When I first learnt about this I didn’t believe it. Afterall why would a country conduct nuclear tests on the moon bearing enormous costs and risk of a mid-air explosion in the early stages of space research?
It was the late 1950s, and the Cold War was extremely chilly. Someone in the US Government got the bright idea of nuking the Moon, and in 1958 the Air Force Special Weapons Center spearheaded the project (labeled A119, "A Study of Lunar Research Flights").
The idea was to shock the Soviet Union, with a massive display of American nuclear might. What better demonstration than an atomic explosion on our closest celestial neighbour? According to the project's reports, the flash would've been visible to the naked eye on Earth. (It's been suggested that another motivation may have been to use the Moon as a test range, thus avoiding the problems with irradiating our home planet.)
Although scientist spearheading the project had warned the U.S. Government about the enormous cost of this project, the authorities were concerned only about its effects in the politics back at Earth. But the irony is after the whole blue-print of the project A119 was prepared it simply went away, much like all other “classified” documents.
But this wasn’t the only time an U.S. government agency had thought of nuking our distant neighbour.In 1956, W.W. Kellogg of RAND Corporation considered the possibility of launching an atomic bomb to the Moon. In 1957, NASA's Jet Propulsion Laboratory put forth “Project Red Socks”, the first serious proposal to send a spacecraft to the Moon. One of its lesser suggestions was to nuke the Moon in order to send lunar rocks hurtling back to Earth, where they could be collected and studied. The creator of the hydrogen bomb, physicist Edward Teller, similarly mused about dropping atomic bombs on the Moon in order to study the seismic waves they would create.
The Communists back at The Soviet Union were also not much behind. In the late 1950s, the setup Project E-4 which would've used a probe armed with an A-bomb to blast the Moon, apparently as a display of its dominance in space research. The idea reached the stage of a full-scale model but was aborted for fear of the probe falling back to Earth.
One can barely imagine the consequences had both of these Superpowers been successful in nuking the moon. As we all know the moon and Earth balance each others orbit and many other attributes. And in my opinion had the nuke tests in the moon been rampant, it would have led to a significant change in the lunar mass which according to Newton’s Universal Gravitational Law could have adverse effects back here. But this is merely a speculation, and thankfully indeed.