A study of libration points in CR3BP under albedo effect

Idrisi, M. Javed

doi:10.14419/ijaa.v5i1.6852

“…As we know that almost complete source of natural radiation in the solar system is Sun. By the study of article [5]; a celestial body or surface having zero albedos implies that the body is 'blackbody' and that suck all the occurred radiations, whereas the unit albedo of a celestial body depicts a 'white-body' which is a surpassing reflector that reflects all the occurred radiations absolutely and homogeneously in all the directions. For example, the albedo of the snow is 0.95 which reflects about 95% of the total incoming radiation, whereas the reflection of the incoming radiation of the water is approximately 10%, so in the resulting sense, the albedo of the water is 0.1.…”

Section: Introductionmentioning

confidence: 99%

“…It is confirmed here by relation, Q Ai strictly increases ⇐⇒ σ i strictly decreases ∀, i = 0, 1, 2, ......6. By research article [5], where L 0 is the luminosity of the center of mass primary m 0 , L i is the luminosity of the primary of mass m i = m, i = 1, 2, ....6, G is the universal gravitational constant, c is the speed of light and k is mass per unit area and σ i = σ for all, i = 1, 2, .......6; the luminosity L i = L,∀, i = 1, 2, .......6. Whenever σ i ≡ 0, ∀, i = 1, 2, .....6; σ 0 is radiation factor and σ i , i = 1, 2, ....6 is the albedo factor of the peripheral primaries.…”

Section: Introductionmentioning

confidence: 99%

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

Kumar

¹

,

Kushvah

²

2022

Preprint

0

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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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“…The classical Newtonian model in the framework of three or more body problem in different aspects is studied by many researchers in the last decades. For instance, the effect of albedos on the infinitesimal mass in restricted three-body problem is studied by Idrisi [4,5] and Idrisi and Ullah [6][7][8][9]. Jain and Aggarwal [10], Idrisi and Jain [11], and Idrisi and Ullah [12] have investigated the circular restricted three-body problem under the consideration Stokes drag.…”

Section: Introductionmentioning

confidence: 99%

Triangular Equilibria in R3BP under the Consideration of Yukawa Correction to Newtonian Potential

Idrisi

¹

,

Eshetie

²

,

Tilahun

³

et al. 2022

Journal of Applied Mathematics

5

0

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We study the triangular equilibrium points in the framework of Yukawa correction to Newtonian potential in the circular restricted three-body problem. The effects of α and λ on the mean-motion of the primaries and on the existence and stability of triangular equilibrium points are analyzed, where α ∈ − 1 , 1 is the coupling constant of Yukawa force to gravitational force, and λ ∈ 0 , ∞ is the range of Yukawa force. It is observed that as λ ⟶ ∞ , the mean-motion of the primaries n ⟶ 1 + α 1 / 2 and as λ ⟶ 0 , n ⟶ 1 . Further, it is observed that the mean-motion is unity, i.e., n = 1 for α = 0 , n > 1 if α > 0 and n < 1 when α < 0 . The triangular equilibria are not affected by α and λ and remain the same as in the classical case of restricted three-body problem. But, α and λ affect the stability of these triangular equilibria in linear sense. It is found that the triangular equilibria are stable for a critical mass parameter μ c = μ 0 + f α , λ , where μ 0 = 0.0385209 ⋯ is the value of critical mass parameter in the classical case of restricted three-body problem. It is also observed that μ c = μ 0 either for α = 0 or λ = 0.618034 , and the critical mass parameter μ c possesses maximum ( μ c max ) and minimum ( μ c min ) values in the intervals − 1 < α < 0 and 0 < α < 1 , respectively, for λ = 1 / 3 .

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“…As we know that almost complete origin of the natural radiation in the solar system is Sun. The study of article [10]; a celestial body or surface having zero albedos implies that the body is a 'black-body' and that sucks all the occurred radiations, whereas the unit albedo of a celestial body depicts a 'hoary-body' which is a surpassing reflector that reflects all the occurred radiations absolutely and homogeneously in all the directions. For example, the albedo of the snow is 0.95 which reflects about 95% of the total incoming radiation, whereas the reflection of the incoming radiation of the water is approximately 10%, so in the resulting sense, the albedo of the water is 0.1.…”

Section: Introductionmentioning

confidence: 99%

Analysis of albedo as well as disc effects at the Jacobi constant and their stability of equilibrium points in the generalized restricted four-body problem

Kumar

¹

,

Kushvah

²

2022

Preprint

0

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The valuable facets of the dynamics are its stability and the components that disturb stability behavior. Our purpose in this research work is to examine the fundamental analysis of equilibrium points and their linear stability under the solar radiation pressure, albedo force effects, and radiatingoblateness in the generalized restricted four-body problem. The significant elements of this problem are mass parameter µ and other disturbing parameters to the unique influential potential function and its required derivatives to the primaries. An important relation in albedo parameters and their possible range is derived. The analysis of the albedo and disc effect is observed on the Jacobi’s constant and the positions of the existing equilibrium points and their stability regions are discussed. The inhibited zone of motion by the infinitesimal body is shown for different planetary systems. The particular as well as the joint effect of solar radiation pressure at first, albedo at second, and radiating-oblateness at both primaries of the mass, a disc is observed. The scatter diagram of locations of the mass as well as equilibrium points plotted for planetary systems. The behavior of monotonicity of the existing equilibrium points is analyzed for the presence as well as the absence of perturbations of taken planetary systems. Due to such prevalence, the considered perturbing forces give a significant perturbation in the RFBP. This current study can be extended later to the design of orbits for the different planetary systems.

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A study of libration points in CR3BP under albedo effect

Cited by 13 publications

References 17 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

Triangular Equilibria in R3BP under the Consideration of Yukawa Correction to Newtonian Potential

Analysis of albedo as well as disc effects at the Jacobi constant and their stability of equilibrium points in the generalized restricted four-body problem

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