The study of the fractal basins of convergence linked with equilibrium points in the perturbed (<i>N</i>+ 1)‐body ring problem

Suraj, Sanam; Aggarwal, Rajiv; Mittal, Amit; Meena, Om Prakash; Asique, Chand

doi:10.1002/asna.202013789

Cited by 3 publications

(1 citation statement)

References 39 publications

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“…The particle Q(x, y, z) is orbiting in the connected gravitational field of the complete primaries system. For comparison purpose, by the article [21], the mass parameter of RTBP, we define µ =…”

Section: Fundamental Equations Of the Motion Of Celestial Bodiesmentioning

confidence: 99%

A study of libration points and analysis of their stability behavior in-ring body problem under albedo effect

Kumar

Kushvah

2022

Preprint

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Our intention in this article is to analyze the fundamental analysis of the zones and their existing libration points under the solar radiation pressure and albedo effects. We can feel about albedos at any Nature’s property wherever the Sun rays exist. As we know that important phase of the dynamical system of any celestial body is its stability and the factors which change its behavior of motion. This research article presents an explicit analysis of the albedo effect for ring body problems for a specific value of v = 6, which explains the behavior of existing zone’s stability, shifting of their libration points with monotonicity and the characteristic roots of δ confirms the behavior of stability condition for existing zones as well as their existing libration points in a synodic frame of references. We observed that in this problem from an experimental point of view, a little change in v, changes the complete behavior of the problem and leaves a nice platform of the proof. In this problem, β plays a significant role, which affects firstly the whole dynamics of peripheral primaries, the mass parameters β = 0 and β ≠ 0 generally confirm that this synodic system wears, an absence of a center of mass and the presence of the center of mass, respectively. We have observed in this article is the libration point L0, which exists in the center and has peripheral primary P0, remains unchanged throughout applying the albedo effect. The stability analysis confirms the location of the libration points, whether it is stable, unstable, etc., but here we have seen the more interesting things i.e., most of the locations of the libration points except exceptionals are found unstable. This article also shows the momentum of the position of all the libration points with their existing zone as well as peripheral primaries, by the effect of the radiation pressure and albedo. It is also analyzed here that this complete problem works in a certain short and very sensitive range set (−1.75, 1.75) because this problem is filled with trigonometric periodic functions. In this problem, we have considered only the real roots of the axis x, y, whereas imaginary roots are not considered. For stability analysis, we have taken both real and complex roots of δ. Results of this article for v = 6 may help us to analyze an imaginary behavior of our solar system’s planets in a blank paper, provided by certain rules and regulations by equations of motion because real behavior may be far away from us. By the present study, it is found that the whole behavior of the system for various v whenever change, which can be extended later in another way.

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Section: Fundamental Equations Of the Motion Of Celestial Bodiesmentioning

confidence: 99%

A study of libration points and analysis of their stability behavior in-ring body problem under albedo effect

Kumar

Kushvah

2022

Preprint

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Basins of Escape of the Particle’s Planar Motion in the Rectilinear (3 $$\varvec{+}$$ 1)-Body Ring Problem

Belgharbi,

Navarro

2023

Few-Body Syst

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The objective of this work is to study the motion of an infinitesimal particle in the gravitational field of three big bodies in a ring configuration consisting of two peripheral and one central bodies, when the energy of the particle does not allow the escape from the potential well of the system. We have numerically determined the basins of escape using a new surface of section. Additionally, we have computed and analyzed the geometry of the set of asymptotic trajectories of the periodic orbit that governs the escape from the neighborhood of one of the two satellites, which also defines the limiting curves of the basins of escape from this region.

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Analysis of the geometry of the zero-velocity curves in the N-body ring problem depending on the mass ratio parameter

Boureghda,

Martínez-Belda,

Navarro

2024

Eur. Phys. J. Plus

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The purpose of the present study is the investigation of the effect of the mass ratio parameter, $$\beta$$ β , on the geometry of the zero-velocity curves, when there are $$N=3,4,\ldots ,100$$ N = 3 , 4 , … , 100 peripheral bodies. It is well known that there is a bifurcation value of the $$\beta$$ β parameter in the N-body ring problem that produces a change in the number of stationary solutions in the system from 5N to 3N. By examining the behavior of the critical values of the Jacobi constant that define each of the zones of stationary solutions, we have unveiled the existence of other bifurcations or critical values of $$\beta$$ β in the scenario with 5N stationary solutions, which cause different changes in the geometry of the zero-velocity curves, which in turn affect the threshold for the total opening of the curves of zero velocity.

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The study of the fractal basins of convergence linked with equilibrium points in the perturbed (N+ 1)‐body ring problem

Cited by 3 publications

References 39 publications

A study of libration points and analysis of their stability behavior in-ring body problem under albedo effect

A study of libration points and analysis of their stability behavior in-ring body problem under albedo effect

Basins of Escape of the Particle’s Planar Motion in the Rectilinear (3 $$\varvec{+}$$ 1)-Body Ring Problem

Analysis of the geometry of the zero-velocity curves in the N-body ring problem depending on the mass ratio parameter

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