Abstract
A diffractive sail is a solar sail whose exposed surface is covered by an advanced diffractive metamaterial film with engineered optical properties. This study examines the optimal performance of a diffractive solar sail with a Sun-facing attitude in a typical orbit-to-orbit heliocentric transfer. A Sun-facing attitude, which can be passively maintained through the suitable design of the sail shape, is obtained when the sail nominal plane is perpendicular to the Sun–spacecraft line. Unlike an ideal reflective sail, a Sun-facing diffractive sail generates a large transverse thrust component that can be effectively exploited to change the orbital angular momentum. Using a recent thrust model, this study determines the optimal control law of a Sun-facing ideal diffractive sail and simulates the minimum transfer times for a set of interplanetary mission scenarios. It also quantifies the performance difference between Sun-facing diffractive sail and reflective sail. A case study presents the results of a potential mission to the asteroid 16 Psyche.
![](http://media.springernature.com/lw685/springer-static/image/art%3A10.1007%2Fs42064-023-0158-4/MediaObjects/42064_2023_158_Fig1_HTML.jpg)
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Abbreviations
- \(\mathbb{A}\) :
-
state matrix with generic entry Aij; see Eq. (9)
- a :
-
semi-major axis (au)
- a c :
-
characteristic acceleration (m/s2)
- a p :
-
propulsive acceleration vector (mm/s2)
- {a pR, a pT, a pN}:
-
components of ap in \({{\cal T}_{{\rm{RTN}}}}\)
- C :
-
spacecraft center-of-mass
- c :
-
speed of light in vacuum (km/s)
- D :
-
dimensionless performance parameter; see Eq. (41)
- d :
-
vector; see Eq. (9)
- e :
-
eccentricity
- \({\cal H}\) :
-
Hamiltonian function
- I ⊕ :
-
solar irradiance at 1 au (W/m2)
- i :
-
orbital inclination (deg)
- \(\{ {{{\boldsymbol{\hat i}}}_x},{{{\boldsymbol{\hat i}}}_y},{{{\boldsymbol{\hat i}}}_z}\} \) :
-
unit vectors of \({\cal T}\)
- \(\{ {{{\boldsymbol{\hat i}}}_R},{{{\boldsymbol{\hat i}}}_T},{{{\boldsymbol{\hat i}}}_N}\} \) :
-
unit vectors of \({{\cal T}_{{\rm{RTN}}}}\)
- J :
-
performance index (days)
- \({{\boldsymbol{\hat K}}}\) :
-
grating momentum unit vector
- m :
-
spacecraft total mass (kg)
- {p, f, g, h, k, L}:
-
modified equinoctial orbital elements
- \({\cal T}(C;x,y,z)\) :
-
body reference frame
- \({{\cal T}_{{\rm{RTN}}}}(C;R,T,N)\) :
-
radial–tangential–normal reference frame
- r :
-
Sun–spacecraft distance (au)
- r ⊕ :
-
reference distance (1 au)
- t :
-
time (days)
- x :
-
spacecraft state vector
- δ :
-
clock angle (deg)
- λ :
-
costate vector
- ν :
-
spacecraft true anomaly (deg)
- Ω:
-
right ascension of the ascending node (deg)
- ω :
-
argument of perihelion (deg)
- 0:
-
initial value
- i:
-
parking orbit
- f:
-
final value, target orbit
- IRS:
-
related to IRS
- SFIDS:
-
related to SFIDS
- ·:
-
time derivative
- ★:
-
optimal value
- ′:
-
depending on the control δ
References
Fu, B., Sperber, E., Eke, F. Solar sail technology—A state of the art review. Progress in Aerospace Sciences, 2016, 86: 1–19.
Gong, S. P., MacDonald, M. Review on solar sail technology. Astrodynamics, 2019, 3(2): 93–125.
Bassetto, M., Quarta, A. A., Caruso, A., Mengali, G. Optimal heliocentric transfers of a Sun-facing heliogyro. Aerospace Science and Technology, 2021, 119: 107094.
Tsuda, Y., Mori, O., Funase, R., Sawada, H., Yamamoto, T., Saiki, T., Endo, T., Yonekura, K., Hoshino, H., Kawaguchi, J. Achievement of IKAROS—Japanese deep space solar sail demonstration mission. Acta Astronautica, 2013, 82(2): 183–188.
Tsuda, Y., Ono, G., Mimasu, Y. Classification of solar sail attitude dynamics with and without angular momentum. Astrodynamics, 2019, 3(3): 207–216.
Mori, O., Okuizumi, N., Chujo, T., Takao, Y. Improvement of sail storage and deployment mechanism for spin-type solar power sail. Astrodynamics, 2020, 4(3): 223–231.
Pezent, J., Sood, R., Heaton, A. High-fidelity contingency trajectory design and analysis for NASA’s near-earth asteroid (NEA) Scout solar sail mission. Acta Astronautica, 2019, 159: 385–396.
Pezent, J. B., Sood, R., Heaton, A., Miller, K., Johnson, L. Preliminary trajectory design for NASA’s Solar Cruiser: A technology demonstration mission. Acta Astronautica, 2021, 183: 134–140.
McInnes, C. R. Solar Sailing: Technology, Dynamics and Mission Applications. London: Springer, 1999: 13–14, 46–54.
Zola, D., Circi, C., Vulpetti, G., Scaglione, S. Photon momentum change of quasi-smooth solar sails. Journal of the Optical Society of America A, 2018, 35(8): 1261–1271.
Pino, T., Circi, C., Vulpetti, G. Wrinkling analysis for small solar-photon sails: An experimental and analytic approach for trajectory design. Advances in Space Research, 2019, 63(11): 3675–3690.
Davoyan, A. R., Munday, J. N., Tabiryan, N., Swartzlander, G. A., Johnson, L. Photonic materials for interstellar solar sailing. Optica, 2021, 8(5): 722–734.
Firuzi, S., Gong, S. P. Refractive sail and its applications in solar sailing. Aerospace Science and Technology, 2018, 77: 362–372.
Firuzi, S., Song, Y., Gong, S. P. Gradient-index solar sail and its optimal orbital control. Aerospace Science and Technology, 2021, 119: 107103.
Aspnes, E., Milster, T. D., Visscher, K. Optical force model based on sequential ray tracing. Applied Optics, 2009, 48(9): 1642–1650.
Bassetto, M., Caruso, A., Quarta, A. A., Mengali, G. Optimal steering law of refractive sail. Advances in Space Research, 2021, 67(9): 2855–2864.
Ashkin, A. Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime. Biophysical Journal, 1992, 61(2): 569–582.
Swartzlander, G. A. Radiation pressure on a diffractive sailcraft. Journal of the Optical Society of America B, 2017, 34(6): C25–C30.
Swartzlander, G. A. Flying on a rainbow: A solar-driven diffractive sailcraft. Journal of the British Interplanetary Society, 2018, 71(4): 130–132.
Srivastava, P. R., Swartzlander, G. A. Optomechanics of a stable diffractive axicon light sail. The European Physical Journal Plus, 2020, 135(7): 570.
Serak, S. V., Roberts, D. E., Hwang, J. Y., Nersisyan, S. R., Tabiryan, N. V., Bunning, T. J., Steeves, D. M., Kimball, B. R. Diffractive waveplate arrays. Journal of the Optical Society of America B, 2017, 34(5): B56–B63.
Srivastava, P. R., Chu, Y.-J. L., Swartzlander, G. A. Stable diffractive beam rider. Optics Letters, 2019, 44(12): 3082–3085.
Chu, Y., Firuzi, S., Gong, S. P. Controllable liquid crystal diffractive sail and its potential applications. Acta Astronautica, 2021, 182: 37–45.
Chu, Y.-J. L., Meem, M., Srivastava, P. R., Menon, R., Swartzlander, G. A. Parametric control of a diffractive axicon beam rider. Optics Letters, 2021, 46(20): 5141–5144.
Dubill, A. L., Swartzlander, G. A. Circumnavigating the Sun with diffractive solar sails. Acta Astronautica, 2021, 187: 190–195.
Quarta, A. A., Mengali, G., Niccolai, L. Smart dust option for geomagnetic tail exploration. Astrodynamics, 2019, 3(3): 217–230.
Quarta, A. A., Mengali, G., Denti, E. Optimal inorbit repositioning of Sun-pointing smart dust. Acta Astronautica, 2019, 154: 278–285.
Niccolai, L., Bassetto, M., Quarta, A. A., Mengali, G. A review of Smart Dust architecture, dynamics, and mission applications. Progress in Aerospace Sciences, 2019, 106: 1–14.
Vulpetti, G., Circi, C., Pino, T. Coronal Mass Ejection early-warning mission by solar-photon sailcraft. Acta Astronautica, 2017, 140: 113–125.
Bassetto, M., Niccolai, L., Boni, L., Mengali, G., Quarta, A. A., Circi, C., Pizzurro, S., Pizzarelli, M., Pellegrini, R. C., Cavallini, E. Sliding mode control for attitude maneuvers of Helianthus solar sail. Acta Astronautica, 2022, 198: 100–110.
Caruso, A., Quarta, A. A., Mengali, G. Comparison between direct and indirect approach to solar sail circle-to-circle orbit raising optimization. Astrodynamics, 2019, 3(3): 273–284.
Quarta, A. A., Mengali, G., Bassetto, M. Optimal solar sail transfers to circular Earth-synchronous displaced orbits. Astrodynamics, 2020, 4(3): 193–204.
Heiligers, J., Fernandez, J. M., Stohlman, O. R., Wilkie, W. K. Trajectory design for a solar-sail mission to asteroid 2016 HO3. Astrodynamics, 2019, 3(3): 231–246.
Tsuda, Y., Takeuchi, H., Ogawa, N., Ono, G., Kikuchi, S., Oki, Y., Ishiguro, M., Kuroda, D., Urakawa, S., Okumura, S. I., et al. Rendezvous to asteroid with highly uncertain ephemeris: Hayabusa2’s Ryuguapproach operation result. Astrodynamics, 2020, 4(2): 137–147.
Mori, O., Matsumoto, J., Chujo, T., Matsushita, M., Kato, H., Saiki, T., Tsuda, Y., Kawaguchi, J., Terui, F., Mimasu, Y., et al. Solar power sail mission of OKEANOS. Astrodynamics, 2020, 4(3): 233–248.
Walker, M. J. H., Ireland, B., Owens, J. A set modified equinoctial orbit elements. Celestial Mechanics, 1985, 36(4): 409–419.
Walker, M. J. H. A set of modified equinoctial orbit elements. Celestial Mechanics, 1986, 38(4): 391–392.
Betts, J. T. Very low-thrust trajectory optimization using a direct SQP method. Journal of Computational and Applied Mathematics, 2000, 120(1–2): 27–40.
Wright, J. L. Space Sailing. Taylor & Francis, 1992: 223–233.
Bassetto, M., Quarta, A. A., Mengali, G., Cipolla, V. Trajectory analysis of a Sun-facing solar sail with optical degradation. Journal of Guidance, Control, and Dynamics, 2020, 43(9): 1727–1732.
Bassetto, M., Quarta, A. A., Mengali, G., Cipolla, V. Spiral trajectories induced by radial thrust with applications to generalized sails. Astrodynamics, 2021, 5(2): 121–137.
Mengali, G., Quarta, A. A. Optimal control laws for axially symmetric solar sails. Journal of Spacecraft and Rockets, 2005, 42(6): 1130–1133.
McInnes, C. R. Passive control of displaced solar sail orbits. Journal of Guidance, Control, and Dynamics, 1998, 21(6): 975–982.
Pathak, S. Photonics integrated circuits. In: Nanoelectronics. Amsterdam: Elsevier, 2019: 219–270.
Dachwald, B., Mengali, G., Quarta, A. A., MacDonald, M. Parametric model and optimal control of solar sails with optical degradation. Journal of Guidance, Control, and Dynamics, 2006, 29(5): 1170–1178.
Vulpetti, G., Apponi, D., Zeng, X. Y., Circi, C. Wrinkling analysis of solar-photon sails. Advances in Space Research, 2021, 67(9): 2669–2687.
Bianchi, C., Niccolai, L., Mengali, G., Quarta, A. A. Collinear artificial equilibrium point maintenance with a wrinkled solar sail. Aerospace Science and Technology, 2021, 119: 107150.
Mengali, G., Quarta, A. A. Optimal three-dimensional interplanetary rendezvous using non-ideal solar sail. Journal of Guidance, Control, and Dynamics, 2005, 28(1): 173–177.
Caruso, A., Niccolai, L., Quarta, A. A., Mengali, G. Effects of attitude constraints on solar sail optimal interplanetary trajectories. Acta Astronautica, 2020, 177: 39–47.
Mengali, G., Quarta, A. A. Rapid solar sail rendezvous missions to asteroid 99942 Apophis. Journal of Spacecraft and Rockets, 2009, 46(1): 134–140.
Stengel, R. F. Optimal Control and Estimation. Dover Publications, 1994: 222–254.
Betts, J. T. Survey of numerical methods for trajectory optimization. Journal of Guidance, Control, and Dynamics, 1998, 21(2): 193–207.
Bryson, A. E., Ho, Y. C. Applied Optimal Control. New York: Hemisphere Publishing Corporation, 1975: 71–89.
Shampine, L. F., Reichelt, M. W. The MATLAB ODE suite. SIAM Journal on Scientific Computing, 1997, 18(1): 1–22.
Palmeri, F., Tortorici, D., Laurenzi, S., Circi, C., Santonicola, M. G., Pizzarelli, M., Pizzurro, S., Pellegrini, R., Cavallini, E. Structural design of booms for the solar sail of helianthus sailcraft. In: Proceedings of the 73rd International Astronautical Congress, Paris, France, 2022.
Quarta, A. A., Mengali, G. Semi-analytical method for the analysis of solar sail heliocentric orbit raising. Journal of Guidance, Control, and Dynamics, 2012, 35(1): 330–335.
Sirohi, R., Moore, R. R., Deforrest, L. R., Thornton, M. S., Larson, K. L., Wenkert, D. D., Kazz, G. J. Psyche mission’s end-to-end information system architecture: Advantages, challenges, and operability. In: Space Operations. Cham: Springer, 2022: 107–139.
Elkins-Tanton, L., Asphaug, E., Bell, J., Bierson, C., Bills, B., Bottke, W., Courville, S., Dibb, S., Jun, I., Lawrence, D., et al. Distinguishing the origin of asteroid (16) Psyche. Space Science Reviews, 2022, 218(3): 17.
Jaumann, R., Bell, J., Polanskey, C., Raymond, C., Aspaugh, E., Bercovici, D., Bills, B., Binzel, R., Bottke, W., Christoph, J., et al. The psyche topography and geomorphology investigation. Space Science Reviews, 2022, 218(2): 7.
Collinson, G. A., Chen, L. J., Jian, L. K., Dorelli, J. The solar wind at (16) Psyche: Predictions for a metal world. The Astrophysical Journal Letters, 2022, 927(2): 202.
Funding
Open Access funding provided by Università di Pisa within the CRUI-CARE Agreement.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
The authors have no competing interests to declare that are relevant to the content of this article.
Additional information
Alessandro A. Quarta received his Ph.D. degree in aerospace engineering from the University of Pisa in 2005 and, currently, he is a professor of flight mechanics at the Department of Civil and Industrial Engineering of the University of Pisa. His main research areas include spaceflight simulation, spacecraft mission analysis and design, low-thrust trajectory optimization, solar sail, and E-sail dynamics and control.
Giovanni Mengali received his Doctor Engineer degree in aeronautical engineering in 1989 from the University of Pisa. Since 1990, he has been with the Department of Aerospace Engineering (now Department of Civil and Industrial Engineering) of the University of Pisa, first as a Ph.D. student, then as an assistant and an associate professor. Currently, he is a professor of space flight mechanics. His main research areas include spacecraft mission analysis, trajectory optimization, solar sails, electric sails, and aircraft flight dynamics and control.
Marco Bassetto received his Ph.D. degree in civil and industrial engineering at the Department of Civil and Industrial Engineering of the University of Pisa. From January 2020 to June 2021, he was the holder of a scholarship entitled “Dynamic analysis and control of an E-Sail” at the same department, where he also was a research assistant from July 2021 to June 2022, and he is currently an assistant professor of aerospace systems. His research activity focuses on trajectory design and attitude control of spacecraft propelled with low-thrust propulsion systems such as solar sails and electric solar wind sails.
Lorenzo Niccolai received his Ph.D. degree in industrial engineering (aerospace curriculum) from the University of Pisa in 2018. He was a research assistant at the Department of Civil and Industrial Engineering of the University of Pisa from 2019 to 2020. He is currently an assistant professor of spaceflight mechanics at the same department. His research interests include mission design, low-thrust trajectory analysis and control, with special attention on innovative propulsive concepts such as solar sails and electric solar wind sails.
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Quarta, A.A., Mengali, G., Bassetto, M. et al. Optimal interplanetary trajectories for Sun-facing ideal diffractive sails. Astrodyn 7, 285–299 (2023). https://doi.org/10.1007/s42064-023-0158-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s42064-023-0158-4