Hill restricted four-body problem with variable mass

Abstract

The presentation of the paper consists the extended version of the Hill restricted three-body problem i.e. the Hill restricted four-body problem where the mass of the fourth smallest body is supposed to variable with time and also suppose that the other three massive bodies are remain fixed at the apices of an equilateral triangle. After shifting the origin and using the various transformations, we determine the equations of motion and quasi-Jacobi integral for this model. The properties like the equilibrium points and stability are performed analytically.