Publications (33)15.71 Total impact
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ABSTRACT: The problem of the critical inclination is treated in the Hamiltonian framework taking into consideration postNewtonian corrections as well as the main correction term of sectorial harmonics for an earthlike planet. The Hamiltonian is expressed in terms of Delaunay canonical variables. A canonical transformation is applied to eliminate short period terms. A modified critical inclination is obtained due to relativistic and the first sectorial harmonics corrections.Astrophysics and Space Science 05/2014; 351(1). · 2.06 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: The photogravitational restricted three bodies within the framework of the postNewtonian approximation is carried out. The mass of the primaries are assumed changed under the effect of continuous radiation process and oblateness effects of the two primaries. New perturbed locations of the triangular points are computed. In order to introduce a semianalytical 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, the relativistic corrections and/or oblateness effects. All the obtained figures are analyzed.Astrophysics and Space Science 05/2014; 351(1). · 2.06 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: In the present work, the two body problem using a potential of a continued fractions procedure is reformulated. The equations of motion for two bodies moving under their mutual gravity is constructed. The integrals of motion, angular momentum integral, center of mass integral, total mechanical energy integral are obtained. New orbit equation is obtained. Some special cases are followed directly. Some graphical illustrations are shown. The only included constant of the continued fraction procedure is adjusted so as to represent the so called J 2 perturbation term of the Earth’s potential.Astrophysics and Space Science 04/2014; 350(2). · 2.06 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: The photogravitational restricted three body within the framework of the postNewtonian 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 semianalytical 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.Astrophysics and Space Science 01/2014; 349(1). · 2.06 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: The problem of restricted three bodies is considered. The treatment is carried out within the framework of the postNewtonian 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 photogravitational effects and/or the relativistic corrections. Analyses of these figures are addressed.Mathematical Problems in Engineering 09/2013; 2013. · 1.38 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: In this work the left and right RiemannLiouville derivatives are introduced. A generalized operator based on left/right RiemannLiouville derivatives is obtained. Basic definitions, lemmas and theorems in the fractional calculus which is related to our purpose are presented. The fractional form of Lagrange expansion theorem is obtained.Journal of Taibah University for Science. 01/2013;  [Show abstract] [Hide abstract]
ABSTRACT: In this paper some basic definitions of fractional vector calculus are introduced. A fractional form of Maxwell's equations using these definitions are obtained. The first pair of Maxwell's equations are generalized. The gravity is introduced into Maxwell's equations. Some fractional covariant forms are deduced. The fractional Maxwell's field strength tensor is unchanged under a gauge transformation. Fractional continuity equation and the charge conservation are proved.Journal of Taibah University for Science. 01/2013; 7(3):173–179.  [Show abstract] [Hide abstract]
ABSTRACT: Using RiemannLiouville fractional differential operator, a fractional extension of the Lagrange inversion theorem and related formulas are developed. The required basic definitions, lemmas, and theorems in the fractional calculus are presented. A fractional form of Lagrange's expansion for one implicitly defined independent variable is obtained. Then, a fractional version of Lagrange's expansion in more than one unknown function is generalized. For extending the treatment in higher dimensions, some relevant vectors and tensors definitions and notations are presented. A fractional Taylor expansion of a function of N dimensional polyadics is derived. A fractional N dimensional Lagrange inversion theorem is proved.Abstract and Applied Analysis 01/2013; 2013. · 1.10 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: 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. The relativistic corrections and the direct solar radiation pressure to the equations of motion, 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 augmented 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.Indian Journal of Science and Technology. 09/2012; 5(9):114.  [Show abstract] [Hide abstract]
ABSTRACT: The orbital dynamics of an artificial satellite in the Earth's atmosphere is considered. An analytic firstorder atmospheric drag theory is developed using Lagrange's planetary equations. The short periodic perturbations due to the geopotential of all orbital elements are evaluated. And to construct a secondorder analytical theory, the equations of motion become very complicated to be integrated analytically; thus we are forced to integrate them numerically using the method of RungeKutta of fourth order. The validity of the theory is checked on the already decayed Indian satellite ROHINI where its data are available.Journal of Applied Mathematics 01/2012; 2012. · 0.83 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Modeling the force of laser pressure on the dynamics of an artificial satellite is studied. The atmospheric effects are taken into consideration. Some important details of the model arising from the thermooptical satellite surface properties are clarified. The model has been exemplified by computing the laser perturbing acceleration for a passive Earth's satellite (e.g. the satellite Ajisai). To illustrate the role of the Earth's atmosphere in the radiative force modeling, the model has been compared with that neglecting the atmospheric effects.International Journal of Nonlinear Science. 01/2012; 14(1):107114.  [Show abstract] [Hide abstract]
ABSTRACT: 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 inorbit plane changes are derived. Explicit expressions for the errors in the missile range due to the outoforbit plane changes are derived when the burnout point is assumed on the equator.ISRN Applied Mathematics. 10/2011; 2011.  [Show abstract] [Hide abstract]
ABSTRACT: The equations of motion of a missile under the air drag effects are constructed. The modified TD88 is surveyed. Using Lagrange's planetary equations in Gauss form, the perturbations, due to the air drag in the orbital elements, are computed between the eccentric anomalies of the burn out and the reentry points $[{E}_{bo},2\pi {E}_{bo}]$ , respectively. The range equation is expressed as an infinite series in terms of the eccentricity e and the eccentric anomaly E. The different errors in the missilefree range due to the drag perturbations in the missile trajectory are obtained.Journal of Applied Mathematics 01/2011; · 0.83 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: The problem of coorbital motion will be formulated in the Hamiltonian form in case when the primary is oblate. The problem considered will be assumed spatial and not circular. Different forms of the disturbing function will be outlined; the relevant form is developed in terms of Laplace coefficients. The Hamiltonian of the problem will be formed in Dalaunylike canonical elements. The ratio of the primary mass is considered as a small parameter of the first order while the leading oblateness term of the primary is considered of second order.05/2009;  [Show abstract] [Hide abstract]
ABSTRACT: The present work is concerned with the twobody problem with varying mass in case of isotropic mass loss from both components of the binary systems. The law of mass variation used gives rise to a perturbed Keplerian problem depending on two small parameters. The problem is treated analytically in the Hamiltonian framework and the equations of motion are integrated using the Lie series developed and applied, separately by Delva (1984) and Hanslmeier (1984). A second order theory of the two bodies eject mass is constructed, returning the terms of the rate of change of mass up to second order in the small parameters of the problem.Journal of Astrophysics and Astronomy 01/2009; 30(3):187205. · 0.34 Impact Factor  04/2008;
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ABSTRACT: This paper analysis the disadvantages of the methods used for determining two artificial satellites closest approach. A new method of close approach determination is presented. This method is based on performing a successive scanning over the two orbits, for one revolution, to find an initial guess to start iterations using the method of Newton Raphson. In order to apply the method on different types of orbits, it has been examined in three cases; for two nearly circular orbits, for two orbits of high eccentricity and for two orbits; one of high eccentricity and the other is nearly circular one.NRIAG Journal of Astronomy and Geophysics. 01/2008; Special Issue.  [Show abstract] [Hide abstract]
ABSTRACT: Searching for an accurate model to evaluate the orbital position of the operating satellites and space debris is very important at the time being. This is actually to design different maneuvering schemes to avoid catastrophic consequences of collision. In the present paper a second order theory of perturbations (in the sense of the Hori–Lie perturbation method) is developed. The most dominating perturbations, namely geopotential effects, lunisolar perturbations, solar radiation pressure and atmospheric drag are included. Resonance and very long period perturbations are modeled with the use of semisecular terms for short time span predictions. A comparison of our analytical solution with a numerical integration (Burlich–Stoer) of the equations of motion for chosen artificial satellites at (LEO, MEO, GEO) is presented. The computations are carried out for different satellite with different areatomass ratios showing a good accuracy of the theory.Applied Mathematics and Computation. 01/2007;  [Show abstract] [Hide abstract]
ABSTRACT: To explore the dynamics of a test particle in the nearMercury’s environment, the orbital motion of an orbiter around Mercury is considered. Different perturbing forces, namely the Mercurian gravity field, the solar radiation pressure, the solar wind and the coronal mass ejections, are taken into account. The order of magnitude of each perturbing term is assessed. The equations of motion in canonical representation are obtained. The Hamiltonian in terms of Hansen coefficients is expressed. A procedure for solution is presented. The short and long periodic terms are removed from the Hamiltonian and the solution is obtained. Long periodic perturbations on the orbital dynamics of an orbiter around Mercury due to the solar events are found as revealed by Eq. (26) in the text. Resonance cases are discussed and the different resonant inclinations are obtained. A procedure for the computation of the position and velocity is presented.New Astronomy. 01/2007; 
Article: Periodic motions of spinning rigid spacecraft under influence of gravitational and magnetic fields
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ABSTRACT: The motion of a magnetized axisymmetric spacecraft about its center of mass in a circular orbit is considered, taking the gravitational and magnetic effects of the central body into account. Equations of motion of the reduced system are transformed to equations of plane motion of a charged particle under the action of electric and magnetic fields. Stationary motions of the system are determined and periodic motions near to them are constructed using the Lyapounoff theorem of the holomorphic integral.Applied Mathematics and Mechanics 07/2006; 27(8):10611069. · 0.65 Impact Factor
Publication Stats
12  Citations  
15.71  Total Impact Points  
Top Journals
Institutions

2011–2014

Taibah University
AlSabya, Jīzān, Saudi Arabia


2004–2014

Cairo University
 Department of Astronomy
Al Qāhirah, Al Qāhirah, Egypt


2007

National Research Institute of Astronomy and Geophysics
Al Qāhirah, Al Qāhirah, Egypt
