 99%

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Existence and Stability of Equilibrium Points in the R3BP With Triaxial-Radiating Primaries and an Oblate Massless Body Under the Effect of the Circumbinary Disc

Vincent¹,

Perdiou

Perdios

2022

Front. Astron. Space Sci.

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The aim of this article is to study the existence, location, and stability of equilibrium points in a generalized restricted three-body problem (R3BP) that consists of an oblate infinitesimal body when the primaries are radiating sources with triaxiality of the two stars surrounded by a belt (circumbinary disc). The existence, number, location, and stability of the collinear and triangular Lagrangian equilibrium points of the problem depend on the mass parameter and the perturbing forces involved in the equations of motion. We find numerically that four additional collinear equilibrium pointsLni,i= 1, 2, 3, 4, exist, in addition to the three Eulerian pointsLi,i= 1, 2, 3, of the classical case, making up a total of up to seven collinear points.Ln1andLn2result due to the potential from the belt, whileLn3andLn4arise from the effect of triaxiality. The positions of the equilibrium points are affected by the presence of perturbations, since they are deviated from the classical R3BP on thex-axis and out of thex-axis, respectively. The stability of the equilibrium points, for a particular set of the parameters, is analyzed, and it is concluded that all the collinear points are unstable exceptLn1, which is always linearly stable. The range of stability of the Lagrangian pointsL4,5is determined analytically and found that being stable for 0 <μ<μcritand unstable forμcrit≤μ≤ 1/2, whereμcritis the critical mass ratio which depends on the combined effects of the perturbing forces. It is noticed that the critical mass ratio decreases with the increase in the values of the radiation pressure, triaxiality, and oblate infinitesimal body; however, it increases with the increase in the value of mass of the disc. All three of the former and the latter one possess destabilizing and stabilizing behavior, respectively. The net effect is that the size of the region of stability that decreases when the value of these parameters increases. In our model, the binary HD155876 system is used, and it is found that there exists one stable collinear equilibrium pointviz. Ln1.

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Section: Equations and Integral Of Motionmentioning

confidence: 64%

Section: Equations and Integral Of Motionmentioning

confidence: 99%

“…So, the triangular equilibrium points come in pairs. Using the perturbation technique as that in Gyegwe et al (2022), Eqs 8, 9 yield:…”

Section: Equilibrium Points and Zero-velocity Surfacesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Existence and Stability of Equilibrium Points in the R3BP With Triaxial-Radiating Primaries and an Oblate Massless Body Under the Effect of the Circumbinary Disc

Vincent¹,

Perdiou

Perdios

2022

Front. Astron. Space Sci.

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Analysis of the dynamics of the resonant planetary system HD 45364

Mia

Paul

2022

Preprint

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The aim of this work is to analyse the orbital dynamics and stability of exoplanetary system in which two planets are in nearly 3:2 MMR. We have taken HD 45364 system for our study in which two planets are most likely in a 3:2 MMR. We have plotted two resonant angles and the relative apsidal longitudes and it is observed that they are librating around a constant value. From this observation our opinion is that there exist nearly 3:2 MMR between HD 45364b and HD 45364c. The perturbative solution is obtained for the time variation of the semi-major axes. The short and long term variations of semimajor axes are studied. For the validation of our analytical results we have compared our analytical solutions with the numerical solutions. The effect of planetary perturbations on eccentricity is studied with the help of secular resonance dynamics theory. The short and long term variations of eccentricities of HD 45364b and HD 45364c are shown graphically. Moreover, using the latest stability criteria, we have studied the dynamical stability of HD 45364 system.

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