Preliminary Results on Optimal Establishment of Solar Sail Formations
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Preliminary Results on Optimal Establishment of Solar Sail Formations Khashayar Parsay1
· Hanspeter Schaub1
Published online: 10 May 2019 © American Astronautical Society 2019
Abstract The solar sail formation establishment problem is solved for Earth-centered SunSynchronous orbits using optimal control theory, assuming that the deputy solar sail is capable of changing its attitude and that the chief solar sail flies in a Sunsynchronous orbit and does not employ active control. Because there is no analytic solution, numerical techniques are used to solve the optimal formation establishment problem. This paper demonstrates the existence of locally-optimal solutions to the solar sail formation establishment problem and provides a quantification of the solar sail’s control effort. Keywords Solar sail · Formation flying · Magnetosphere Nomenclature Solar radiation pressure acceleration [km/s2 ] as œ Array containing classical orbital elements [a, e, ω, M]T . a: semi-major axis [km], e: eccentricity, ω: argument of perigee [rad], M: mean anomaly [rad] δœ Differential orbital elements of deputy with respect to chief λs Sun longitude measured from vernal equinox [rad] k Characteristic acceleration of solar sail [km/s2 ] O Local-vertical-local-horizontal (LVLH) frame c Denotes the chief solar sail Electronic supplementary material The online version of this article (https://doi.org/10.1007/s40295-018-00147-y) contains supplementary material, which is available to authorized users. Khashayar Parsay
[email protected] Hanspeter Schaub [email protected] 1
University of Colorado (Boulder), Boulder, CO, USA
The Journal of the Astronautical Sciences (2019) 66:32–45
d RE SRP
33
Denotes the deputy solar sail Earth radius Solar radiation pressure
Introduction The ability of solar sails to create non-Keplerian orbits can significantly increase the science gain of certain space missions. Past and current magnetosphere missions employ conventional spacecraft formations for in situ observations of the geomagnetic tail. Conventional spacecraft flying in inertially fixed Keplerian orbits are only aligned with the geomagnetic tail once per year, since the geomagnetic tail is always aligned with the Earth-Sun line, and therefore, rotates annually. National Aeronautics and Space Administration’s (NASA) Time History of Events and Macroscale Interactions during Substorms (THEMIS), Magnetospheric Multi-Scale (MMS), and Radiation Belt Storm Probes (RBSP) missions, along with European Space Agency’s (ESA) Cluster II mission are some of the currently active magnetosphere missions that employ multiple spacecraft flying in Keplerian orbits to achieve their scientific objectives [1–3]. As illustrated in Fig. 1, solar sails are able to artificially create sun-synchronous orbits such that the orbit apse line remains aligned with the geomagnetic tail line throughout the entire year [4–6]. This continuous presence in the geomagnetic tail can significantly increase the science phase for magnetosphere missions. McInnes an
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