Dr. Musgrave first flew on STS-6, which launched from the Kennedy Space Center, Florida, on April 4, 1983, and landed at Edwards Air Force Base, California, on April 9, 1983. During this maiden voyage of Space Shuttle Challenger, the crew performed the first Shuttle deployment of an IUS/TDRS satellite, and Musgrave and Don Peterson conducted the first Space Shuttle extravehicular activity (EVA) to test the new space suits and construction and repair devices and procedures. Mission duration was 5 days, 23 minutes, 42 seconds.
On STS-51F/Spacelab-2, the crew aboard Challenger launched from the Kennedy Space Center, Florida, on July 29, 1985, and landed at Edwards Air Force Base, California, on August 6, 1985. This flight was the first pallet-only Spacelab mission, and the first mission to operate the Spacelab Instrument Pointing System (IPS). It carried 13 major experiments in astronomy, astrophysics, and life sciences. During this mission, Dr. Musgrave served as the systems engineer during launch and entry, and as a pilot during the orbital operations. Mission duration was 7 days, 22 hours, 45 minutes, 26 seconds.
On STS-33, he served aboard the Space Shuttle Discovery, which launched at night from the Kennedy Space Center, Florida, on November 22, 1989. This classified mission operated payloads for the Department of Defense. Following 79 orbits, the mission concluded on November 27, 1989, with a landing at sunset on Runway 04 at Edwards Air Force Base, California. Mission duration was 5 days, 7 minutes, 32 seconds.
STS-44 also launched at night on November 24, 1991. The primary mission objective was accomplished with the successful deployment of a Defense Support Program (DSP) satellite with an Inertial Upper Stage (IUS) rocket booster. In addition the crew also conducted two Military Man in Space Experiments, three radiation monitoring experiments, and numerous medical tests to support longer duration Shuttle flights. The mission was concluded in 110 orbits of the Earth with Atlantis returning to a landing on the lakebed at Edwards Air Force Base, California, on December 1, 1991. Mission duration was 6 days, 22 hours, 50 minutes, 42 seconds.
STS-61 was the first Hubble Space Telescope (HST) servicing and repair mission. Following a night launch from Kennedy Space Center on December 2, 1993, the Endeavour rendezvoused with and captured the HST. During this 11-day flight, the HST was restored to its full capabilities through the work of two pairs of astronauts during a record 5 spacewalks. Dr. Musgrave performed 3 of these spacewalks. After having travelled 4,433,772 miles in 163 orbits of the Earth, Endeavour returned to a night landing in Florida on December 13, 1993. Mission duration was 10 days, 19 hours, 59 minutes. On STS-80 (November 19 to December 7, 1996), the crew aboard Space Shuttle Columbia deployed and retrieved the Wake Shield Facility (WSF) and the Orbiting Retrievable Far and Extreme Ultraviolet Spectrometer (ORFEUS) satellites. The free-flying WSF created a super vacuum in its wake in which to grow thin film wafers for use in semiconductors and the electronics industry. The ORFEUS instruments, mounted on the reusable Shuttle Pallet Satellite, studied the origin and makeup of stars. In completing this mission he logged a record 278 earth orbits, traveled over 7 million miles in 17 days, 15 hours, 53 minutes.


