B727 CREW HAD TRACK DEV IN SAT CLASS E AIRSPACE.

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WE WERE CLRED VIA CENTEX VOR 205 DEG RADIAL TO MARCS INTXN AND RESUME THE MARCS ARR. (THE 205 DEG RADIAL FROM CENTEX TO INTERCEPT IS NOT PART OF THE ARR; SO THERE IS NO DME FROM CENTEX VOR TO INDICATE MARCS). THE FO'S (PF'S) VOR WAS ON CENTEX 205 DEGS AND THE CAPT'S (PNF) WAS ON SAT 056 DEG RADIAL (236 DEG COURSE INBOUND). THE FO WAS TRACKING HIS COURSE AND RELYING ON THE CAPT'S VOR TO INTERCEPT THE COURSE. NEITHER ONE OF US REALIZED THAT THE CAPT'S VOR HAD FAILED UNTIL APCH CTL CALLED OUT TFC AND GAVE US A 270 DEG HDG FOR SPACING; AND THE FO TUNED IN SAT VOR AND WE SAW THE DISCREPANCY. WE WROTE UP THE CAPT VOR; BUT IT WORKED OK ON ANOTHER VOR IN THE AREA AND WORKED OK ON SAT VOR AFTER LNDG. SUPPLEMENTAL INFO FROM ACN 479749: THE CAPT'S VOR WAS TUNED TO THE SAT 056 DEG RADIAL. AFTER RECEIVING A VECTOR FROM APCH TO FY A 270 DEG HDG; AND A TFC 1000 FT ABOVE CALL; WE REALIZED THE CAPT'S VOR HAD FAILED AND WAS SHOWING A TO/FROM INDICATOR IN THE WRONG DIRECTION. THE CAPT'S VOR WAS NOT INDICATING A FLAG OF ANY KIND. ALSO THE CDI (NEEDLE) WAS SHOWING FULL SCALE L THE ENTIRE TIME. I WAS BASING MY TURN ON THE SID BY THE CAPT'S CDI. SINCE IT NEVER CAME OFF THE CAGE; I FAILED TO MAKE THE TURN. HAD I CHKED MY RMI INDICATOR EARLIER; I WOULD HAVE NOTICED THE CAPT'S VOR PAINTING 180 DEGS IN THE WRONG DIRECTION. WE MADE A MAINT WRITE-UP IN SAT AND NOTED A PRIOR WRITE-UP 3 DAYS PRIOR. BOTH WRITE-UPS WERE CLRED. THE PRIOR WITH A PART CHANGE -- THE LATER AS 'COULD NOT DUPLICATE.'