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1968, it is with the episode "Assignment: Earth" featuring Gary Seven that we first see a clearly divergent history, that is not "fixed" at the end of the episode. Indeed, Spock determines that the U.S.S. Enterprise intervention in 1968 was, in fact, an established and important part of history. Additionally, 1968 is shown to be a year of such critical importance that aliens have sent an emissary, Gary Seven, to help guide the Earth. In addition, Starfleet actually sends the Enterprise back in time to do historical research.
July 1969 After nearly colliding with a black hole, The U.S.S. Enterprise (NCC-1701) is accidentally sent into Earth's past and accidentally captures a U.S. Air Force pilot.
In the episode, having arrived in the 20th century, the Enterprise crew and the mysterious Gary Seven both try to prevent an nuclear conflict, however, they hinder each other in doing so. The result of the uncoordinated efforts is a nuclear explosion in the atmosphere about 100 miles above the surface, which is exactly the reason for the time travel.
It could of course be argued that 1968 was a critical year in many ways in our own history - but the key reason for the involvement of both Gary Seven and the Enterprise crew is the destabilizing effect of the deployment of space based nuclear missile platforms, something which did not happen in actual history, and is a significant departure.
July 1969 First manned lunar landing. The crew of Apollo 11, Neil A. Armstrong, Edwin E. Aldrin, Jr., and Michael Collins, set down in the Sea of Tranquility, collect moon rocks, and return to earth.
1969 Khan Noonien Singh, one of the first of the genetic supermen, is born - a product of genetic engineering.
1969 Dr. Stravos Keniculus, the first cloned human, is born.
1969 Dr. Henry Starling introduces a new computer chip in 1969 and his company, Chronowerx, starts the late twentieth century computer revolution and comes to dominate the new industry.
1970 Captain Shaun Geoffrey Christopher is born in the United States.
1972 The Pioneer 10 Jupiter flyby space probe sends 500 images of this enormous planet, and amazing technical data, back to Earth.