STS-34 was a NASA Space Shuttle mission using the Atlantis orbiter. It was the 31st shuttle mission overall, and the fifth flight for Atlantis. STS-34 launched from Kennedy Space Center, Florida, on 18 October 1989, and landed at Edwards Air Force Base, California, on 23 October. During the mission, the Jupiter-bound Galileo probe was deployed into space.
The real tell on this particular patch is the size of the "USA" on the wing. This has a very large bold "USA".