FLC OF A B737-300 WENT AROUND AFTER HAVING AN UNSAFE R MAIN LNDG POS INDICATION ON FINAL RESULTING IN A FLY-BY FOR TWR AND COMPANY MAINT CHK. LNDG GEAR EQUIP PROB DISSIPATED AND A SUCCESSFUL LNDG WAS MADE.

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ON FINAL FOR RWY 26R; AFTER ALL LNDG CHKS COMPLETE (GEAR DOWN 3 GREEN; SPD BRAKE ARMED GREEN LIGHT; FLAPS 30 DEGS GREEN LIGHT); AT APPROX 800 FT AGL THE R MAIN LNDG GEAR WENT FROM GREEN (SAFE) TO RED (UNSAFE) AND GEAR WARNING HORN SOUNDED. I INITIATED A GAR AND HAD FO INFORM TWR. WE WENT AROUND. I DID NOT RETRACT THE LNDG GEAR FEARING I MAY MAKE THINGS WORSE. I CALLED MAINT CTL AND INFORMED THEM OF SIT AND ASKED IF THEY HAD ANY IDEAS. THEY REALLY HAD NONE EXCEPT TO FOLLOW QRH AND CHK WHEEL WELL THROUGH SIGHT GLASS. I HAD FO GO BACK AND CHK ALIGNMENT MARKS ON GEAR. SHE CAME BACK AND SAID R GEAR ALIGNMENT MARKS WERE MISALIGNED BY APPROX THE WIDTH OF THE ALIGNMENT MARK (3/8 INCH TO 1/2 INCH) AND L MAIN ALIGNMENT MARKS ALIGNED PERFECTLY. I RELAYED THIS TO MAINT CTL AND TOLD THEM WE WOULD DO FLY-BY ON RWY 26R FOR MAINT TO DO A VISUAL INSPECTION. I REQUESTED AND WE DID FLY-BY. TWR ADVISED GEAR APPEARED DOWN. WE WENT AROUND. PRIOR TO THIS FLY-BY; I BRIEFED FIRST FLT ATTENDANT THAT WE WOULD BE DOING FLY-BY; AND THEN RETURN TO LAND. I TOLD HER I FELT THE GEAR WAS DOWN AND LOCKED BUT I WANTED HER TO PREPARE THE CABIN JUST IN CASE AND WE WOULD GIVE 'BRACE' COMMAND AT 500 FT AGL. WE CAME BACK AROUND AND FO AND MYSELF COMPLETED THE PARTIAL OR GEAR UP LNDG CHKLIST. ON FINAL; FLAPS 40 DEGS; AT APPROX 1200 FT AGL; THE R GEAR LIGHT WENT FROM UNSAFE (RED) TO SAFE (GREEN). THAT WAS BACKED UP BY NO GEAR WARNING HORN. THE 'BRACE; BRACE' COMMAND WAS GIVEN AT 500 FT AGL. THE LNDG WAS UNEVENTFUL AND I PULLED THE ACFT OFF THE RWY ONTO TXWY AND STOPPED WHILE I STARTED APU; SHUT DOWN ENGS AND WAITED FOR MAINT TO INSPECT ACFT AND INSTALL GEAR PINS. AFTER MAINT INSTALLED GEAR PINS AND INSPECTED ACFT; THEY GAVE US OK TO TAXI TO GATE; WHICH WE DID. PAX DEPLANED AT GATE AND SEEMED IN GOOD SPIRITS.