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This paper describes design of the trajectory and analysis of the stabilityof collinear point $L_2$ in the Sun-Earth system. The modified restricted threebody problem with additional gravitational potential from the belt is used asthe model for the Sun-Earth system. The effect of radiation pressure of the Sunand oblate shape of the Earth are considered. The point $L_2$ is asymptoticallystable upto a specific value of time $t$ correspond to each set of values ofparameters and initial conditions. The results obtained from this study wouldbe applicable to locate a satellite, a telescope or a space station around thepoint $L_2$.

Trajectory and stability of Lagrangian point $L_2$ in the Sun-Earth system