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