WRONG ARPT APCH AND LNDG IN AN EMB120. NAV ERROR; HDG TRACK POS DEV.

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THIS WAS A SCHEDULED FLT FROM AEX TO GTR. ZME GAVE US A DSCNT FROM FL210 TO 2000 FT AND ASKED US TO RPT THE FIELD IN SIGHT. THE FO (WHO WAS FLYING) AND I BOTH USED THE NAVAIDS AVAILABLE; INITIALLY AN OFF-ARPT VOR AND EVENTUALLY LOC BACK COURSE TO CONFIRM IDENT OF ARPT. PASSING THROUGH ABOUT 5000 FT WE CALLED THE ARPT IN SIGHT TO ZME AND THEY TERMINATED RADAR SVC AND TOLD US TO SWITCH TO ADVISORY. ON APCH; I POINTED OUT TO THE FO THE SIMILARITIES BTWN THE ARPT WE WERE APCHING AND WHAT TURNED OUT TO BE THE ACTUAL GTR ARPT. ON SHORT FINAL; I RPTED TO ZME THAT LNDG WAS ASSURED; PLEASE CLOSE FLT PLAN. THEY TOLD US THAT COLUMBUS APCH WAS OPEN AND TO CONTACT THEM FOR CLRNC OUT OF GTR AND ATL. FO CONTINUED WITH LNDG AND I TOOK CTL AT END OF LNDG ROLLOUT. AFTER TURNING ON TO TXWY; I REALIZED THAT WE WERE AT THE WRONG ARPT. SHUT DOWN AND CALLED FLT CTL -- THEY MADE ARRANGEMENTS TO BUS PAX TO GTR. HUMAN FACTORS: IF THIS HAD BEEN AT NIGHT (APCH LIGHTS) ON IN IMC (INST APCH) THIS INCIDENT PROBABLY WOULD NOT HAVE HAPPENED. GTR IS 1 OF 4 RWYS SIMILAR IN LENGTH AND ALIGNMENT ALL LOCATED WITHIN 5-10 MI OF EACH OTHER AND ALL UNCTLED. THE FO AND I BOTH SAW WHAT WE WANTED TO SEE AND DIDN'T GET ANY INFO TO CONVINCE US OTHERWISE. ZME DID NOT TELL US WE WERE AIMING FOR THE WRONG ARPT AND WHEN I CHKED THE LOC ON FINAL; IT WAS LINED UP. (I CAN HONESTLY NOT TELL YOU WHETHER I SAW OR DID NOT SEE AN OFF FLAG.) ONE THING THAT MIGHT HAVE HELPED WOULD HAVE BEEN ZME CALLING THE ARPT AT 10 O'CLOCK POS AND 15 MI -- THAT MIGHT HAVE GIVEN US A CLUE. SUPPLEMENTAL INFO FROM ACN 358822: WE WERE TALKING WITH ZME BECAUSE COLUMBUS APCH WAS INOP; AND THEY SAID; 'THE ARPT WAS 11-12 O'CLOCK AND 10 MI.' A RWY; WHICH LOOKED LIKE GTR; HANGARS ON THE CORRECT SIDE; AND CORRECT RWY ALIGNMENT WAS IN THAT POS. I HAVE BEEN TO GTR BEFORE ABOUT 4 TIMES; BUT IT HAS BEEN A COUPLE OF MONTHS SINCE I WAS LAST THERE. MY CAPT ALSO HAD BEEN TO GTR; BUT SHE THOUGHT IT HAD ONLY BEEN AT NIGHT. AGAIN WE WERE HIGH; MAYBE 6000 FT MSL SO I ATTRIBUTED THIS TO THE FACT I MAY HAVE AGAIN NOT BEEN AGGRESSIVE ENOUGH IN THE DSCNT. WE WERE CLRED FOR THE VISUAL APCH EARLY AND WERE PROBABLY BELOW ZME RADAR COVERAGE ON THE APCH. AND BY IDENTING THE LOC BACK COURSE WE COULD HAVE BEEN SURE THAT IT WAS WORKING PROPERLY.