Complex sentence: Formerly I worked as a computer programmer and analyst specializing in Celestial Mechanics and Numerical Analysis, as a contractor, mostly for NASA, NRL, and other government agencies from 1982--2006.
Split into simpler sentences: Formerly I worked as a scientific software developer and analyst specializing in Celestial Mechanics and Numerical Analysis. I did that as a contractor for NASA, NRL, and other government agencies from 1982--2006.