John Burke was a Human scientist, the chief astronomer at the Royal Academy in Old Britain during the mid-21st century.
He was responsible for mapping the area of space that included Sherman's Planet in 2067. (TOS: "The Trouble with Tribbles"; ENT: "In a Mirror, Darkly, Part II")
During a 2268 mission briefing for this incident, Ensign Chekov mistakenly remembered Burke as being a Russian named "Ivan Burkoff." (TOS: "The Trouble with Tribbles")
It is possible that Burke was also the discoverer and namesake of the comet named Burke.