https://doi.org/10.1140/epjp/i2017-11500-3
Regular Article
Fully analytical solution of the electromagnetic perturbations on the motion of the charged satellites in earth’s magnetic field
1
Department of Mathematics, Faculty of Science, Taibah University, Al-Madinah, Saudi Arabia
2
Department of Astronomy, Faculty of Science, Cairo University, 12613, Cairo, Egypt
3
Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt
* e-mail: f.a.abdelsalam@gmail.com
Received:
19
January
2017
Accepted:
25
March
2017
Published online:
2
May
2017
In this work, the perturbations in all orbital elements due to the motion of the charged satellites in the Earth’s magnetic field using Lagrange’s planetary equations are solved exactly. The geomagnetic and electric force components in terms of orbital elements in full analytic expressions are derived. Lagrange’s planetary equations after substitution with the considered perturbations in Keplerian orbital elements are obtained. To solve the problem in full analytical way, some integrals by Ahmed (Astron. J. 107, 1900 (1994)) are utilized. The time rate of change of all orbital elements of the spacecraft are integrated and represented in matrix notations.
© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg, 2017
