Nagel became a NASA astronaut in August 1979.[7] His technical assignments included: backup T-38chase pilot for STS-1; support crew and backup entry spacecraft (CAPCOM) for STS-2; support crew and primary entry CAPCOM for STS-3; software verification at the Shuttle Avionics Integration Laboratory (SAIL) and the Flight Simulation Laboratory (FSL); representing the Astronaut Office in the development of a crew escape system for the Space Shuttle; Acting Chief of the Astronaut Office (1991). With the completion of his fourth flight, Nagel had logged a total of 723 hours in space. Nagel retired from the Air Force, effective February 28, 1995. He retired from the Astronaut Office, effective March 1, 1995, to assume the full-time position of Deputy Director for Operations Development, Safety, Reliability, and Quality Assurance Office, Johnson Space Center, Houston, Texas. In September 1996, Nagel transferred to Aircraft Operations Division where he performed duties as a Research Pilot. Nagel was a veteran of four space flights (STS-51-G and STS-61-A in 1985, STS-37 in 1991, and STS-55 in 1993) as described below:
Nagel first flew as a mission specialist on STS-51G, which launched from the Kennedy Space Center, Florida, on June 17, 1985. The crew aboard the Shuttle Discovery deployed communications satellites for Mexico (Morelos), the Arab League (Arabsat), and the United States (AT&T Telstar). They used the Remote Manipulator System (RMS) to deploy and later retrieve the SPARTAN satellite which performed 17 hours of x-rayastronomy experiments while separated from the Space Shuttle. In addition, the crew activated the Automated Directional Solidification Furnace (ADSF), six "Getaway Specials," participated in biomedical experiments, and conducted a laser tracking experiment as part of the Strategic Defense Initiative. After completing approximately 170 hours of space flight, Discovery landed at Edwards Air Force Base, California, on June 24, 1985.
Nagel then flew as pilot on STS-61A, the West German D-1 Spacelab mission, which launched from Kennedy Space Center, Florida, on October 30, 1985. This mission was the first in which payload activities were controlled from outside the United States. More than 75 scientific experiments were completed in the areas of physiological sciences, materials processing, biology, and navigation. After completing 111 orbits of the Earth, Shuttle Challenger landed at Edwards Air Force Base, California on November 6, 1985.
On his third flight, Nagel was commander of STS-37, which launched into orbit on April 5, 1991, from Kennedy Space Center, Florida, and landed on April 11, 1991, at Edwards Air Force Base, California. During this mission, the crew aboard the Shuttle Atlantis deployed the Compton Gamma Ray Observatory for the purpose of exploring gamma ray sources throughout the universe. The crew and conducted the first scheduled space walk in more than five and one-half years, and the first successful unscheduled spacewalk to free a stuck antenna on the satellite.
Nagel also served as commander of STS-55, the German D-2 Spacelab mission. After launching on April 26, 1993, on the Shuttle Columbia; the crew landed 10 days later on May 6, 1993, at Edwards Air Force Base, California. During the ambitious mission 89 experiments were performed in many disciplines such as materials processing, life sciences, robotics, technology, astronomy and earth mapping.
In 2011, Nagel and his wife Linda moved to Columbia, Missouri, where they both were teaching at the University of Missouri. Nagel was a retention specialist in the College of Engineering and instructor in the Mechanical and Aerospace Engineering Department, specializing in aerospace propulsion; Godwin was a professor in the physics department, specializing in astronomy.