Skip to main content

Displaced Non-Keplerian Orbits for Sun and Inner Planet Observation

  • Chapter
  • First Online:
Handbook of Space Resources

Abstract

A displaced non-Keplerian orbit is a trajectory whose orbital plane does not contain the center of mass of the primary body, so that its orbital maintenance requires the application of a suitable continuous thrust. Although the latter could be provided, in principle, by a low-thrust electric propulsion system, innovative propellantless propulsive technologies are well suited to such a mission scenario, due to their ability to generate thrust without requiring any propellant, thus significantly extending mission lifetime. This chapter focuses on the possibility of maintaining a displaced non-Keplerian orbit by means of both solar sails and electric solar wind sails (or E-sails). In fact, these advanced propulsion systems are both capable of generating a propulsive acceleration without consuming any propellant, by exploiting the solar radiation pressure (in case of solar sails) or the solar wind dynamic pressure (E-sails). This analysis uses recent models to provide a mathematical description of the propulsive acceleration generated by both propulsion systems, and different scenarios involving non-Keplerian orbits are analyzed. Particular focus is given to Type II displaced orbits, non-Keplerian orbits lying on the ecliptic plane, and heliostationary positions. Performance and attitude requirements are provided for each scenario. A linear stability analysis is also performed, in order to identify the combination of orbital parameters that characterize stable non-Keplerian orbits. The results suggest the feasibility of the mission scenarios discussed, but for most of them performance requirements are very demanding. A possible exception is non-Keplerian orbits lying on the ecliptic, which represent a very promising near-term scenario.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 349.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 299.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Free shipping worldwide - see info
Hardcover Book
USD 449.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Abbreviations

CR3BP :

Circular restricted three-body problem

DNKO :

Displaced non-Keplerian orbit

E-sail :

Electric solar wind sail

L 1 :

First collinear Lagrangian point

PDFO :

Planet following displaced orbit

References

  • Aliasi, G., G. Mengali, and A.A. Quarta. 2011. Artificial equilibrium points for a generalized sail in the circular restricted three-body problem. Celestial Mechanics and Dynamical Astronomy 110 (4): 343–368. https://doi.org/10.1007/s10569-011-9366-y.

  • Aliasi, G., G. Mengali, and A.A. Quarta. 2012. Passive control feasibility of collinear equilibrium points with solar balloons. Journal of Guidance, Control, and Dynamics 35 (5): 1657–1661. https://doi.org/10.2514/1.57393.

  • Aliasi, G., G. Mengali, and A.A. Quarta. 2013a. Artificial equilibrium points for an electric sail with constant attitude. Journal of Spacecraft and Rockets 50 (6): 1295–1298. https://doi.org/10.2514/1.A32540.

  • Aliasi, G., G. Mengali, and A.A. Quarta. 2013b. Artificial lagrange points for solar sail with electrochromic material panels. Journal of Guidance, Control, and Dynamics 3 6(5): 1544–1550. https://doi.org/10.2514/1.58167.

  • Aliasi, G., G. Mengali, and A.A. Quarta. 2015. Artificial periodic orbits around L1-type equilibrium points for a generalized sail. Journal of Guidance, Control, and Dynamics 38 (9): 1847–1852. https://doi.org/10.2514/1.G000904.

  • Ancona, E., and R.Y. Kezerashvili. 2017. Temperature restrictions for materials used in aerospace industry for the near-Sun orbits. Acta Astronautica 140: 565–569. https://doi.org/10.1016/j.actaastro.2017.09.002.

    Article  Google Scholar 

  • Baig, S. and C.R. McInnes. 2008. Artificial three-body equilibria for hybrid low-thrust propulsion. Journal of Guidance, Control, and Dynamics 31 (6): 1644–1655. https://doi.org/10.2514/1.36125.

  • Bassetto, M. et al. 2018. Plasma brake approximate trajectory. Part II: relative motion. In: 4th IAA conference on university satellite missions and Cubesat workshop, vol. 163, 249–259.

    Google Scholar 

  • Battin, R.H. 1987. An Introduction to the mathematics and methods of astrodynamics. AIAA. Chap. 8: 371–381.

    MathSciNet  MATH  Google Scholar 

  • Betts, B., D.A. Spencer, J.M. Bellardo, et al. 2019. LightSail 2: controlled solar sail propulsion using a CubeSat. In: 70th international astronautical congress. Washington (DC), USA.

    Google Scholar 

  • Biggs, J.D., and C.R. McInnes. 2010. Passive orbit control for space- based geo-engineering. Journal of Guidance, Control and Dynamics 33 (3): 1017–1020. https://doi.org/10.2514/3.21211.

  • Bookless, J., and C.R. McInnes. 2006. Dynamics and control of displaced periodic orbits using solar-sail propulsion. Journal of Guidance, Control, and Dynamics 29 (3): 527–537. https://doi.org/10.2514/1.15655.

  • Caruso, A., G. Mengali, and A.A. Quarta. 2019. Elliptic displaced or- bit approximation with equally spaced impulses. Journal of Guidance, Control, and Dynamics 42 (2): 411–415. https://doi.org/10.2514/1.G003900.

  • Caruso, A. et al. 2020. Solar sail optimal control with solar irradiance fluctuations. In Advances in space research. In press. https://doi.org/10.1016/j.asr.2020.05.037.

  • Ceriotti, M., C.R. McInnes, and B.L. Diedrich. 2011. The pole-sitter mission concept: an overview of recent developments and possible future applications. In: 62nd international astronautical congress, vol. 3, 2543–2559. Cape Town, South Africa.

    Google Scholar 

  • Ceriotti, M., J. Heiligers, and C.R. McInnes. 2014. Trajectory and spacecraft design for a pole-sitter mission. Journal of Spacecraft and Rockets 51 (1): 311–326. https://doi.org/10.2514/1.A32477.

  • Dachwald, B. 2004. Minimum transfer times for nonperfectly reflecting solar sailcraft. Journal of Spacecraft and Rockets 41 (4): 693–695. https://doi.org/10.2514/1.6279.

  • Forward, R.L. 1984. Light-levitated geostationary cylindrical orbits using perforated light sails. Journal of the Astronautical Sciences 32: 221–226.

    Google Scholar 

  • Fu, B., E. Sperber, and F. Eke. 2016. Solar sail technology - A state of the art review. Progress in Aerospace Sciences 86: 1–19. https://doi.org/10.1016/j.paerosci.2016.07.001.

    Article  Google Scholar 

  • Funase, R. et al. 2011. 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.

    Google Scholar 

  • Funase, R. et al. 2012. IKAROS, a solar sail demonstrator and its application to Trojan asteroid exploration. In 53rd AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics and materials conference. Honolulu, HI, USA. https://doi.org/10.2514/6.2012-1748.

  • Gong, S., and J. Li 2014a. Solar sail heliocentric elliptic displaced orbits. Journal of Guidance, Control, and Dynamics 37 (6): 2021–2025. https://doi.org/10.2514/1.G000660.

  • Gong, S., and J. Li. 2014b. Spin-stabilized solar sail for displaced solar orbits. Aerospace Science and Technology 32 (1): 188–199. https://doi.org/10.1016/j.ast.2013.10.002.

  • Heaton, A.F., and A.B. Artusio-Glimpse. 2015. An update to NASA reference sail thrust model. In AIAA SPACE 2015 conference and exposition. Pasadena, CA, USA. https://doi.org/10.2514/6.2015-4506.

  • Heaton, A., N. Ahmad, and K. Miller. 2017. Near earth asteroid scout thrust and torque model. In The 4th international symposium on solar sailing, vol. 17055. Kyoto, Japan.

    Google Scholar 

  • Heiligers, J., and C.R. McInnes. 2014. New families of sun-centered non-Keplerian orbits over cylinders and spheres. Celestial Mechanics and Dynamical Astronomy 120 (2): 163–194. https://doi.org/10.1007/s10569-014-9570-7.

  • Heiligers, J., M. Ceriotti, C.R. McInnes, et al. 2011. Displaced geostationary orbit design using hybrid sail propulsion. Journal of Guidance, Control, and Dynamics 34 (6): 1852–1866. 10.2514/1. 53807.

    Google Scholar 

  • Huo, M., G. Mengali, and A.A. Quarta. 2018. Electric sail thrust model from a geometrical perspective. Journal of Guidance, Control, and Dynamics 41 (3): 734–740. https://doi.org/10.2514/1.G003169.

  • Janhunen, P. 2004. Electric sail for spacecraft propulsion. Journal of Propulsion and Power 20 (4): 763–764. https://doi.org/10.2514/1.8580.

  • Janhunen, P. 2010. Electrostatic plasma brake for deorbiting a satellite. Journal of Propulsion and Power 26 (2): 370–372. https://doi.org/10.2514/1.47537.

  • Johnson, L. et al. 2011. NanoSail-D: a solar sail demonstration mission. Acta Astronautica 68 (5–6): 571–575. https://doi.org/10.1016/j.actaastro.2010.02.008.

  • Kestilä, A., T. Tikka, P. Peitso, et al. 2013. Aalto-1 nanosatellite–technical description and mission objectives. Geoscientific Instrumentation, Methods and Data Systems 2: 121–130. https://doi.org/10.5194/gi-2-121-2013.

    Article  Google Scholar 

  • Kezerashvili, R.Y. 2008. Solar sail interstellar travel: 1. Thickness of solar sail films. Journal of the British Interplanetary Society 61 (11): 430–439.

    Google Scholar 

  • Kezerashvili, R.Y. 2014. Advances in solar sailing. In M. Macdonald, ed. Springer Praxis. Chap. 3, 573–592. https://doi.org/10.1007/978-3-642-34907-2_36.

  • Khurshid, O. et al. 2014. Accommodating the plasma brake experiment on- board the Aalto-1 satellite. Proceedings of the Estonian Academy of Sciences 63 (2S): 258–266. https://doi.org/10.3176/proc.2014.2S.07.

  • Koon, W.S. et al. 2011. Dynamical systems, the three-body problem and space mission design. Marsden Books. ISBN: 978–0–615–24095–4.

    Google Scholar 

  • Lätt, S. et al. 2014. ESTCube-1 nanosatellite for electric solar wind sail in-orbit technology demonstration. Proceedings of the Estonian Academy of Sciences 63 (2S): 200–209. https://doi.org/10.3176/proc.2014.2S.01.

  • Lücking, C.M., C. Colombo, and C.R. McInnes. 2012. Electrochromic orbit control for smart-dust devices. Journal of Guidance, Control and Dynamics 35 (5): 1548–1558. https://doi.org/10.2514/1.55488.

  • Macdonald, M., R.J. McKay, M. Vasile, et al. 2011. Low-thrust-enabled highly-non-Keplerian orbits in support of future Mars exploration. Journal of Guidance, Control, and Dynamics 34(5): 1396–1411. https://doi.org/10.2514/1.52602.

  • McInnes, C.R. 2011. Displaced non-Keplerian orbits using impulsive thrust. Celestial Mechanics and Dynamical Astronomy 110: 199–215. https://doi.org/10.1007/s10569-011-9351-5.

    Article  MathSciNet  MATH  Google Scholar 

  • McInnes, C.R. 1998. Dynamics, stability, and control of displaced non-Keplerian orbits. Journal of Guidance, Control, and Dynamics 21 (5): 799–805. https://doi.org/10.2514/2.4309.

  • McInnes, C.R. 1999. Solar sailing: technology, dynamics and mission applications. Springer. ISBN: 978-1-85233-102-3. https://doi.org/10.1007/978-1-4471-3992-8.

  • McInnes, C.R. 2003. Inverse solar sail trajectory problem. Journal of Guidance, Control, and Dynamics 26 (2): 369–371. https://doi.org/10.2514/2.5057.

  • McKay, R.J., M. Macdonald, J.D. Biggs, et al. 2011. Survey of highly-non-Keplerian orbits with low-thrust propulsion. Journal of Guidance, Control, and Dynamics 34 (3): 645–666. https://doi.org/10.2514/1.52133.

  • McNutt, L. et al. 2014. Near-earth asteroid (NEA) scout. In AIAA SPACE 2014 conference and exposition. Paper AIAA 2014–4435. San Diego (CA), 4–7 August. https://doi.org/10.2514/6.2014-4435.

  • Mengali, G., and A.A. Quarta. 2007b. Tradeoff performance of hybrid low-thrust propulsion system. Journal of Spacecraft and Rockets 44 (6): 1263–1270. ISSN: 0022- 4650. https://doi.org/10.2514/1.30298.

  • Mengali, G., and A.A. Quarta. 2005. Optimal three-dimensional interplanetary rendezvous using nonideal solar sail. Journal of Guidance, Control, and Dynamics 28 (1): 173–177. ISSN: 0731–5090. https://doi.org/10.2514/1.8325.

  • Mengali, G., and A.A. Quarta. 2007a. Optimal heliostationary missions of high-performance sailcraft. Acta Astronautica 60 (8–9): 676–683. ISSN: 0094–5765. https://doi.org/10.1016/j.actaastro.2006.07.018.

  • Mengali, G., and A.A. Quarta. 2007c. Trajectory design with hybrid low-thrust propulsion system. Journal of Guidance, Control, and Dynamics 30 (2): 419–426. https://doi.org/10.2514/1.22433.

  • Mengali, G., and A.A. Quarta. 2009. Non-Keplerian orbits for electric sails. Celestial Mechanics and Dynamical Astronomy 105 (1): 179–195. https://doi.org/10.1007/s10569-009-9200-y.

  • Mengali, G., and A.A. Quarta. 2016. Heliocentric trajectory analysis of sun-pointing smart dust with electrochromic control. Advances in Space Research 57 (4): 991–1001. https://doi.org/10.1016/j.asr.2015.12.017.

  • Mengali, G., A.A. Quarta, and P. Janhunen. 2008. Electric sail performance analysis. Journal of Spacecraft and Rockets 45 (1): 122–129. ISSN: 0022–4650. https://doi.org/10.2514/1.31769.

  • Mengali, G. et al. 2007a. Refined solar sail force model with mission application. Journal of Guidance, Control, and Dynamics 30 (2): 512–520. ISSN: 0731–5090. https://doi.org/10.2514/1.24779.

  • Monk, P.M.S., R.J. Mortimer, and D.R. Rosseinsky. 2007b. Electrochromism: fundamentals and applications. Wiley-VCH.

    Google Scholar 

  • Mori, O., J. Mastumoto, T. Chujo, et al. 2019. Solar power sail mission of OKEANOS. Astrodynamics 4 (3): 233–248. https://doi.org/10.1007/s42064-019-0067-8.

  • Mori, O. et al. 2010. Attitude control of IKAROS solar sail spacecraft and its flight results. In 61st international astronautical congress. Paper IAC-10.C1.4.3. Prague, Czech Republic.

    Google Scholar 

  • Morimoto, M.Y., H. Yamakawa, and K. Uesugi. 2007. Artificial equilibrium points in the low-thrust restricted three-body problem. Journal of Guidance, Control, and Dynamics 30 (5): 1563–1568. https://doi.org/10.2514/1.26771.

  • Niccolai, L., A.A. Quarta, and G. Mengali. 2017. Electric sail elliptic displaced orbits with advanced thrust model. Acta Astronautica 138: 503–511. https://doi.org/10.1016/j.actaastro.2016.10.036.

    Article  Google Scholar 

  • Niccolai, L., A.A. Quarta, and G. Mengali. 2018. Electric sail-based displaced orbits with refined thrust model. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 232 (3): 423–432. https://doi.org/10.1177/0954410016679195.

  • Niccolai, L. et al. 2017. Plasma brake approximate trajectory. Part I: geocentric motion. In 4th IAA conference on university satellite missions and Cubesat workshop, vol. 163, 235–247.

    Google Scholar 

  • Niccolai, L. et al. 2019. Effects of optical parameter measurement uncertainties and solar irradiance fluctuations on solar sailing. In Advances in Space Research. In press. https://doi.org/10.1016/j.asr.2019.11.037.

  • Niccolai, L. et al. 2020a. Artificial collinear lagrangian point maintenance with electric solar wind sail. In IEEE Transactions on Aerospace and Electronic Systems. In press. https://doi.org/10.1109/TAES.2020.2990805.

  • Niccolai, L. et al. 2020b. Feedback control law of solar sail with variable surface reflectivity at Sun-Earth collinear equilibrium points. In Aerospace Science and Technology 106. https://doi.org/10.1016/j.ast.2020.106144.

  • Nye, B., and E. Greeson. 2016. The Lightsail story, public outreach strategies & results. In 67th international astronautical congress. Pasadena, CA, USA.

    Google Scholar 

  • Orsini, L., et al. 2018. Plasma brake model for preliminary mission analysis. Acta Astronautica 144: 297–304. https://doi.org/10.1016/j.actaastro.2017.12.048.

  • Pan, X., et al. 2019. Nonlinear dynamics of displaced non-Keplerian orbits with low-thrust propulsion. Communications in Nonlinear Science and Numerical Simulation 66: 61–83. https://doi.org/10.1016/j.cnsns.2018.06.005.

    Article  MathSciNet  MATH  Google Scholar 

  • Pan, X. et al. 2020. Linearized relative motion and proximity control of E-sail-based displaced orbits. In Aerospace Science and Technology, vol. 99. https://doi.org/10.1016/j.ast.2019.105574.

  • Pezent, J., R. Sood, and A. Heaton. 2019. High-fidelity contingency trajectory design and analysis for NASA’s near-earth asteroid (NEA) Scout solar sail Mission. Acta Astronautica 159: 385–396. https://doi.org/10.1016/j.actaastro.2019.03.050.

    Article  Google Scholar 

  • Quarta, A.A., G. Mengali, and L. Niccolai. 2020. Solar sail optimal transfer between heliostationary points. Journal of Guidance, Control, and Dynamics 43 (10): 1935–1942. https://doi.org/10.2514/1.G005193.

  • Quarta, A.A., and G. Mengali. 2016. Minimum-time trajectories of electric sail with advanced thrust model. Aerospace Science and Technology 55: 419–430. https://doi.org/10.1016/j.ast.2016.06.020.

    Article  Google Scholar 

  • Russell Lockett, T. et al. 2019. Near-Earth asteroid scout flight mission. IEEE Aerospace and Electronic Systems Magazine 35 (3): 20–29. https://doi.org/10.1109/MAES.2019.2958729.

  • Simo, J. 2017. A comparative study of displaced non-Keplerian orbits with impulsive and continuous thrust. In: 27th AAS/AIAA space flight mechanics meeting. San Antonio (TX), USA.

    Google Scholar 

  • Slavinskis, A. et al. 2015. ESTCube-1 in-orbit experience and lessons learned. IEEE Aerospace and Electronic Systems Magazine 30 (8): 12–22. https://doi.org/10.1109/MAES.2015.150034.

  • Song, M., X. He, and D. He. 2016. Displaced orbits for solar sail equipped with reflectance control devices in Hill’s restricted three-body problem with oblateness. Astrophysics and Space Science 361 (10). 10. 1007/s10509–016–2915–9.

    Google Scholar 

  • Stone, E.C. et al. 1998. The advanced composition explorer. Space Science Reviews 86 (1–4):1–22.

    Google Scholar 

  • Szebehely, V.G. 1967. Theory of orbits - The restricted problem of three bodies. Academic Press. ISBN: 978–0124124318.

    Google Scholar 

  • Toivanen, P.K., and P. Janhunen. 2013. Spin plane control and thrust vectoring of electric solar wind sail. Journal of Propulsion and Power 29 (1): 178–185. https://doi.org/10.2514/1.B34330.

  • Toivanen, P.K., and P. Janhunen. 2017. Thrust vectoring of an electric solar wind sail with a realistic sail shape. Acta Astronautica 131: 145–151. https://doi.org/10.1016/j.actaastro.2016.11.027.

    Article  Google Scholar 

  • Tsuda, Y. et al. 2011. Achievement of IKAROS - Japanese deep space solar sail demonstration mission. In 7th IAA symposium on realistic advanced scientific space. Aosta, Italy. https://doi.org/10.1016/j.actaastro.2012.03.032.

  • Vulpetti, G., C. Circi, and T. Pino. 2017. Coronal Mass ejection early-warning mission by solar-photon sailcraft. Acta Astronautica 140: 113–125. https://doi.org/10.1016/j.actaastro.2017.07.042.

    Article  Google Scholar 

  • Vulpetti, G., L. Johnson, and G.L. Matloff. 2015. Solar sails: a novel approach to interplanetary travel. Chichester, UK: Springer-Praxis. ISBN: 978–1–4939–0940–7. https://doi.org/10.1007/978-1-4939-0941-4.

  • Vulpetti, G. 2013. Fast solar sailing: astrodynamics of special sailcraft trajectories, Chap. 6, 165– 254. Springer. ISBN: 978–94–007–4776–0. https://doi.org/10.1007/978-94-007-4777-7.

  • Wright, J.L. 1992. Space sailing. Gordon and Breach, ed., 223–233 Philadelphia, PA: Gordon and Breach Science Publishers.

    Google Scholar 

  • Zola, D. et al. 2018. Photon momentum change of quasi-smooth solar sails. Journal of the Optical Society of America A: Optics and Image Science, and Vision 35 (8): 1261–1271. https://doi.org/10.1364/JOSAA.35.001261.

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Lorenzo Niccolai .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2023 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Niccolai, L., Quarta, A.A., Mengali, G. (2023). Displaced Non-Keplerian Orbits for Sun and Inner Planet Observation. In: Badescu, V., Zacny, K., Bar-Cohen, Y. (eds) Handbook of Space Resources. Springer, Cham. https://doi.org/10.1007/978-3-030-97913-3_1

Download citation

Publish with us

Policies and ethics