Equilibrium Points and Zero Velocity Surfaces in the Restricted Four Body Problem with Solar Wind Drag

TL;DR

This paper investigates the motion of an infinitesimal mass in a restricted four-body system considering solar wind drag, deriving equations, analyzing equilibrium points, and examining stability through Poincaré sections and Lyapunov exponents.

Contribution

It introduces a comprehensive analysis of the restricted four-body problem including solar wind drag, deriving new equations and stability criteria not previously explored.

Findings

Number of collinear equilibrium points varies with radiation factor β.

Stability analysis shows regular trajectories with negative Lyapunov exponents.

Zero velocity surfaces and equilibrium points depend on radiation pressure and drag.

Abstract

We have analyzed the motion of an infinitesimal mass in the restricted four body problem with solar wind drag. It is assumed that forces which govern the motion are mutual gravitational attractions of the primaries, radiation pressure force and solar wind drag. We have derived the equations of motion and find the Jacobi integral, zero velocity surfaces and particular solutions of the system. It is found that three collinear points are real when radiation factor $0<\beta<0.1$ whereas only one real point obtained when $0.125<\beta<0.2$. Again, stability property of the system is examined with the help of Poincar\'{e} surface of section (PSS) and Lyapunov characteristic exponents (LCEs). It is found that in presence of drag forces LCE is negative for a specific initial condition, hence the corresponding trajectory is regular whereas regular islands in the PSS are expanded.