Research Will Explore Novel Method to Improve Space Travel Efficiency
A new $100,000 grant from the National Aeronautics and Space Administration (NASA)’s Jet Propulsion Lab (JPL) will support faculty and students at Yeshiva University as they develop a revolutionary space travel technique that will enable spacecraft to save time, energy and cost during their journeys.
Dr. Marian Gidea, chair of the mathematics department at Stern College for Women and professor in YU’s graduate programs in mathematical sciences, has been awarded the grant in conjunction with JPL and the Georgia Institute of Technology as part of NASA’S Strategic University Research Partnership program. Together with his students, Gidea is exploring how a well-known concept in mathematics, the Arnold diffusion mechanism, could be applied to the design of space routes to cut back on the long detours associated with more recent fuel-efficient paths.
“In space dynamics, the intertwining gravitational fields of the earth, moon, sun and planets determine certain ‘routes,’ which are like space superhighways, that a spacecraft can follow without using any rocket fuel,” said Gidea, noting that several space missions had already exploited this concept. “In fact, current Yeshiva faculty member Dr. Edward Belbruno was the first scientist ever to the find such a low-energy orbit, from the earth to moon. However, these types of routes may require large detours and may take a long time. The main objective of this collaborative research with NASA’s Jet Propulsion Laboratory is how to accelerate these orbits.”
According to Gidea, the key lies in application of the Arnold diffusion mechanism, which has been the focus of his work for many years. “In a nutshell, the Arnold diffusion mechanism states that small amounts of force, applied at the right moments, can produce large effects over time,” he said. “A familiar example is pushing a playground swing: with a tiny push on the swing each time it comes back to you, the amplitude of the swing will keep increasing. In the case of space missions, this small forcing translates into firing the rocket’s engine at the right place and the right moment to accelerate the orbit when the natural dynamics is slow; for the rest of the time, the spacecraft will coast along the ‘space superhighway’ at zero cost.”
Besides its implications for space travel, the Arnold diffusion mechanism can also be used to understand the long-term dynamics of comets and asteroids. Gidea’s doctoral students, Wai-Ting Lam and Maxwell Musser, are exploring possible applications of this idea in their research. Lam is modeling the dynamics of a spacecraft near Jupiter’s Trojan asteroid, while Musser works on modeling the dynamics of Jupiter’s comet Oterma. Both teach undergraduate mathematics courses at Yeshiva College and Stern College for Women in addition to their research.
“Before attending YU, I was interested in the theoretical side of mathematics—however, since I started my research, I’ve learned that the application of mathematics in the sciences, particularly celestial mechanics, can generate interesting and challenging problems,” said Musser. “Professor Gidea has been very generous with his time. I’m able to ask him questions and meet with him frequently. He has also provided with some excellent resources – including textbooks and articles – that have aided my work.”
“Since the research was related to spatial missions, which I was fascinated by when I was young, I was excited to join the program,” said Lam, who completed an internship at JPL this summer. “My internship was a very unique experience which allowed me to learn about different cutting-edge research, meet experts who work in the field and contribute as a mathematician to upcoming spatial missions. Since Dr. Gidea is very active in the field, there are many opportunities for us to attend conferences and workshops in other schools.”
In addition to supporting Gidea and his students’ research, the grant will also allow them to organize training workshops and video lectures and facilitate other student visits and internships at JPL. “Ultimately, we hope our work could have applications for New Europa Mission/Lander options, ARM targets, cost savings for tours of outer planets like Jupiter, Saturn, Neptune, and Uranus, and asteroid diversion strategies, among other things,” said Gidea. “We also hope that, in the long run, it will attract young, talented professionals to NASA’s workforce.”