A generalized framework for the collinear restricted four-body problem with a central dominant mass

Area of Science:

• Celestial Mechanics
• Astrophysics
• N-body problem

Background:

• The classical circular restricted three-body problem (CR3BP) is a foundational model in celestial mechanics.
• Real planetary systems often involve more than three bodies, necessitating more complex models.

Purpose of the Study:

• To extend the CR3BP by incorporating a dominant central primary, creating a collinear restricted four-body problem (CR4BP).
• To investigate the existence, location, and stability of libration points in this CR4BP.
• To demonstrate the model's applicability using the Saturn-Janus-Epimetheus system.

Main Methods:

• Development of a dynamically consistent CR4BP model with specific mass parameter constraints.
• Analysis of libration point emergence through saddle-node bifurcation.
• Linear stability analysis of both collinear and non-collinear libration points.

Main Results:

• Identified six libration points: four collinear and two symmetric non-collinear.
• Determined conditions for the emergence and movement of non-collinear points.
• Established stability intervals for the L2 collinear point and the non-collinear points.
• Demonstrated linear instability for L1, L3, and L4 collinear points.

Conclusions:

• The CR4BP model provides a more realistic representation of planetary system dynamics.
• Specific mass ratios govern the number and stability of libration points.
• The model's application to the Saturn-Janus-Epimetheus system validates its practical relevance for space mission design and orbital dynamics research.