Peterson's education has included receiving a Bachelor of Science degree from the United States Military Academy at West Point in 1955, and a Master's Degree in Nuclear Engineering from the Air Force Institute of Technology, Wright-Patterson Air Force Base in 1962.

After graduating from West Point, Peterson was assigned various posts including flight instructor, military training officer with the Air Training Command, nuclear systems analyst and fighter pilot. In total, he has logged over 5,300 hours flying time-including more than 5,000 hours in jet aircraft. It was during his career with the Air Force that Peterson was awarded the Air Force Commendation Medal and the Meritorious Service Medal.

In September of 1969, Peterson became a NASA astronaut. He was one of the third groups of astronauts assigned to the USAF Manned Orbiting Laboratory Program. Peterson retired from the USAF with the rank of colonel after having completed more than 24 years of active service. Upon retirement, Peterson continued his NASA assignment as a civilian astronaut.

Peterson was a mission specialist on STS-6, which launched on April 4, 1983. During this maiden voyage of the spacecraft Challenger, the STS-6 crew conducted numerous experiments in materials processing, recorded lightning activities, deployed the first Tracking and Data Relay Satellite (TRRS-A), and activated three Getaway Specials. Peterson, along with Story Musgrave, conducted an EVA to test the validity of the newly redesigned space suits, tools and Shuttle airlock for future space shuttle construction and repairs.

After successfully completing his mission, Peterson resigned from NASA in November 1984, and since that time has worked as a consultant in the area of manned aerospace operations.