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The federation for international auto racing issued a statement saying Whiting died on Thursday morning in Melbourne.
FIA President Jean Todt said he was shocked by the sudden death of the long-time F1 official and described Whiting "a great Race Director, a central and inimitable figure in Formula One who embodied the ethics and spirit of this fantastic sport."
A pulmonary embolism is a blockage in the lung, usually caused by a blood clot.
Whiting began his F1 career in 1977 working at the Hesketh team. He joined the FIA in 1988 and became a race director in 1997.
"Formula One has lost a faithful friend and a charismatic ambassador in Charlie," Todt said in a statement. "All my thoughts, those of the FIA and entire motor sport community go out to his family, friends, and all Formula One lovers."
The Red Bull Racing team said Formula One had "lost one of its most loyal and hard-working ambassadors."
"I am deeply saddened to hear the terrible news," Red Bull team principal Christian Horner said. "Charlie has played a key role in this sport and has been the referee and voice of reason as Race Director for many years.
"He was a man with great integrity who performed a difficult role in a balanced way. At heart, he was a racer with his origins stretching back to his time at Hesketh and the early days of Brabham."