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Using a Graduate Student Developed Trajectory Generation Program to Facilitate Undergraduate Spacecraft / Mission Capstone Design Projects

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2013 ASEE Annual Conference & Exposition


Atlanta, Georgia

Publication Date

June 23, 2013

Start Date

June 23, 2013

End Date

June 26, 2013



Conference Session

Aerospace Division Technical Session 2

Tagged Division


Page Count


Page Numbers

23.1303.1 - 23.1303.16



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Paper Authors


Martin James Brennan University of Texas, Austin

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Martin James Brennan developed a passion for Science and Mathematics at Mississippi State University (MSU), where he met his wife Holly. In December 2008, he received a Bachelor of Science degree in Aerospace Engineering with an emphasis in Astrodynamics, a Bachelor of Science degree in Physics, and a minor in Mathematics. He began his graduate career in Aerospace Engineering with a focus in Orbital Mechanics in January 2009 at the University of Texas at Austin, where he is pursuing his Ph.D. He enjoys flying radio controlled aircraft, tinkering with projects, and loving life with his wife.

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Adam Wayne Nokes The University of Texas at Austin

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Adam Nokes is currently a doctoral student at the University of Texas and resides in Austin with his wife Travis and dog Motley. His educational experience includes a B.S. from Cornell University in Mechanical and Aerospace Engineering, an M.Eng. from Cornell in Engineering Management, and an M.S. from the University of Colorado at Boulder in Aerospace Engineering. His current research focus is trajectory optimization and mission design. Nokes is also a teaching assistant for the undergraduate spacecraft mission design course. He enjoys fishing, hiking and biking in the great outdoors any chance that he gets.

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Wallace T. Fowler P.E. University of Texas, Austin

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Wallace Fowler holds the Paul D. and Betty Robertson Meek Centennial Professorship in the Department of Aerospace Engineering and Engineering Mechanics at the University of Texas at Austin, where he has been on the faculty since 1965. His areas of teaching and research are dynamics, orbital mechanics, spacecraft and space mission design, and aircraft flight testing. He is the recipient of several teaching awards, including the AIAA/ASEE John Leland Atwood Award and the ASEE Fred Merryfield Design Award. He is a member of the University of Texas Academy of Distinguished Teachers. He is a fellow of both the AIAA and the ASEE. He served as president of ASEE of 2000-2001.

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Using a Graduate Student Developed Trajectory Generation Program to Facilitate Undergraduate Spacecraft / Mission Capstone Design Projects A stumbling block in undergraduate spacecraft/mission design projects is the earlygeneration of plausible baseline trajectories for missions outside of Earth orbit. Many studentteams rely almost totally on the literature for their baseline trajectories, and often do not progressvery far beyond these baseline trajectories in their final designs. The problem is that trajectorydesign for interplanetary missions has many options and senior aerospace engineering studentshave neither the experience nor the time to explore the options well. In 2010-2011, the lead author developed a robust preliminary trajectory generationprogram for his MS thesis project. The goal was to develop a program that could be used byundergraduate students to explore the solution space for many interplanetary missions. Thisprogram is based on three dimensional conic trajectories and features deep space maneuvers,powered and unpowered planetary flybys, and JPL planetary ephemerides. The program hasbeen used to replicate the Voyager missions, the Cassini mission, the Ulysses mission, the Junomission, etc. A pedagogical strength of allowing students to use the program is that the trajectory toolsused are only those covered in the basic undergraduate orbital mechanics course. These are twobody motion, gravity assists, impulsive maneuvers, and Lambert targeting. The program takes astudent provided initial mission architecture (powered/unpowered flyby sequence, estimates of{start date, maneuver dates, arrival date}) and creates a Lambert targeted baseline missiontrajectory. The program then uses one of two MatLab optimizing procedures to move the eventdates, while allowing the possibility of inserting deep space maneuvers between flybys. Theresult is a local optimum in the vicinity of the initial estimates that conforms to the initialmission flyby sequence. The way that the program is used in the classroom is as follows. The graduate studentwho wrote the program (the first author) and the design class teaching assistant (the secondauthor) create a sample trajectory with one of the logical mission flyby sequences for eachstudent design project. The code then enables the student to search over a wide range of potentialdeparture dates and total transit times. Though optimization procedures gravitate towards localsolutions within the neighborhood of initial inputs, an expansive search routine implemented bythe second author provides insight into the range of inputs that produce desirable missionparameters. Further understanding is gained by plotting procedures that compare the top resultsside by side, allowing the student teams to select the most preferable for their chosen mission.The baseline trajectory and search range are used as a tutorial tool for the student(s) in the designteam who are responsible for trajectory generation on their team’s mission. Each team is givenits own copy of the program and must decide on its own mission architecture and generate itsown trajectories. The following figures display a sample of the three dimensional trajectoryviewing capability that is customizable for any vantage point. Figure 1: Cassini mission trajectory incorporates Venus, Earth, and Jupiter unpowered gravity assists and a deep space maneuver to arrive at SaturnFigure 2: Ulysses mission utilizes a Jupiter gravity assist to dramatically change its orbital plane and enable viewing the Sun and solar system from a new perspective

Brennan, M. J., & Nokes, A. W., & Fowler, W. T. (2013, June), Using a Graduate Student Developed Trajectory Generation Program to Facilitate Undergraduate Spacecraft / Mission Capstone Design Projects Paper presented at 2013 ASEE Annual Conference & Exposition, Atlanta, Georgia. 10.18260/1-2--22688

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