Elliptic Restricted Three Body Problem Under the Effect of Circumstellar Belt

The dynamics of the infinitesimal for the planar elliptic restricted three body model interacting with circumstellar belt is studied. Analytic exploration of the problem reveals the existence of more than three collinear equilibrium points and a pair of triangular equilibrium points. Stability analysis based on Grebnikov’s averaging method gave the value of critical mass ratio for the stable behaviour of triangular equilibrium point. Also the criteria for stability of collinear points are explored analytically. Applying these analytical results to the Sun–Earth system under the influence of Asteroid belt and the star Epsilon–Eridani-its planet Eridani-b and the circumstellar belt show the presence of four or more collinear and a pair of equilibrium points in the pulsating rotating plane. We found that only the triangular equilibrium point is stable for most of the cases. The zero velocity curves (ZVC) and fractal basin of convergence for the two systems are also plotted. It was found that the ZVC are affected by the mass of the belt. On other hand the basin of convergence for particular equilibrium points are found to be reduced on increasing the value of mass of belt.