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New families of Sun-centered non-Keplerian orbits over cylinders and spheres

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Abstract

This paper introduces new families of Sun-centered non-Keplerian orbits (NKOs) that are constrained to a three-dimensional, cylindrical or spherical surface. As such, they are an extension to the well-known families of displaced NKOs that are confined to a two-dimensional plane. The cylindrical and spherical orbits are found by investigating the geometrically constrained spacecraft dynamics. By imposing further constraints on the orbit’s angular velocity and propulsive acceleration, the set of feasible orbits is defined. Additionally, the phase spaces of the orbits are explored and a numerical analysis is developed to find periodic orbits. The richness of the problem is further enhanced by considering both an inverse square acceleration law (mimicking solar electric propulsion) and a solar sail acceleration law to maintain the spacecraft on the three-dimensional surface. The wealth of orbits that these new families of NKOs generate allows for a range of novel space applications.

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Notes

  1. L’Garde—Sunjammer, http://www.lgarde.com/programs/space-propulsion/sunjammer. Accessed 8 May 2013.

References

  • Baig, S., McInnes, C.: Light-levitated geostationary cylindrical orbits are feasible. J. Guid. Control Dyn. 33(3), 782–793 (2010)

    Article  ADS  Google Scholar 

  • Biddy C., Svitek T.: LightSail-1 solar sail design and qualification. In: Proceedings of the 41st Aerospace Mechanisms Symposium, Pasadena, CA (2012)

  • Heiligers, J., Ceriotti, M., McInnes, C., Biggs, J.: Displaced geostationary orbit design using hybrid sail propulsion. J. Guid. Control Dyn. 34(6), 1852–1866 (2011)

    Article  ADS  Google Scholar 

  • Johnson, L., Whorton, M., Heaton, A., Pinson, R., Laue, G., Adams, C.: Nanosail-D: a solar sail demonstration mission. Acta Astronaut. 68, 571–575 (2011)

    Article  ADS  Google Scholar 

  • Kawaguchi, J., Fujiwara, A., Uesugi, T.: Hayabusa—its technology and science accomplishment summary and Hayabusa-2. Acta Astronaut. 62(1011), 639–647 (2008)

    Article  ADS  Google Scholar 

  • Macdonald, M., McInnes, C., Alexander, D., Sandman, A.: Geosail: exploring the magnetosphere using a low-cost solar sail. Acta Astronaut. 59, 757–767 (2006)

    Article  ADS  Google Scholar 

  • McInnes, C.: The existence and stability of families of displaced two-body orbits. Celest. Mech. Dyn. Astron. 67(2), 167–180 (1997)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  • McInnes, C.: Dynamics, stability, and control of displaced non-Keplerian orbits. J. Guid. Control Dyn. 21(5), 799–805 (1998)

    Article  ADS  Google Scholar 

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

    Book  Google Scholar 

  • McInnes, C.: Displaced non-keplerian orbits using implisve thrust. Celest. Mech. Dyn. Astron. 110(3), 199–215 (2011)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  • McInnes, C., Simmons, J.: Solar sail halo orbits. Part I—heliocentric case. J. Spacecr. Rockets 29(4), 466–471 (1992)

    Article  ADS  Google Scholar 

  • Mengali, G., Quarta, A.: Non-Keplerian orbits for electric sails. Celest. Mech. Dyn. Astron. 105(1–3), 179–195 (2009)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  • Meserve, B.: Fundamental Concepts of Algebra. Dover Publications, New York (1982)

    Google Scholar 

  • Muzi, D., Allasio, A.: Goce: the first core earth explorer of ESA’s earth observation programme. Acta Astronaut. 54(3), 167–175 (2004)

    Article  ADS  Google Scholar 

  • Russell, C.T., Coradini, A., Christensen, U., De Sanctis, M.C., Feldman, W.C., Jaumann, R., et al.: Dawn: a journey in space and time. Planet. Space Sci. 52(56), 465–489 (2004)

    Article  ADS  Google Scholar 

  • Spilker, T.: Saturn ring observer. Acta Astronaut. 52, 259–265 (2003)

    Article  ADS  Google Scholar 

  • Tsuda, Y., Mori, O., Funase, R., Sawada, H., Yamamoto, T., Saiki, T., et al.: Flight status of IKAROS deep space solar sail demonstrator. Acta Astronaut. 69(9–10), 833–840 (2011)

    Article  ADS  Google Scholar 

Download references

Acknowledgments

This work was funded by the European Research Council Advanced Investigator Grant-227571: Visionary Space Systems: Orbital Dynamics at Extremes of Spacecraft Length-Scale.

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Authors and Affiliations

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

    Jeannette Heiligers & Colin R. McInnes

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  1. Jeannette Heiligers
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  2. Colin R. McInnes
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Correspondence to Jeannette Heiligers.

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Heiligers, J., McInnes, C.R. New families of Sun-centered non-Keplerian orbits over cylinders and spheres. Celest Mech Dyn Astr 120, 163–194 (2014). https://doi.org/10.1007/s10569-014-9570-7

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  • DOI: https://doi.org/10.1007/s10569-014-9570-7

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