His doctoral dissertation, The physical conditions pertaining to some possible supernova remnants, was supervised by Guido Münch.

[2] Prior to his selection for astronaut training, Parker was an associate professor of astronomy at the University of Wisconsin–Madison.

[3] He was a member of the Astronaut Support Crews for the Apollo 15 and 17 missions, and was the person to whom the final words spoken by a man standing on the surface of the Moon (Gene Cernan) were addressed.

[4][5] Parker was director of the Division of Policy and Plans for the Office of Space Flight at NASA Headquarters from January 1991 to December 1991.

In August 1997, Parker was named director of the NASA Management Office at the Jet Propulsion Laboratory in Pasadena, California.