Solar Sailing pp 112-170 | Cite as

# Solar sail orbital dynamics

## Abstract

The orbital dynamics of solar sail spacecraft are similar in many respects to the orbital dynamics of other spacecraft utilising low thrust propulsion. That is, a small continuous thrust is used to modify the spacecraft orbit over an extended period of time. However, a solar-electric propulsion system may orient its thrust vector in any direction, whereas solar sails are constrained to thrust vector orientations within 90° of the Sun-line. For some mission applications this constraint leads to significant differences between the spacecraft trajectories. For example, to transfer from a prograde to a retrograde orbit, a solar-electric propulsion system may direct its thrust vector perpendicular to the Sun-line to lose prograde angular momentum and then gain retrograde angular momentum. However, for solar sails the transfer is made by increasing the spacecraft ecliptic inclination to greater than 90° by alternately orienting the solar radiation pressure force vector above and below the ecliptic plane. The analysis of such cranking orbit manoeuvres is of importance for some mission applications for both initial mission design and sail sizing. It is this type of preliminary orbit analysis that will be addressed in this chapter. In particular, closed form analytical solutions will be derived wherever possible to provide physical insight. Such analytical solutions also provide a simple and effective means of generating trajectory data for preliminary mission design. More specialised optimal trajectories which require a numerical solution will also be discussed later in this chapter.

## Keywords

Solar Radiation Pressure Solar Sail Orbit Radius Orbital Dynamic Spiral Angle## Preview

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## Further Reading

## Sun-centred trajectories

- Bacon, R.H., ‘Logarithmic Spiral — an Ideal Trajectory for an Interplanetary Vehicle with Engines of Low Sustained Thrust’,
*American Journal of Physics*,**27**, 12–18, 1959.Google Scholar - Tsu, T.C., ‘Interplanetary Travel by Solar Sail’,
*American Rocket Society Journal*,**29**, 422–427, 1959.Google Scholar - London, H.S., ‘Some Exact Solutions of the Equations of Motion of a Solar Sail With a Constant Setting’,
*American Rocket Society Journal*,**30**, 198–200, 1960.zbMATHGoogle Scholar - Kiefer, J.W., ‘Feasibility Considerations for a Solar-Powered Multi-Mission Probe’,
*Proceedings of the 15th International Astronautical Congress*, Warsaw,**1**, 383–416, 1965.Google Scholar - Sauer, C.G., ‘A Comparison of Solar Sail and Ion Drive Trajectories for a Halley’s Comet Rendezvous’, AAS-77-4,
*AAS/AIAA Astrodynamics Conference*, September 1977.Google Scholar - Van der Ha, J.C. & Modi, V.J., ‘Long-term Evaluation of Three-Dimensional Heliocentric Solar Sail Trajectories with Arbitrary Fixed Sail Setting’,
*Celestial Mechanics*,**19**, 113–138, 1979.ADSzbMATHCrossRefGoogle Scholar - Koblik, V.V.
*et al.*, ‘Controlled Solar Sailing Transfer Flights into Near-Sun Orbits Under Restrictions on Sail Temperature’,*Cosmic Research*,**34**, 572–578, 1996.ADSGoogle Scholar

## Minimum time trajectories

- Zhukov, A.N. & Lebedev, V.N., ‘Variational Problem of Transfer Between Heliocentric Circular Orbits by Means of a Solar Sail’,
*Cosmic Research*,**2**, 41–44, 1964.Google Scholar - Sauer, C.G., ‘Optimum Solar Sail Interplanetary Trajectories’, AIAA-76-792,
*AAS/ AIAA Astrodynamics Conference*, August 1976.Google Scholar - Green, A.J., ‘Optimal Escape Trajectory From a High Earth Orbit by Use of Solar Radiation Pressure’, T-652, Master of Science Thesis, Massachusetts Institute of Technology, 1977.Google Scholar
- Sackett, L.L. & Edelbaum, T.N., ‘Optimal Solar Sail Spiral to Escape’,
*AAS/AIAA Astrodynamics Conference*, September 1977.Google Scholar - Sun, H. & Bryson, A.E., ‘Minimum Time Solar Sailing from Geosynchronous Orbit to the Sun-Earth L
_{2}Point’, AIAA-92-4657,*AAS/AIAA Astrodynamics Conference*, August 1992.Google Scholar - Simon, K. & Zakharov, Y., ‘Optimisation of Interplanetary Trajectories with Solar Sail’, IAF-95-A.2.08,
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## Planet-centred trajectories

- Sands, N., ‘Escape from Planetary Gravitational Fields by use of Solar Sails’,
*American Rocket Society Journal*,**31**, 527–531, 1961.Google Scholar - Fimple, W.R., ‘Generalised Three-Dimensional Trajectory Analysis of Planetary Escape by Solar Sail’,
*American Rocket Society Journal*,**32**, 883–887, 1962.zbMATHGoogle Scholar - Isayev, Y.N. & Kunitsyn, A.L., ‘To the Problem of Satellite’s Perturbed Motion Under the Influence of Solar Radiation Pressure’,
*Celestial Mechanics*,**6**, 44–51, 1972.ADSCrossRefGoogle Scholar - Van der Ha, J.C. & Modi, V.J.,’ solar Pressure Induced Orbital Perturbations and Control of a Satellite in an Arbitrary Orbit’, AIAA-77-32,
*AIAA 15th Aerospace Sciences Meeting*, January 1977.Google Scholar - Fekete, T.A.
*et al.*, ‘Trajectory Design for Solar Sailing from Low-Earth Orbit to the Moon’, AAS-92-184,*AAS/AIAA Spaceflight Mechanics Meeting*, February 1992.Google Scholar

## Miscellaneous

- Roy, A.E.,
*Orbital Motion*, Adam Hilger, Bristol, 1982.Google Scholar - Battin, R.H.,
*An Introduction to the Methods and Mathematics of Astrodynamics*, AIAA Education Series, New York, 1987.zbMATHGoogle Scholar