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Dynamics near equilibria in the Jupiter-Europa system using the Lie-series technique
Dina Tarek1, Magdy A Sirwah2, M Radwan3
1Mathematics Dept., Faculty of Science, Tanta University, Tanta, Egypt. dina.tarek@science.tanta.edu.eg.
Scientific Reports
|July 14, 2026
Summary
Investigating Jupiter-Europa dynamics is key for space missions. Perturbations from Jupiter and Europa
Area of Science:
- Celestial mechanics
- Astrodyamics
Background:
- Investigating dynamics near planetary satellites is crucial for space mission design.
- The Jupiter-Europa system presents a complex three-body problem scenario.
Purpose of the Study:
- To investigate the dynamics around equilibrium points in the Jupiter-Europa system.
- To incorporate perturbations from the oblateness of Jupiter and Europa, and Europa's equatorial ellipticity.
- To analyze the stability and accessibility conditions for spacecraft missions.
Main Methods:
- Constructed equations of motion under considered perturbations.
- Applied the Lie-integration method for analytical approximate solutions.
- Utilized the CVODE software package for numerical validation.
- Generated horseshoe and tadpole orbits using the Lie-series method.
- Investigated linear stability and analyzed zero-velocity surfaces.
Main Results:
- Confirmed close agreement between Lie series and numerical approaches.
- Generated various orbital trajectories around equilateral points.
- Determined the Jupiter-Europa system remains stable up to a critical mass ratio.
- Identified accessibility conditions for spacecraft transit based on the Jacobi constant.
Conclusions:
- The Lie-integration method provides accurate analytical solutions for perturbed three-body problems.
- Orbital dynamics and stability in the Jupiter-Europa system are significantly influenced by oblateness and ellipticity.
- Spacecraft accessibility is constrained by the Jacobi constant, with transit possible below a specific threshold.
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