Skip to main content
SpringerLink
Log in

On the third-body perturbations of high-altitude orbits

  • Original Article
  • Published:
Celestial Mechanics and Dynamical Astronomy Aims and scope Submit manuscript

Abstract

The long-term effects of a distant third-body on a massless satellite that is orbiting an oblate body are studied for a high order expansion of the third-body disturbing function. This high order may be required, for instance, for Earth artificial satellites in the so-called MEO region. After filtering analytically the short-period angles via averaging, the evolution of the orbital elements is efficiently integrated numerically with very long step-sizes. The necessity of retaining higher orders in the expansion of the third-body disturbing function becomes apparent when recovering the short-periodic effects required in the computation of reliable osculating elements.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Anselmo L., Pardini C.: Long-term dynamical evolution of high area-to-mass ratio debris released into high earth orbits. Acta Astronaut. 67, 204–216 (2010)

    Article  ADS  Google Scholar 

  • Boccaletti D., Pucacco G.: Theory of Orbits. 2: Perturbative and Geometrical Methods, pp. 10. Springer, Berlin (1998)

    Google Scholar 

  • Broucke R.A.: Long-term third-body effects via double averaging. J. Guidance Control Dyn. 26(1), 27–32 (2003)

    Article  Google Scholar 

  • Brouwer D.: Solution of the problem of aritifical satellite theory without drag. Astron. J. 64(1274), 378–396 (1959)

    Article  MathSciNet  ADS  Google Scholar 

  • Brouwer D., Clemence G.M.: Methods of Celestial Mechanics, pp. 296ff. Academic Press, New York (1961)

    Google Scholar 

  • Campbell J.A., Jefferys W.H.: Equivalence of the perturbation theories of Hori and Deprit. Celest. Mech. 2(4), 467–473 (1970)

    Article  ADS  MATH  Google Scholar 

  • Cefola, P., Broucke, R.: On the Formulation of the Gravitational Potential in Terms of Equinoctial Variables. Paper AIAA 75-9, American Institute of Aeronautics and Astronautics (1975)

  • Cefola, P.J., Yurasov, V.S., Folcik, Z.J., Phelps, E.B., Proulx, R.J., Nazarenko, A.I.: Comparison of the DSST and the USM Semi-Analytical Orbit Propagators. Paper AAS 03-236, American Astronautical Society (2003)

  • Chao C.C., Gick R.A.: Long-term evolution of navigation satellite orbits: GPS/GLONASS/Galileo. Adv. Space Res. 34, 1221–1226 (2004)

    Article  ADS  Google Scholar 

  • Coffey S.L., Deprit A., Miller B.R.: The critical inclination in artificial satellite theory. Celest. Mech. 39(4), 365–406 (1986)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Collins, S.K.: Long Term Prediction of High Altitude Orbits. PhD Thesis, MIT (1981)

  • Collins, S.K., Cefola, P.J.: Double Averaged Third Body Model for Prediction of Super-Synchronous Orbits over Long Time Spans, p. 63. Paper AAS 79-135, American Astronautical Society (1979)

  • Deprit A.: Canonical transformations depending on a small parameter. Celest. Mech. 1(1), 12–30 (1969)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Deprit A.: Delaunay normalisations. Celest. Mech. 26(1), 9–21 (1982)

    Article  MathSciNet  ADS  Google Scholar 

  • Deprit A., Rom A.: The main problem of artificial satellite theory for small and moderate eccentricities. Celest. Mech. 2, 166–206 (1970)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Ely T.A.: Eccentricity impact on east-west stationkeeping for global positioning system class orbits. J. Guidance Control Dyn. 25(2), 352–357 (2002)

    Article  Google Scholar 

  • Ely T.A., Howell K.C.: Long term evolution of artificial satellite orbits due to resonant tesseral harmonics. J. Astronaut. Sci. 44, 167–190 (1996)

    Google Scholar 

  • Ely T.A., Howell K.C.: Dynamics of artificial satellite orbits with tesseral resonances including the effects of luni-solar perturbations. Int. J. Dyn. Stab. Syst. 12(4), 243–269 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  • Gedeon G.S.: Tesseral resonance effects on satellite orbits. Celest. Mech. 1(2), 167–189 (1969)

    Article  ADS  MATH  Google Scholar 

  • Giacaglia G.: Lunar perturbations of artificial satellites of the earth. Celest. Mech. 9, 239–267 (1974)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Green, A.J.: Orbit Determination and Prediction Processes for Low Altitude Satellites. PhD Thesis, MIT (1979)

  • Hori G.-i.: Theory of general perturbation with unspecified canonical variable. Publ. Astron. Soc. Jpn. 18(4), 287–296 (1966)

    ADS  Google Scholar 

  • Kelly T.S.: A note on first-order normalizations of perturbed Keplerian systems. Celest. Mech. Dyn. Astron. 46, 19–25 (1989)

    Article  ADS  MATH  Google Scholar 

  • Kozai, Y.: On the Effects of the Sun and the Moon upon the Motion of a Close Earth Satellite, p. 10, SAO Special Report #22 Smithsonian Astrophysical Observatory, Cambridge, MA (1959)

  • Kozai Y.: Second-order solution of artificial satellite theory without air drag. Astron. J. 67(7), 446–461 (1962)

    Article  MathSciNet  ADS  Google Scholar 

  • Lara M., Palacián J.F., Russell R.P: Mission design through averaging of perturbed Keplerian systems: the paradigm of an enceladus orbiter. Celest. Mech. Dyn. Astron. 108(1), 1–22 (2010)

    Article  ADS  MATH  Google Scholar 

  • Laskar J., Boué G.: Explicit expansion of the three-body disturbing function for arbitrary eccentricities and inclinations. Astron. Astrophys. 522(A60), 11 (2010)

    Google Scholar 

  • McClain, W.D.: A Recursively Formulated First-Order Semianalytic Artificial Satellite Theory Based on the Generalized Method of Averaging, Volume 1: The Generalized Method of Averaging Applied to the Artificial Satellite Problem, Computer Sciences Corporation CSC/TR-77/6010 (1977)

  • Métris G.: Mean values of particular functions in the elliptic motion. Celest. Mech. Dyn. Astron. 52, 79–84 (1991a)

    Article  ADS  MATH  Google Scholar 

  • Métris, G.: Théorie du mouvement des satellites artificiels—Développement des équations du mouvement moyen—Application à l’étude des longues périodes, p. 188, PhD Thesis, Observatoire de Paris (1991b)

  • Métris G., Exertier P.: Semi-analytical theory of the mean orbital motion. Astron. Astrophys. 294, 278–286 (1995)

    ADS  Google Scholar 

  • Meyer K.R., Hall G.R.: Introduction to Hamiltonian Dynamical Systems and the N-Body Problem, Vol. 90. Springer, New York (1992)

    Google Scholar 

  • Montenbruck O., Gill E.: Satellite Orbits Models Methods and Applications. Springer, New york (2001)

    Google Scholar 

  • Osácar C., Palacián J.F.: Decomposition of functions for elliptic orbits. Celest. Mech. Dyn. Astron. 60, 207–223 (1994)

    Article  ADS  MATH  Google Scholar 

  • Palacián J.F.: Dynamics of a satellite orbiting a planet with an inhomogeneous gravitational field. Celest. Mech. Dyn. Astron. 98, 219–249 (2007)

    Article  ADS  MATH  Google Scholar 

  • Prado A.F.B.A.: Third-body perturbation in orbits around natural satellites. J. Guidance Control Dyn. 26(1), 33–40 (2003)

    Article  Google Scholar 

  • Proulx, R., McClain, W.C., Early, L., Cefola, P.: A Theory for the Short Periodic Motion due to the Tesseral Harmonic Gravity Field, p. 20, Paper AAS 81-180, American Astronautical Society, (1981)

  • Rossi A.: Resonant dynamics of Medium earth orbits: space debris issues. Celest. Mech. Dyn. Astron. 100(4), 267–286 (2008)

    Article  ADS  Google Scholar 

  • Slutsky, M.: First Order Short Periodic Motion of and Artificial Satellite Due to Third-Body Perturbations: Numerical Evaluation, p. 22, Paper 83-393, American Astronautical Society (1983)

  • Steichen, D.: An averaging method to study the motion of lunar artificial satellites. Celest. Mech. Dyn. Astron. 68, 205–224; (part I) and 225–247 (part II) (1998)

    Google Scholar 

  • Valk S., Lemaître A., Deleflie F.: Semi-analytical theory of mean orbital motion for geosynchronous space debris under gravitational influence. Adv. Space Res. 43, 1070–1082 (2009)

    Article  ADS  Google Scholar 

  • Vashkov’yak M.A.: A numerical-analytical method for studying the orbital evolution of distant planetary satellites. Astron. Lett. 31(1), 64–72 (2005)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Columnas de Hercules 1, 11100, San Fernando, Spain

    Martin Lara

  2. Departamento de Matemáticas y Computación, Universidad de La Rioja, Logroño, Spain

    Juan F. San-Juan

  3. Departamento de Ingeniería Mecánica, Universidad de La Rioja, Logroño, Spain

    Luis M. López

  4. University at Buffalo, The State University of New York, Amherst, 14260-440, NY, USA

    Paul J. Cefola

Authors
  1. Martin Lara
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Juan F. San-Juan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Luis M. López
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Paul J. Cefola
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Juan F. San-Juan.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lara, M., San-Juan, J.F., López, L.M. et al. On the third-body perturbations of high-altitude orbits. Celest Mech Dyn Astr 113, 435–452 (2012). https://doi.org/10.1007/s10569-012-9433-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10569-012-9433-z

Keywords

Search

Navigation