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Abstract <p>This study explores the existence and stability of equilibrium points in the restricted three-body problem, where the more massive primary is treated as a radiating body, and the less massive primary is modeled as a heterogeneous spheroid with four distinct layers. The analysis identifies five equilibrium points, three collinear and two non-collinear. While the collinear equilibrium points are linearly unstable, the non-collinear points exhibit linear stability under specific conditions, specifically when the mass parameter (μ) falls within the interval 0 &lt; μ ≤ μ<sub>c</sub>, where μ<sub>c</sub> represents a critical threshold beyond which instability arises. Applying these findings to the Sun–Earth system, where Earth is represented as a four-layered heterogeneous body consisting of the crust, mantle, outer core, and inner core, we find that the density parameter is nearly negligible (λ ≈ 0.938911&#xa0;× 10<sup>−24</sup>), meaning that it has no significant impact on the existence and stability of equilibrium points. Instead, their behavior is entirely dictated by the radiation factor (α). The collinear equilibrium points remain unstable across the entire range of α, while non-collinear equilibrium points maintain linear stability only within a narrow interval of α ∈ [0, 0.00780552], emphasizing the limited range in which stability is preserved. These results enhance our understanding of the dynamical behavior of equilibrium points in planetary systems where the smaller primary possesses a layered structure and the bigger one is a source of radiation.</p>

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Equilibrium Structures and Stability in Radiating Oblate Binary Systems with Heterogeneity

  • 期刊论文

  • 发表日期：

    2025年11月1日

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  • M. Javed Idrisi,
  • Keshav,
  • Advin Masih

摘要

Abstract

This study explores the existence and stability of equilibrium points in the restricted three-body problem, where the more massive primary is treated as a radiating body, and the less massive primary is modeled as a heterogeneous spheroid with four distinct layers. The analysis identifies five equilibrium points, three collinear and two non-collinear. While the collinear equilibrium points are linearly unstable, the non-collinear points exhibit linear stability under specific conditions, specifically when the mass parameter (μ) falls within the interval 0 < μ ≤ μc, where μc represents a critical threshold beyond which instability arises. Applying these findings to the Sun–Earth system, where Earth is represented as a four-layered heterogeneous body consisting of the crust, mantle, outer core, and inner core, we find that the density parameter is nearly negligible (λ ≈ 0.938911 × 10−24), meaning that it has no significant impact on the existence and stability of equilibrium points. Instead, their behavior is entirely dictated by the radiation factor (α). The collinear equilibrium points remain unstable across the entire range of α, while non-collinear equilibrium points maintain linear stability only within a narrow interval of α ∈ [0, 0.00780552], emphasizing the limited range in which stability is preserved. These results enhance our understanding of the dynamical behavior of equilibrium points in planetary systems where the smaller primary possesses a layered structure and the bigger one is a source of radiation.