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In this work, the Restricted Four-Body Problem is formulated in Hamiltonian form. The canonical form for the system is obtained which represents the equations of motion. The collinear libration points are obtained, we have five collinear libration points. The non-collinear libration points are found which are three non collinear libration points, they are obtained for different angles between the sight of Sun and the plane of Earth-Moon. The periodic orbits around each of these libration points are studied using two methods. The first method depends on the reduction of order of differential equations and the second method depends on the Eigen values of the characteristic equation. Two codes of MATHEMATICA are constructed to apply these two methods on the Sun- Earth-Moon-Spacecraft. The Poincare sections are obtained using the first method, these sections are used to illustrate the intersect points of the trajectories with the plane perpendicular to the plane of motion about each of the collinear libration points. Mirror symmetry is explored about each of these points. The Lyapunov orbits, and the Lissajous orbits about each of the collinear libration points are the results obtained by the second method. The eccentricities and the periods of each orbit are obtained. This study illustrates that the motion about the libration point L2 is more stable than the motion about any other collinear libration points.

This work demonstrates the potential of Moringa oleifera seeds powder as an adsorbent for the removal of heavy metals from wastewater. The moringa oleifera seeds powder is characterized as an adsorbent for the removal of heavy metals from wastewater using FTIR, XRD, pHpzc, SEM and BET techniques. Several processing parameters such as; contact time, adsorbent dose, initial lead ion concentrations, pH, and temperature are optimized. The equilibrium data for bio-sorption are analyzed by using Langmuir, Freundlich, Temkin and Dubinin–Radushkevich isotherm models to define the best correlation for lead ions. Among the four isotherm models, both Temkin and Freundlich models best describe the experimental data for Pb(II).The adsorption of the metal ions, Pb (II) is well defined by the pseudo-second order model (R2 > 0.99). The interaction of the cationic species with the MOS powder is predominately via chemisorption rather than physisorption. The thermodynamic parameters such as ΔS, ΔH and ΔG are also determined.