Skip to main content
SpringerLink
Log in

Natural and sail-displaced doubly-symmetric Lagrange point orbits for polar coverage

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

Abstract

This paper proposes the use of doubly-symmetric, eight-shaped orbits in the circular restricted three-body problem for continuous coverage of the high-latitude regions of the Earth. These orbits, for a range of amplitudes, spend a large fraction of their period above either pole of the Earth. It is shown that they complement Sun-synchronous polar and highly eccentric Molniya orbits, and present a possible alternative to low thrust pole-sitter orbits. Both natural and solar-sail displaced orbits are considered. Continuation methods are described and used to generate families of these orbits. Starting from ballistic orbits, other families are created either by increasing the sail lightness number, varying the period or changing the sail attitude. Some representative orbits are then chosen to demonstrate the visibility of high-latitude regions throughout the year. A stability analysis is also performed, revealing that the orbits are unstable: it is found that for particular orbits, a solar sail can reduce their instability. A preliminary design of a linear quadratic regulator is presented as a solution to stabilize the system by using the solar sail only. Finally, invariant manifolds are exploited to identify orbits that present the opportunity of a ballistic transfer directly from low Earth orbit.

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

  • Anderson, P.C., Macdonald, M.: Extension of Earth orbits using low-thrust propulsion. In: 61st International Astronautical Congress (IAC 2010), Prague, Czech Republic, IAF (2010)

  • Archambeau G., Augros P., Trélat E.: Eight-shaped Lissajous orbits in the Earth-Moon system. MathS In Action 4(1), 1–23 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  • Baig S., McInnes C.R.: Artificial three-body equilibria for hybrid low-thrust propulsion. J. Guid. Control Dyn. 31(6), 1644–1655 (2008). doi:10.2514/1.36125

    Article  Google Scholar 

  • Baig S., McInnes C.R.: Artificial halo orbits for low-thrust propulsion spacecraft. Celest. Mech. Dyn. Astron. 104(4), 321–335 (2009). doi:10.1007/s10569-009-9215-4

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Baoyin H., McInnes C.R.: Solar sail orbits at artificial Sun-Earth libration points. J. Guid. Control Dyn. 28(6), 1328–1331 (2005). doi:10.2514/1.14598

    Article  Google Scholar 

  • Broucke R., Lass H., Boggs D.: A note on the solution of the variational equations of a class of dynamical systems. Celest. Mech. 14(3), 383–392 (1976). doi:10.1007/bf01228524

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Bryson A.E., Ho Y.-C.: Applied Optimal Control: Optimization, Estimation, and Control (Revised printing). Taylor & Francis Group, New York (1975)

    Google Scholar 

  • Ceriotti, M., McInnes, C.R.: Hybrid solar sail and SEP propulsion for novel Earth observation missions. In: 61st International Astronautical Congress (IAC 2010), Prague, Czech Republic, IAF (2010)

  • Ceriotti M., McInnes C.R.: Generation of optimal trajectories for Earth hybrid pole-sitters. J. Guid. Control Dyn. 34(3), 847–859 (2011). doi:10.2514/1.50935

    Article  Google Scholar 

  • Ceriotti, M., McInnes, C.R., Diedrich, B.L.: The pole-sitter mission concept: an overview of recent developments and possible future applications. In: 62nd International Astronautical Congress (IAC2011), Cape Town, South Africa (2011)

  • Dachwald B., Mengali G., Quarta A.A., Macdonald M.: Parametric model and optimal control of solar sails with optical degradation. J. Guid. Control Dyn. 29(5), 1170–1178 (2006). doi:10.2514/1.20313

    Article  Google Scholar 

  • Dichmann, D.J., Doedel, E.J., Paffenroth, R.C.: The computation of periodic solutions of the 3-body problem using the numerical continuation software AUTO. In: International Conference on Libration Point Orbits and Applications, Aiguablava, Spain, 10–14 June 2002 (2002)

  • Driver J.M.: Analysis of an arctic polesitter. J. Spacecr. Rocket. 17(3), 263–269 (1980). doi:10.2514/3.57736

    Article  ADS  Google Scholar 

  • Farrés A., Farrés A.: Periodic and quasi-periodic motions of a solar sail close to SL1 in the Earth-Sun system. Celest. Mech. Dyn. Astron. 107(1), 233–253 (2010). doi:10.1007/s10569-010-9268-4

    Article  ADS  MATH  Google Scholar 

  • Farrés, A., Jorba, À.: Station keeping of a solar sail around a halo orbit. In: 1st IAA Conference on Dynamics and Control of Space Systems (DyCoSS 2012), Porto, Portugal (2012)

  • Folta, D., Young, C., Adam, R.: Unique non-Keplerian orbit vantage locations for Sun-Earth connection and Earth science vision roadmaps. In: Flight Mechanics Symposium, 1 June 2001, pp. 41–51 (2001)

  • Forward R.L.: Statite: a spacecraft that does not orbit. J. Spacecr. Rocket. 28(5), 606–611 (1991). doi:10.2514/3.26287

    Article  ADS  Google Scholar 

  • Funase, R., Mori, O., Tsuda, Y., Shirasawa, Y., Saiki, T., Mimasu, Y., et al.: Attitude control of IKAROS solar sail spacecraft and its flight results. In: 61st International Astronautical Congress (IAC 2010), Prague, Czech Republic 2010. IAF (2010)

  • Gómez G., Jorba A., Masdemont J.J., Simó C.: Study of the transfer from the Earth to a halo orbit around the equilibrium point L1. Celest. Mech. Dyn. Astron. 56(4), 541–562 (1993). doi:10.1007/bf00696185

    Article  ADS  MATH  Google Scholar 

  • Goudas C.L.: Three-dimensional periodic orbits and their stability. Icarus 2, 1–18 (1963). doi:10.1016/0019-1035(63)90003-4

    Article  ADS  Google Scholar 

  • Hénon M.: Vertical stability of periodic orbits in the restricted problem. II. Hill’s case. Astron. Astrophys. 30, 317–321 (1974)

    ADS  MATH  Google Scholar 

  • Howell K.C.: Families of orbits in the vicinity of the collinear libration points. J. Astronaut. Sci. 49(1), 107–125 (2001)

    MathSciNet  Google Scholar 

  • Howell, K.C., Mains, D.L., Barden, B.T.: Transfer trajectories from Earth parking orbits to Sun-Earth halo orbits. In: Proceedings of the 4th AAS/AIAA Spaceflight Mechanics Meeting. Cocoa Beach, FL, USA 1994. Advances in the Astronautical Sciences, pp. 399–410. Univelt (1994)

  • Kazantzis P.G.: Families of three-dimensional axisymmetric periodic orbits in the restricted three-body problem: Sun-Jupiter case. Astrophys. Space Sci. 61, 477–486 (1979). doi:10.1007/BF00640543

    Article  ADS  MATH  Google Scholar 

  • Kazantzis P.G.: Numerical determination of families of three-dimensional double-symmetric periodic orbits in the restricted three-body problem. I. Sun-Jupiter case. Astrophys. Space Sci. 65(2), 493–513 (1979). doi:10.1007/BF00648513

    Article  ADS  MATH  Google Scholar 

  • Kazantzis P.G.: Numerical determination of families of three-dimensional double-symmetric periodic orbits in the restricted three-body problem. II. Sun-Jupiter case. Astrophys. Space Sci. 69(2), 353–368 (1980). doi:10.1007/BF00661923

    Article  ADS  MATH  Google Scholar 

  • Koon W.S., Lo M.W., Marsden J.E., Ross S.D.: Dynamical Systems, the Three-Body Problem, and Space Mission Design. Marsden Books, Wellington (2006)

    Google Scholar 

  • Lappas, V.J., Wokes, S., Leipold, M., Falkner, P.: Attitude control design for solar sail missions. In: 6th International ESA Conference on Guidance, Navigation and Control Systems, Loutraki, Greece. European Space Agency, Special Publication ESA SP, pp. 191–194 (2005)

  • Lazzara, M.A., Coletti, A., Diedrich, B.L.: The possibilities of polar meteorology, environmental remote sensing, communications and space weather applications from Artificial Lagrange Orbit. Adv. Space Res. 48(11) (2011). doi:10.1016/j.asr.2011.04.026

  • McInnes C.R.: Solar Sailing: Technology, Dynamics and Mission Applications. Springer-Praxis Books in Astronautical Engineering. Springer, Berlin (1999)

    Google Scholar 

  • McInnes C.R., McDonald A.J., Simmons J.F.L., MacDonald E.W.: Solar sail parking in restricted three-body systems. J. Guid. Control Dyn. 17(2), 399–406 (1994)

    Article  ADS  MATH  Google Scholar 

  • Moulton F.R.: Periodic Orbits. Carnegie Institution of Washington Publications, Washington, USA (1920)

    MATH  Google Scholar 

  • Senent J., Ocampo C., Capella A.: Low-thrust variable-specific-impulse transfers and guidance to unstable periodic orbits. J. Guid. Control Dyn. 28(2), 280–290 (2005). doi:10.2514/1.6398

    Article  Google Scholar 

  • Thurman, R., Worfolk, P.A.: The Geometry of Halo Orbits in the Circular Restricted Three-Body Problem. Techinical Report GCG95. University of Minnesota, Minneapolis, MN (1996)

  • Waters T.J., McInnes C.R.: Periodic orbits above the ecliptic in the solar-sail restricted three-body problem. J. Guid. Control Dyn. 30(3), 687–693 (2007). doi:10.2514/1.26232

    Article  Google Scholar 

  • Wertz, J.R., Larson, W.J. (eds.): Space Mission Analysis and Design. 3rd edn. Microcosm Press/Kluwer, El Segundo, CA, USA (1999)

    Google Scholar 

  • Wie B.: Solar sail attitude control and dynamics, part 1. J. Guid. Control Dyn. 27(4), 526–535 (2004). doi:10.2514/1.11134

    Article  MathSciNet  Google Scholar 

  • Zagouras C., Markellos V.V.: Axisymmetric periodic orbits of the restricted problem in three dimensions. Astron. Astrophys. 59, 79–89 (1977)

    MathSciNet  ADS  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Advanced Space Concepts Laboratory, Department of Mechanical and Aerospace Engineering, University of Strathclyde, 75 Montrose Street, James Weir Building, Glasgow, G1 1XJ, UK

    Matteo Ceriotti & Colin R. McInnes

Authors
  1. Matteo Ceriotti
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Colin R. McInnes
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Matteo Ceriotti.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ceriotti, M., McInnes, C.R. Natural and sail-displaced doubly-symmetric Lagrange point orbits for polar coverage. Celest Mech Dyn Astr 114, 151–180 (2012). https://doi.org/10.1007/s10569-012-9422-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10569-012-9422-2

Keywords

Search

Navigation