Logarithmic spiral trajectories generated by Solar sails

  • Marco Bassetto
  • Lorenzo Niccolai
  • Alessandro A. Quarta
  • Giovanni Mengali
Original Article
  • 36 Downloads
Part of the following topical collections:
  1. Innovative methods for space threats: from their dynamics to interplanetary missions

Abstract

Analytic solutions to continuous thrust-propelled trajectories are available in a few cases only. An interesting case is offered by the logarithmic spiral, that is, a trajectory characterized by a constant flight path angle and a fixed thrust vector direction in an orbital reference frame. The logarithmic spiral is important from a practical point of view, because it may be passively maintained by a Solar sail-based spacecraft. The aim of this paper is to provide a systematic study concerning the possibility of inserting a Solar sail-based spacecraft into a heliocentric logarithmic spiral trajectory without using any impulsive maneuver. The required conditions to be met by the sail in terms of attitude angle, propulsive performance, parking orbit characteristics, and initial position are thoroughly investigated. The closed-form variations of the osculating orbital parameters are analyzed, and the obtained analytical results are used for investigating the phasing maneuver of a Solar sail along an elliptic heliocentric orbit. In this mission scenario, the phasing orbit is composed of two symmetric logarithmic spiral trajectories connected with a coasting arc.

Keywords

Solar sail Logarithmic spiral trajectories Orbit phasing 

References

  1. Bacon, R.H.: Logarithmic spiral: an ideal trajectory for the interplanetary vehicle with engines of low sustained thrust. Am. J. Phys. 27(3), 164–165 (1959).  https://doi.org/10.1119/1.1934788 ADSCrossRefMATHGoogle Scholar
  2. Battin, R.H.: An Introduction to the Mathematics and Methods of Astrodynamics, chap. 3, Revised Edition. AIAA, pp. 126–127 (1999)Google Scholar
  3. Betts, B., Nye, B., Vaughn, J., Greeson, E., Chute, R., Spencer, D., et al.: Lightsail 1 mission results and public outreach strategies. In: The 4th International Symposium on Solar Sailing. Kyoto Research Park, Kyoto, Japan (17–20 Jan 2017a)Google Scholar
  4. Betts, B., Spencer, D., Nye, B., Munakata, R., Bellardo, J., Wong, S., et al.: Lightsail 2: Controlled solar sailing using a CubeSat. In: The 4th International Symposium on Solar Sailing. Kyoto Research Park, Kyoto, Japan (17–20 Jan 2017b)Google Scholar
  5. Dachwald, B., Macdonald, M., McInnes, C.R., Mengali, G., Quarta, A.A.: Impact of optical degradation on solar sail mission performance. J. Spacecr. Rockets 44(4), 740–749 (2007).  https://doi.org/10.2514/1.21432 ADSCrossRefGoogle Scholar
  6. 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).  https://doi.org/10.2514/1.20313 ADSCrossRefGoogle Scholar
  7. Funase, R., Kawaguchi, J., Mori, O., Sawada, H., Tsuda, Y.: IKAROS, a solar sail demonstrator and its application to Trojan asteroid exploration. In: 53rd Structural Dynamics and Materials Conference. Honolulu (HI), United States (23–26 April 2012)Google Scholar
  8. Funase, R., Shirasawa, Y., Mimasu, Y., Mori, O., Tsuda, Y., Saiki, T., et al.: Fuel-free and oscillation-free attitude control of IKAROS solar sail spacecraft using reflectivity control device. In: 28th International Symposium on Space Technology and Science. Okinawa, Japan (5–12 June 2011)Google Scholar
  9. Heaton, A.F., Artusio-Glimpse, A.B.: An update to the NASA reference solar sail thrust model. In: AIAA SPACE 2015 Conference and Exposition. Pasadena, California (31 Aug–2 Sept 2015)Google Scholar
  10. Johnson, L., Castillo-Rogez, J., Dervan, J., McNutt, L.: Near earth asteroid (NEA) scout. In: The 4th International Symposium on Solar Sailing. Kyoto Research Park, Kyoto, Japan (17–20 Jan 2017)Google Scholar
  11. Johnson, L., Whorton, M., Heaton, A., Pinson, R., Laue, G., Adams, C.: NanoSail-D: a solar sail demonstration mission. Acta Astronaut. 68(5–6), 571–575 (2011).  https://doi.org/10.1016/j.actaastro.2010.02.008 ADSCrossRefGoogle Scholar
  12. McInnes, C.R.: Passive control of displaced solar sail orbits. J. Guid. Control Dyn. 21(6), 975–982 (1998).  https://doi.org/10.2514/2.4334 ADSCrossRefGoogle Scholar
  13. McInnes, C.R.: Solar Sailing Technology, Dynamics and Mission Applications. Springer-Praxis Series in Space Science and Technology, chap. 4, pp. 129–136. Springer, Berlin (2004)Google Scholar
  14. McKay, R.J., Macdonald, M., Biggs, J., McInnes, C.: Survey of highly-non-keplerian orbits with low-thrust propulsion. J. Guid. Control Dyn. 34(3), 645–666 (2011).  https://doi.org/10.2514/1.52133 ADSCrossRefGoogle Scholar
  15. McNutt, L., Johnson, L., Kahn, P., Castillo-Rogez, J., Frick, A.: Near-earth asteroid (NEA) scout. In: AIAA SPACE 2014 Conference and Exposition. San Diego (CA), paper AIAA 2014-4435 (4–7 Aug 2014)Google Scholar
  16. Mori, O., Tsuda, Y., Shirasawa, Y., Saiki, T., Mimasu, Y., Kawaguchi, J.: Attitude control of IKAROS solar sail spacecraft and its flight results. In: 61st International Astronautical Congress. Prague, Czech Republic, paper IAC-10.C1.4.3 (Sept 27–Oct 1 2010)Google Scholar
  17. Niccolai, L., Quarta, A.A., Mengali, G.: Analytical solution of the optimal steering law for non-ideal solar sail. Aerosp. Sci. Technol. 62, 11–18 (2017).  https://doi.org/10.1016/j.ast.2016.11.031 CrossRefGoogle Scholar
  18. Petropoulos, A.E., Sims, J.A.: A review of some exact solutions to the planar equations of motion of a thrusting spacecraft. In: 2nd International Symposium on Low-Thrust Trajectory (LoTus-2). Toulouse, France (18–20 June 2002)Google Scholar
  19. Roa, J., Pelaez, J., Senent, J.: New analytic solution with continuous thrust: generalized logarithmic spirals. J. Guid. Control Dyn. 39(10), 2336–2351 (2016).  https://doi.org/10.2514/1.G000341 ADSCrossRefGoogle Scholar
  20. Sauer Jr., C.G.: Solar sail trajectories for solar polar and interstellar probe missions. Adv. Astronaut. Sci. 103(1), 547–562 (2000)Google Scholar
  21. Stewart, B., Palmer, P., Roberts, M.: An analytical description of three-dimensional heliocentric solar sail orbits. Celest. Mech. Dyn. Astron. 128, 61–74 (2017).  https://doi.org/10.1007/s10569-016-9740-x ADSMathSciNetCrossRefMATHGoogle Scholar
  22. Svitek, T., Friedman, L., Nye, W., Biddy, C., Nehrenz, M.: Voyage continues—Lightsail-1 mission by the Planetary Society. In: 61st International Astronautical Congress. IAC, Prague, Czech Republic (27 Sept–1 Oct 2010)Google Scholar
  23. Tsu, T.C.: Interplanetary travel by solar sail. ARS J. 29, 422–427 (1959)CrossRefGoogle Scholar
  24. Tsuda, Y., Mori, O., Funase, R., Sawada, H., Yamamoto, T., Takanao, S., et al.: Achievement of IKAROS—Japanese deep space solar sail demonstration mission. In: 7th IAA Symposium on Realistic Advanced Scientific Space, vol. 82. Aosta (Italy), pp. 183–188 (July 2011)Google Scholar
  25. Tychina, P.A., Egorov, V.A., Sazonov, V.V.: Quasi-optimal transfer of a spacecraft with a solar sail between circular heliocentric orbits. Cosm. Res. 34(4), 387–394 (1996)ADSGoogle Scholar
  26. Van Der Ha, J.C., Modi, V.J.: Long-term evaluation of three-dimensional heliocentric solar sail trajectories with arbitrary fixed sail setting. Celest. Mech. 19(2), 113–118 (1979).  https://doi.org/10.1007/BF01796085 ADSCrossRefMATHGoogle Scholar
  27. Wokes, S., Palmer, P., Roberts, M.: Classification of two-dimensional fixed-sun-angle solar sail trajectories. J. Guid. Control Dyn. 31(5), 1249–1258 (2008).  https://doi.org/10.2514/1.34466 ADSCrossRefGoogle Scholar
  28. Wright, J.L.: Space Sailing, pp. 223–226. Gordon and Breach Science Publisher, Berlin (1992)Google Scholar

Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  • Marco Bassetto
    • 1
  • Lorenzo Niccolai
    • 1
  • Alessandro A. Quarta
    • 1
  • Giovanni Mengali
    • 1
  1. 1.Dipartimento di Ingegneria Civile e IndustrialeUniversity of PisaPisaItaly

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