Date of Award

Summer 6-4-2014

Document Type


Degree Name

Doctor of Philosophy (PhD)


Aerospace Engineering Sciences

First Advisor

Hanspeter Schaub

Second Advisor

Zoltan Sternovsky

Third Advisor

Je rey Parker


The high value of operating in the geostationary ring, coupled with increasing numbers of orbital debris, highlights the need for GEO debris remediation techniques. One recent proposed technique for GEO debris mitigation is the electrostatic tractor. Here, a tug vehicle approaches a target debris object and emits a focused electron beam onto it. This results in a negative charge on the debris, and a positive charge on the tug vehicle. Due to the near proximity of the highly charged objects (20 meters or less) an attractive electrostatic force on the order of milliNewtons results. This electrostatic force is used in conjunction with low thrusting by the tug vehicle to tow the debris object into a disposal orbit 200-300 kilometers above the GEO belt.

During the tugging period, the charged relative motion between tug and deputy is stabilized through a feedback control law. This is accomplished using a novel relative motion description that isolates separation distance from the relative orientation. The equations of motion for the relative motion description are derived from the Clohessy-Wiltshire equations, assuming the debris object is in a nearly circular orbit. Lyapunov stability theory is used to derive an asymptotically stable control law for the tug thrusters during the towing period. The control law requires an estimate of the electrostatic force magnitude, and the impacts of improperly modeled charging on control response are determined. If the electrostatic force is under-predicted too severely, a collision may result. A bound on the control gains is determined to prevent such a collision.

Expected reorbiting performance levels achievable with the electrostatic tractor are computed. An open-loop analytical performance study is performed where variational equations are used to predict how much general orbital elements may be changed using the electrostatic tractor over one orbital period for a towed object at geosynchronous altitude. In contrast to earlier work, eccentric orbits and plane changes are also considered. Requirements on relative positioning of the tug and debris for various orbit corrections are identified for the different orbit corrections. In some cases, the tug must maneuver around the debris at particular locations in the orbit, but the incurred performance losses during this repositioning are minimal. Co-planar reorbiting maneuvers with corrections of several kilometers per day are achievable, but large scale plane changes are not.

A first-order analytic current model is used to calculate the charging on tug debris during the charge transfer process. The model includes plasma currents, photoelectron current, secondary electron emission, and electron beam current. The effects of nominal changes (as a function of local time) in GEO space weather conditions on tractor performance are characterized. While the electron beam current can be modified to compensate for these changes, maintaining a fixed beam current achieves similar performance. The impacts of the relative sizes of tug and deputy are studied to determine thresholds where charge transfer is no longer possible, and the effects on tractor performance are considered. The simultaneous emission of an electron beam (onto the debris) and an ion beam (into space) is considered as a means for improving tractor performance. For smaller tug vehicles, this simultaneous emission allows for significant performance increases, enabling the tug to tow larger debris objects. The benefits are not as pronounced for larger tug vehicles. The debris object emits photoelectrons and secondary electrons that may be recaptured by the positively charged tug. NASCAP-2K is used to provide an estimate about the severity of this back flux. It is not found to hinder performance of the electrostatic tractor. Overall, the study supports the feasibility of the electrostatic tractor for GEO debris remediation, and helps to identify areas for further research.