F. A. Abd El-Salam

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.

Invariant relative orbits for satellite constellations: A second order theory

Working with the mean orbit elements, the secular drift of the longitude of the ascending node and the sum of the argument of perigee and mean anomaly are set equal between two neighboring orbits. By having both orbits drift at equal angular rates on the average, they will not separate over time due to the influence of the perturbative effects of the asphericity of the Earth, as is considered in this work. The problem is stated. The expressions for the time rate of change of the longitude of the ascending node and the sum of the argument of perigee and mean anomaly in terms of the Delaunay canonical elements are obtained. The expressions for the second order conditions that guarantee that the drift rates of two neighboring orbits are equal on the average are derived.

Optimization out-of-orbit plane changes using aeroassisted maneuvers

The problem of optimizing the fuel consumption needed for orbital maneuvers is investigated. The normal to the orbit components of the atmospheric drag and lift forces are obtained. The temporal variations in the inclination using Lagrange planetary equation are derived, then are integrated over one revolution. A numerical example is given. The velocity variations required to perform the propulsive maneuvers due to engines on board the satellite are calculated. The performance gain using aerodynamic forces combined with propulsive ones is achieved. The comparison between the totally propulsive maneuvers and partly propulsive with atmospheric maneuvers are illustrated and discussed.

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

An efficient algorithm for orbital evolution of artificial satellite

L_{3}

Some New Locally Optimal Control Laws for Sailcraft Dynamics in Heliocentric Orbits

is computed. A series form of

Analytical treatment of the relativistic and solar radiation pressure effects on an artificial satellite

L_{3}

Extension of the Lie Transform Theory Depending on a Small Parameter for Multi-Parametric dynamical systems

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