Date of Award

Spring 1-1-2016

Document Type


Degree Name

Doctor of Philosophy (PhD)


Aerospace Engineering Sciences

First Advisor

Hanspeter Schaub

Second Advisor

Daniel Scheeres

Third Advisor

Trevor Williams

Fourth Advisor

Dale Lawrence

Fifth Advisor

Webster Cash


Current and past missions that study the Earth's geomagnetic tail require multiple spacecraft to fly in formation about a highly eccentric Keplerian reference orbit that has its apogee inside a predefined science region of interest. Because the geomagnetic tail is directed along the Sun-Earth line and therefore rotates annually, inertially fixed Keplerian orbits are only aligned with the geomagnetic tail once per year. This limitation reduces the duration of the science phase to less than a few months annually.

Solar sails are capable of creating non-Keplerian, Sun-synchronous orbits that rotate with the geomagnetic tail. A solar sail flying in a Sun-synchronous orbit will have a continuous presence in the geomagnetic tail throughout the entire year, which significantly improves the in situ observations of the magnetosphere. To achieve a Sun-synchronous orbit, a solar sail is required to maintain a Sun-pointing attitude, which leads to the artificial precession of the orbit apse line in a Sun-synchronous manner, leaving the orbit apogee inside the science region of interest throughout entire the year.

To study the spatial and temporal variations of plasma in the highly dynamic environment of the magnetosphere, multiple spacecraft must fly in a formation. The objective for this dissertation is to investigate the feasibility of solar sail formation flying in the Earth-centered, Sun-synchronous orbit regime. The focus of this effort is to enable formation flying for a group of solar sails that maintain a nominally fixed Sun-pointing attitude during formation flight, solely for the purpose of precessing their orbit apse lines Sun-synchronously. A fixed-attitude solar sail formation is motivated by the difficulties in the simultaneous control of orbit and attitude in flying solar sails.

First, the secular rates of the orbital elements resulting from the effects of solar radiation pressure (SRP) are determined using averaging theory for a Sun-pointing attitude sail. These averaged rates are used to analytically derive the necessary conditions for a drift-free solar sail formation in Sun-synchronous orbits, assuming a fixed Sun-pointing orientation for each sail in formation. Next, the problem of formation design is solved using nonlinear programming for optimal two-craft, three-craft, and four-craft solar sail formations, in terms of formation quality and stability. Finally, the problem of formation establishment is addressed using optimal control theory, assuming that the sails are capable of making small changes to their orientations with respect to the Sun. These studies demonstrate the feasibility of solar sail formation flying for exploring the geomagnetic tail and improve upon previous work, which only considered unnatural relative motions that require continuous use of active control to remain in formation.

Triangle_OneOrbit_160km.avi (310245 kB)