An astronomical survey was a type of astronomy mission.
In 2365, Dr. Katherine Pulaski disputed Captain Jean-Luc Picard's insistence that he was needed to oversee an astronomical survey of a new pulsar cluster in the Epsilon IX sector, as it was to be done by USS Enterprise-D's science officers. (TNG: "Samaritan Snare")
In 2375, Seven of Nine didn't find USS Voyager's upcoming astronomical survey to be exciting, merely routine. (VOY: "Drone")
In 2376, Captain Kathryn Janeway requested Mortimer Harren's assistance on an astronomical survey mission in the Delta Flyer. (VOY: "Good Shepherd")