  The Lagrange point $L_1$ for the Sun-Earth system is considered due to its
special importance for the scientific community for the design of space
missions. The location of the Lagrangian points with the trajectories and
stability regions of $L_1$ are computed numerically for the initial conditions
very close to the point. The influence of belt, effect of radiation pressure
due to Sun and oblateness effect of second primary(finite body Earth) is
presented for various values of parameters. The collinear point $L_1$ is
asymptotically stable within a specific interval of time $t$ correspond to the
values of parameters and initial conditions.
