Analytical Study of Periodic Solutions on Perturbed Equatorial Two-Body Problem Academic Article uri icon


  • © 2015 World Scientific Publishing Company. This paper presents analytical derivations to study periodic solutions for the two-body problem perturbed by the first zonal harmonic parameter. In particular, three different semianalytical approaches to solve this problem have been studied: (1) the classic perturbation theory, (2) the Lindstedt-Poincaré technique, and (3) the Krylov-Bogoliubov-Mitropolsky method. In addition, the numerical integration by Runge-Kutta algorithm is established. However, the numerical comparison tests show that by increasing the value of angular momentum the solutions provided by Lindstedt-Poincaré and Krylov-Bogoliubov-Mitropolsky methods become similar, and they provide almost identical results using a smaller value for the perturbed parameter which quantify the dynamical flattening of the main body, the Krylov-Bogoliubov-Mitropolsky provides more accurate results to design elliptical periodic solutions than Lindstedt-Poincaré technique when the perturbed parameter has a relatively large value, regardless of the value of angular momentum. This study can be applied to equatorial orbits to obtain closed-form analytical solutions.

altmetric score

  • 1

author list (cited authors)

  • Abouelmagd, E. I., Mortari, D., & Selim, H. H.

citation count

  • 14

publication date

  • December 2015