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<p>Investigating the dynamics near planetary satellites is crucial for space mission design. This work investigates the dynamics around the equilibrium points in the Jupiter-Europa system in the restricted three-body problem framework. The current dynamical model incorporates perturbations due to the oblateness of both Jupiter and Europa, as well as the equatorial ellipticity of Europa. We constructed the equations of motion under the effects of the perturbations considered. Then, we applied the Lie-integration method to solve the equations of motion and derive an analytical approximate solution. Also, we used the <Emphasis FontCategory="NonProportional">C++</Emphasis> software package CVODE to validate our results. The results confirmed close agreement between the Lie series and the numerical approaches. Using the Lie-series method, we applied different initial conditions to generate horseshoe and tadpole orbits around the equilateral points in both the classical circular restricted three-body problem and the perturbed model. In addition, we investigated the linear stability of the Jupiter–Europa system and found that it remains stable up to a critical mass ratio of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mu _c=0.0249882790\)</EquationSource> </InlineEquation>. Furthermore, we used the zero-velocity surfaces to analyze the accessibility condition in the Jupiter-Europa system. We found that the spacecraft transit between the primaries remains possible until the Jacobi constant exceeds the value 3.00382022.</p>

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Dynamics near equilibria in the Jupiter-Europa system using the Lie-series technique

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月14日

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  • Dina Tarek,
  • Magdy A. Sirwah,
  • M. Radwan,
  • H. R. Dwidar

摘要

Investigating the dynamics near planetary satellites is crucial for space mission design. This work investigates the dynamics around the equilibrium points in the Jupiter-Europa system in the restricted three-body problem framework. The current dynamical model incorporates perturbations due to the oblateness of both Jupiter and Europa, as well as the equatorial ellipticity of Europa. We constructed the equations of motion under the effects of the perturbations considered. Then, we applied the Lie-integration method to solve the equations of motion and derive an analytical approximate solution. Also, we used the C++ software package CVODE to validate our results. The results confirmed close agreement between the Lie series and the numerical approaches. Using the Lie-series method, we applied different initial conditions to generate horseshoe and tadpole orbits around the equilateral points in both the classical circular restricted three-body problem and the perturbed model. In addition, we investigated the linear stability of the Jupiter–Europa system and found that it remains stable up to a critical mass ratio of \(\mu _c=0.0249882790\) . Furthermore, we used the zero-velocity surfaces to analyze the accessibility condition in the Jupiter-Europa system. We found that the spacecraft transit between the primaries remains possible until the Jacobi constant exceeds the value 3.00382022.