Computation of the Different Errors in the Ballistic Missiles Range

El-Salam, F. A. Abd; El-Bar, S. E. Abd

doi:10.5402/2011/349737

Cited by 3 publications

(2 citation statements)

References 6 publications

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“…So we need an additional information to fix the position of an ellipse. In articles [1,2], the authors assumed that ellipse passes through the center of Earth but in reality the trajectory plane either contains the normal at the launch or target. If ellipse plane contains the normal at launch or target, there is no compulsion to contain the center of Earth.…”

Section: Numerical Simulationsmentioning

confidence: 99%

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An Efficient Computation of Effective Ground Range Using an Oblate Earth Model

Maturi

Ullah

Ahmad

et al. 2014

Abstract and Applied Analysis

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An effcient method is presented to calculate the ground range of a ballistic missile trajectory on a nonrotating Earth. The spherical Earth model does not provide good approximation of distance between two locations on the surface of Earth. We used oblate spheroid Earth model because it provides better approximations. The effective ground range of a ballistic missile is an arc-length of a planner elliptic (or circle) curve which passes through the launch and target points on the surface of Earth model. A general formulation is presented to calculate the arc-length of an elliptic (or circle) curve which is the intersection of oblate Earth model and a plane. Explicit formulas are developed to calculate the coordinates of center of the ellipse as well as major and minor axes which are necessary ingredients for the calculation of effective ground range.

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Section: Numerical Simulationsmentioning

confidence: 99%

“…Many researchers have investigated numerical methods related to ballistic missiles and satellite launch vehicles. In [1], the authors discussed computation of the different errors in the ballistic missiles range. Estimation and prediction of ballistic missiles are discussed in [2].…”

Section: Introductionmentioning

confidence: 99%

An Efficient Computation of Effective Ground Range Using an Oblate Earth Model

Maturi

Ullah

Ahmad

et al. 2014

Abstract and Applied Analysis

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Air Drag Effects on the Missile Trajectories

El-Salam

2011

Journal of Applied Mathematics

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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 , 2π − 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 missile-free range due to the drag perturbations in the missile trajectory are obtained.

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

El-Bar

El-Salam

2012

Journal of Applied Mathematics

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The orbital dynamics of an artificial satellite in the Earth's atmosphere is considered. An analytic first-order 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 second-order 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 Runge-Kutta of fourth order. The validity of the theory is checked on the already decayed Indian satellite ROHINI where its data are available. 2Journal of Applied Mathematics unforeseen complexity 3-8 . In order to be able to solve the equations of motion including the drag force analytically, one is forced to do many approximations. On the other hand, from the computational point of view, having an analytical solution at hand, we can jump from the initial conditions to the new state, which makes the computation extremely fast.The order of magnitude of the atmospheric drag acting on a satellite depends on the altitude of the satellite. The orbital behavior of an LEO satellite could be strongly influenced by atmospheric drag 4, 9, 10 , and therefore affects the quality of the remote sensing of the satellite 11, 12 . Traditionally, the problem of orbit disturbance by atmospheric drag is solved by numerical integration 13-18 . An analytical solution gives the theoretical integrals and shows the physical effects with very clear spectral properties 19-24 . This may give a direct insight into the physical phenomenon of the disturbance 25-27 . Bezdeka and Vokrouhlicky 28 developed a semianalytic theory of motion for close-Earth spherical satellites including drag and gravitational perturbations. Xu et al. 29 derived an analytical solution of a satellite orbit disturbed by atmospheric drag. They first transformed the disturbance force vector and rotated it to the orbital frame so that it can be used in the simplified Gaussian equations of satellite motion. The disturbances are separated into three parts: shortperiodic terms with triangular functions of the mean anomaly M, longperiodic terms with triangular functions of the argument of perigee and inclination ω, I , and secular terms nonperiodic functions of semimajor axis and eccentricity a, e .The main effects of the force are to bring out large secular decreases in the elements a, the semimajor axis, and e, the eccentricity, that cause the satellite plunges toward Earth. This perturbing influence is one of the most important perturbing forces in the altitude regime from 150 to 600 km which is called the drag force. The drag force, F D , per unit mass of the satellite can be represented by Submit your manuscripts at

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Computation of the Different Errors in the Ballistic Missiles Range

Cited by 3 publications

References 6 publications

An Efficient Computation of Effective Ground Range Using an Oblate Earth Model

An Efficient Computation of Effective Ground Range Using an Oblate Earth Model

Air Drag Effects on the Missile Trajectories

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

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