Approximation of symmetric periodic solutions of the Sitnikov problem

In this study, an approximate solution of the Sitnikov problem was investigated using fourth-order Runge – Kutta method. We confirmed the periodicity and the symmetric nature of the orbits. The various values of eccentricities were obtained which showed that at eccentricity e = 0, the orbit moves in a circular shape and otherwise when e < 0. Also at every values of e, we found the numerical results which we demonstrated by simulations using MATCAD which showed that the range for the search of eccentricities can be narrowed down at different values of e, different sinusoidal frequencies were obtained.