Critical inclination in the main problem of a massive satellite

  • S. Breiter
  • A. Elipe
Conference paper


The classical problem of the critical inclination in artificial satellite theory has been extended to the case when a satellite may have an arbitrary, significant mass and the rotation momentum vector is tilted with respect to the symmetry axis of the planet. If the planet’s potential is restricted to the second zonal harmonic, according to the assumptions of the main problem of the satellite theory, two various phenomena can be observed: a critical inclination that asymptotically tends to the well known negligible mass limit, and a critical tilt that can be attributed to the effect of transforming the gravity field harmonics to a different reference frame. Stability of this particular solution of the two rigid bodies problem is studied analytically using a simple pendulum approximation.


Analytical methods Critical inclination Rigid body rotation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Breiter, S., Melendo, B., Bartczak, P., Wytrzyszczak, I.: Synchronous motion in the Kinoshita problem. Application to satellites and binary asteroids. Astron. Astrophys. 437, 753–764 (2005)CrossRefADSGoogle Scholar
  2. Brouwer, D.: Solution of the problem of artificial satellite theory without drag. Astron. J. 64, 378–397 (1959)CrossRefADSMathSciNetGoogle Scholar
  3. Coffey, S.L., Deprit, A., Miller, B.R.: The critical inclination in artificial satellite theory. Celest. Mech. 39, 365–406 (1986)CrossRefADSMathSciNetzbMATHGoogle Scholar
  4. Coffey, S.L., Deprit, A., Deprit, E.: Frozen orbits for satellites close to an Earth-like planet. Celest. Mech. Dynam Astron. 59, 37–72 (1994)CrossRefADSMathSciNetzbMATHGoogle Scholar
  5. Deprit, A.: Canonical transformation depending on a small parameter. Celest. Mech. 1, 12–30 (1969)CrossRefADSMathSciNetzbMATHGoogle Scholar
  6. Deprit, A., Elipe, A.: Complete reduction of the Euler-Poinsot problem. J. Astron. Sci. 41, 603–628 (1993)MathSciNetGoogle Scholar
  7. Kinoshita, H.: First-order perturbations of the two finite body problem. Publ. Astron. Soc. Japan 24, 423–457 (1972)ADSMathSciNetGoogle Scholar
  8. Koon, W.S., Marsden, J.E., Ross, S.D., Lo, M., Scheeres, D.J.: Geometric mechanics and the dynamics of asteroid pairs. Ann. N.Y. Acad. Sci. 1017, 11–38 (2004)CrossRefADSGoogle Scholar
  9. Scheeres, D.J.: Changes in rotational angular momentum due to gravitational interactions between two finite bodies. Celest. Mech. Dynam. Astron. 81, 39–44 (2001)CrossRefADSzbMATHGoogle Scholar
  10. Scheeres, D.J.: Stability in the full two-body problem. Celest. Mech. Dynam. Astron. 83, 155–169 (2002)CrossRefADSMathSciNetzbMATHGoogle Scholar
  11. Scheeres, D.J.: Stability of relative equilibria in the full two-body problem. Ann. N.Y. Acad. Sci. 1017, 81–94 (2004a)CrossRefADSGoogle Scholar
  12. Scheeres, D.J.: Bounds on rotations periods of disrupted binaries in the full 2-body problem. Celest. Mech. Dynam. Astron. 89, 127–140 (2004b)CrossRefADSMathSciNetzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2006

Authors and Affiliations

  • S. Breiter
    • 1
  • A. Elipe
    • 2
  1. 1.Astronomical Observatory of A. Mickiewicz UniversityPoznańPoland
  2. 2.Grupo de Mecánica EspacialUniversidad de ZaragozaZaragozaSpain

Personalised recommendations