It was military slang used at the Trinity site where the weapon tower was at point 'zero' and moved into general use very shortly after the end of World War II.
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To put this usage into perspective, it should be noted that the total energy of the World Trade Center attack was approximately 0.2 kilotons, mostly consisting of the gravitational potential energy of the towers themselves. If only the kinetic energy and chemical energy of the planes and their fuel is counted, the energy of the attack itself was only 0.02 kT.
This is a small fraction of the energy released by even a small nuclear weapon, to such an extent that the World Trade Center usage of the term can almost be regarded as a euphemism for the real thing.
For comparison, using the upper estimate for the World Trade Center attack energy:
The term is also apparently used by members of the U.S. armed forces to describe the open space at the center of The Pentagon, in a blackly humorous reference to the likelihood of its being a nuclear weapons target in any nuclear war.
There is also a film named Ground Zero[?]. This film is about a documentary filmer who gets into trouble after filming at a site in Australia used by Great Britain for nuclear tests using aboriginal population as guinea pigs,
wikipedia.org dumped 2003-03-17 with terodump