Table of Contents
ISRN Applied Mathematics
Volume 2011, Article ID 349737, 16 pages
http://dx.doi.org/10.5402/2011/349737
Research Article

Computation of the Different Errors in the Ballistic Missiles Range

1Department of Math, Faculty of Science, Taibah University, Al-Madinah Al-Munawarah, Saudi Arabia
2Department of Astronomy, Faculty of Science, Cairo University, Cairo 12613, Egypt
3Department of Applied Mathematics, Faculty of Applied Science, Taibah University, Al-Madinah Al-Munawarah, Saudi Arabia
4Department of Mathematics, Faculty of Science, Tanta university, Tanta, Egypt

Received 8 June 2011; Accepted 25 July 2011

Academic Editor: Z. Huang

Copyright © 2011 F. A. Abd El-Salam and S. E. Abd El-Bar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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 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.