Celestial Mechanics and Dynamical Astronomy

, Volume 108, Issue 4, pp 371–388

Some orbital characteristics of lunar artificial satellites

  • J. P. S. Carvalho
  • R. Vilhena de Moraes
  • A. F. B. A. Prado
Original Article

DOI: 10.1007/s10569-010-9310-6

Cite this article as:
Carvalho, J.P.S., Vilhena de Moraes, R. & Prado, A.F.B.A. Celest Mech Dyn Astr (2010) 108: 371. doi:10.1007/s10569-010-9310-6


In this paper we present an analytical theory with numerical simulations to study the orbital motion of lunar artificial satellites. We consider the problem of an artificial satellite perturbed by the non-uniform distribution of mass of the Moon and by a third-body in elliptical orbit (Earth is considered). Legendre polynomials are expanded in powers of the eccentricity up to the degree four and are used for the disturbing potential due to the third-body. We show a new approximated equation to compute the critical semi-major axis for the orbit of the satellite. Lie-Hori perturbation method up to the second-order is applied to eliminate the terms of short-period of the disturbing potential. Coupling terms are analyzed. Emphasis is given to the case of frozen orbits and critical inclination. Numerical simulations for hypothetical lunar artificial satellites are performed, considering that the perturbations are acting together or one at a time.


Lunar artificial satellite Frozen orbits Orbital perturbations Critical inclination 

Supplementary material

10569_2010_9310_MOESM1_ESM.pdf (35 kb)
ESM 1 (PDF 36 kb)

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  • J. P. S. Carvalho
    • 1
  • R. Vilhena de Moraes
    • 1
  • A. F. B. A. Prado
    • 2
  1. 1.UNESP-Univ Estadual PaulistaGuaratinguetáBrazil
  2. 2.Division of Space Mechanics and ControlINPESão José dos CamposBrazil

Personalised recommendations