Texas A&M researchers uncover elusive answer to Edelbaum’s optimal impulse question

In 1967, prominent aerospace engineer T.N. Edelbaum wanted to know how many velocity impulses – and in what direction and at what time – must be used to allow a spacecraft to “fly” from its starting point to reach a specified destination with a minimum total impulse. It’s an issue that arises in virtually every space flight mission, and Dr. John Junkins and his research team have finally uncovered the rigorous process to answer it over 50 years later.

“How do you optimally fly from A to B?” asked Junkins, distinguished professor and holder of the Royce E. Wisenbaker Chair in the Department of Aerospace Engineering at Texas A&M University. “That's really the kind of problem I'm dealing with in this research, and that’s a tough problem that requires us to combine judicious control forces with gravitational field effects to fly from one moving object to another.”

Recent advances in low-thrust propulsion means that some spacecrafts are literally propelling for decades of powered flight between objects separated by many astronomical units, so the trajectory design problems are getting more difficult as a consequence.

Working alongside Dr. Ehsan Taheri, an aerospace engineering adjunct assistant professor, Junkins’ formulations and algorithms have led to a new way to determine continuous thrust, minimum fuel orbit transfers. By varying the theoretical maximum-thrust allowed by x amount, their approach ultimately reveals the solution for any maximum thrust level. As the theoretical maximum thrust is allowed to approach infinity, longer coasts appear between ever shorter optimal thrust arcs. The limiting case is the answer to Edelbaum’s optimal impulse question for any feasible orbit transfer.

This research is published in a special edition of the Journal of the Astronautical Sciences dedicated to the “50 glorious orbits” of Junkins’ career to date, and it also helped to earn him the Robert H. Goddard Astronautics Award from the American Institute of Aeronautics and Astronautics in May 2019.

“The work Taheri and I did extended and unified existing methodology,” said Junkins, who was also recently awarded a 2020 Texas A&M Engineering Experiment Station Research Impact Award for his contribution to the development of his space navigation and control research. He is also director of the Hagler Institute for Advanced Study and a member of the National Academy of Engineering.

“It’s really amazing that many researchers and flight control engineers worked on this for a half century,” continued Junkins. “And, even though I was born a bit too late to be a key player in the Apollo program during Edelbaum’s time, I wasn't born too late to bring closure to an important question he raised. In the process, I established new tools to design space missions optimally and with computational efficiency.”