Broucke was born on a farm in Veurne. He studied at the Catholic University of Leuven, earning bachelor's and master's degrees in mathematics in 1955 and 1957 respectively, under the mentorship of Georges Lemaître. After completing his military service he worked for the oil industry while earning a second master's degree, in operations research, from the University of Brussels in 1960.[1]
In 1975, Broucke moved to the University of Texas at Austin as an associate professor of aerospace engineering and engineering mechanics. At Austin, he helped found the Texas Institute for Computational Mechanics in 1976.[1]
In the three-body problem, Broucke's doctoral research involved pioneering use of computer simulations to classify stable and unstable orbits.[1] He investigated what happens to this classification for earth–moon–satellite systems in the limit as the ratio of earth to moon mass approaches zero; his conjecture about this limiting behavior, "Broucke's principle", was finally proven correct in 1981 by Lawrence Perko.[1][2] As part of this work, he also developed symbolic computation methods for handling Poisson series.[1]
Later, he studied the anisotropic Kepler problem, a mathematical model of the motion of an electron trapped in a potential well. As he showed, this system is not purely chaotic: it has periodic orbits as well. He also studied the use of gravity assist in finding efficient flight plans for space probes.[1]
Broucke, R. (August 1988), "The celestial mechanics of gravity assist", Astrodynamics Conference, American Institute of Aeronautics and Astronautics, doi:10.2514/6.1988-4220
Broucke, Roger A. (July 2003), "Solution of the elliptic rendezvous problem with the time as independent variable", Journal of Guidance, Control, and Dynamics, 26 (4): 615–621, Bibcode:2003JGCD...26..615B, doi:10.2514/2.5089
^ abcdefghijk"Roger A. Broucke (1932–2005)", Faculty Memorials, The University of Texas at Austin Department of Aerospace Engineering and Engineering Mechanics, retrieved 2017-11-10
