S. E. Abd El-Bar

On the triangular equilibrium points in the photogravitational relativistic restricted three body problem

The photogravitational restricted three body within the framework of the post-Newtonian approximation is carried out. The mass of the primaries are assumed changed under the effect of continuous radiation process. The locations of the triangular points are computed. Series forms of these locations are obtained as new analytical results. In order to introduce a semi-analytical view, a Mathematica program is constructed so as to draw the locations of triangular points versus the whole range of the mass ratio μ taking into account the photogravitational effects and/or the relativistic corrections. All the obtained figures are analyzed. The size of relativistic effects of about.08 normalized distance unit is observed.

Analytical and Semianalytical Treatment of the Collinear Points in the Photogravitational Relativistic RTBP

The problem of restricted three bodies is considered. The treatment is carried out within the framework of the post-Newtonian approximation. The primaries also are assumed to be radiant sources. The locations of the collinear points are computed. Series forms of these locations are obtained as new results. A Mathematica program is constructed so as to draw the locations of collinear points versus the whole range of the mass ratio taking into account the photo-gravitational effects and/or the relativistic corrections. Analyses of these figures are addressed.

Computation of the Different Errors in the Ballistic Missiles Range

The ranges of the ballistic missile trajectories are very sensitive to any kind of errors. Most of the missile trajectory is a part of an elliptical orbit. In this work, the missile problem is stated. The variations in the orbital elements are derived using Lagrange planetary equations. Explicit expressions for the errors in the missile range due to the in-orbit plane changes are derived. Explicit expressions for the errors in the missile range due to the out-of-orbit plane changes are derived when the burnout point is assumed on the equator.

On the collinear point L3 in the generalized relativistic R3BP

Abstract.The photogravitational oblate restricted three-body problem is carried out within the post-Newtonian framework. The primaries are assumed to be oblate as well as radiant sources. The perturbed location of the collinear point

Modelling of charged satellite motion in Earth’s gravitational and magnetic fields

L_{3}

Analytical and Semi-Analytical Treatment of the Satellite Motion in a Resisting Medium

is computed. A series form of

On the Stability of the Triangular Lagrangian Equilibrium Points in the Relativistic Restricted Three-Body Problem

L_{3}

Perturbed Location of L1 point in the photogravitational relativistic restricted three-body problem (R3BP) with oblate primaries

location is obtained as a new analytical results. In order to introduce a semi-analytical view, a Mathematica program is constructed so as to draw the locations of collinear point

Computation of the Locations of the Libration Points in the Relativistic Restricted Three-Body Problem

L_{3}

Fully analytical solution of the electromagnetic perturbations on the motion of the charged satellites in earth’s magnetic field

versus the mass ratio