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<p>This study explores the dynamics of an infinitesimal mass in a modified Sitnikov five-body problem, where four identical primary bodies form a square with unit side length and revolve in circular orbit around their common center of mass. Each primary emits radiation, introducing both radiation pressure and Poynting-Robertson (P-R) drag forces, which influence the motion of the infinitesimal mass. The equations of motion are derived by incorporating these radiative effects. We analyze the stability of the resulting equilibrium point through Lyapunov exponents and eigenvalue analysis and investigate its bifurcation behavior. Furthermore, we compare numerical solutions of the governing nonlinear ordinary differential equations with neural network approximations for two radiation factor values, <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(q=0.99\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>q</mi> <mo>=</mo> <mn>0.99</mn> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(q=0.7\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>q</mi> <mo>=</mo> <mn>0.7</mn> </mrow> </math></EquationSource> </InlineEquation>. Time series plots across various <i>q</i> values offer insights into the system’s dynamical responses. Finally, the orbital structure near the equilibrium point and potential chaotic behavior are examined using the first return map technique. The findings highlight the intricate influence of radiation forces and P-R drag on the stability and evolution of celestial systems.</p>

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Dynamics of the radiating Sitnikov five-body problem with Poynting-Robertson drag

  • 期刊论文

  • 发表日期：

    2026年1月29日

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  • M. Shahbaz Ullah,
  • M. Javed Idrisi

摘要

This study explores the dynamics of an infinitesimal mass in a modified Sitnikov five-body problem, where four identical primary bodies form a square with unit side length and revolve in circular orbit around their common center of mass. Each primary emits radiation, introducing both radiation pressure and Poynting-Robertson (P-R) drag forces, which influence the motion of the infinitesimal mass. The equations of motion are derived by incorporating these radiative effects. We analyze the stability of the resulting equilibrium point through Lyapunov exponents and eigenvalue analysis and investigate its bifurcation behavior. Furthermore, we compare numerical solutions of the governing nonlinear ordinary differential equations with neural network approximations for two radiation factor values, \(q=0.99\) q = 0.99 and \(q=0.7\) q = 0.7 . Time series plots across various q values offer insights into the system’s dynamical responses. Finally, the orbital structure near the equilibrium point and potential chaotic behavior are examined using the first return map technique. The findings highlight the intricate influence of radiation forces and P-R drag on the stability and evolution of celestial systems.