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


  • 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 LindstedtPoincar technique, and (3) the KrylovBogoliubovMitropolsky method. In addition, the numerical integration by RungeKutta algorithm is established. However, the numerical comparison tests show that by increasing the value of angular momentum the solutions provided by LindstedtPoincar and KrylovBogoliubovMitropolsky 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 KrylovBogoliubovMitropolsky provides more accurate results to design elliptical periodic solutions than LindstedtPoincar 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.

published proceedings


altmetric score

  • 1

author list (cited authors)

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

citation count

  • 29

complete list of authors

  • Abouelmagd, Elbaz I||Mortari, Daniele||Selim, Hadia H

publication date

  • December 2015