AN ACR CREW AT FL360 NEAR TNP REPORTS AN UNUSUAL BRIGHT OBJECT TRAVELING FROM THE SOUTHWEST BECOMING INTENSELY BRIGHT AND THEN FADING INTO NORTHWEST.

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WHILE FLYING WE ENCOUNTERED MULTIPLE UNUSUAL SIGHTINGS AT ALT. AROUND XA30Z AT FL360; 20 MI N OF TNP; I WITNESSED THE FIRST SUCH EVENT. I QUERIED ATC ABOUT WHAT I HAD SEEN; BUT WAS NOT TOO CONCERNED AT THIS POINT. IT WAS UNUSUAL AND UNLIKE ANYTHING I HAD SEEN BEFORE; BUT LASTED ONLY AROUND 10 SECONDS. I ASKED THE FO IF HE HAD SEEN WHAT I SAW; AND HE DID NOT. THE COCKPIT LIGHTING WAS DIM INSIDE; SO I HAD GOOD VISIBILITY OUTSIDE. THE NIGHT SKY WAS BRIGHT WITH AN ALMOST FULL MOON BEHIND US. SOME STARS AND PLANETS WERE OUT; BUT THE MILKY WAY WAS BARELY VISIBLE DUE TO THE MOON. A LIGHT; AHEAD AND SLIGHTLY TO THE R INITIALLY CAUGHT MY EYE. IT WENT FROM DIM TO EXTREMELY BRIGHT IN JUST A FEW SECONDS. IT WAS ABOVE THE HORIZON ABOUT 20 DEGS INCLINATION AND AROUND MY 12:30 O'CLOCK POS. IT WAS NOT IN CLOSE TO US; BUT SEEMED OUT THERE A BIT. I HAVE NEVER SEEN SUCH INTENSE; BRIGHT; WHITE AND SILVER LIGHT IN MY LIFE. IT ACTUALLY HAD A VERY DEFINED 360 DEG HALO AROUND IT AT ONE POINT. THEN IT MADE A 45 DEG SHARP CHANGE IN DIRECTION AND FADED AWAY AS IT WENT OUT OF VIEW IN ABOUT 3 SECONDS TIME. DURING THE NEXT 50 MINS; WE EXPERIENCED ALMOST THE EXACT SAME SCENARIO 4 MORE TIMES. THE FO WITNESSED ALL 4 OF THOSE EVENTS. WE MADE 'CIRVIS' TYPE RPTS TO ATC FOR EACH ENCOUNTER THEREAFTER. THE LAST ONE WE SAW WAS ON DSCNT INTO ZZZ AROUND 17000 FT AS WE ENTERED A CLOUD. SUPPLEMENTAL INFO FROM ACN 795850: I DID NOT SEE IT UNTIL 5-10 MINS LATER WHEN IT OCCURRED AGAIN. OBJECT STARTED OUT AS A VERY WEAK-LOOKING STAR; BUT WOULD MOVE SLOWLY L TO R AND GROW MUCH BRIGHTER THAN ANY STAR I HAVE EVER SEEN. IT WOULD THEN BEGIN TO FADE AND MOVE FURTHER R; APPEARING TO MOVE OFF TO THE DISTANT NW. THE CAPT AND I OBSERVED THE SAME PHENOMENON 3 MORE TIMES; EACH OCCURRENCE 5-10 MINS AFTER THE LAST. THE LOWEST ALT AT WHICH IT WAS VISIBLE WAS APPROX FL190. I HAVE BACKGROUND IN THE USAF; AND THE CLOSEST I COULD DESCRIBE THIS POINT OF LIGHT WOULD POSSIBLY BE SIMILAR TO AN AIRBORNE-LAUNCHED MISSILE.