After working on practical orbital mechanics at the Jet Propulsion Laboratory, he became a professor at the University of Texas at Austin.
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 the three-body problem, Broucke's doctoral research involved pioneering use of computer simulations to classify stable and unstable orbits.
[1] Later, he studied the anisotropic Kepler problem, a mathematical model of the motion of an electron trapped in a potential well.