20 July

From Tardis Wiki, the free Doctor Who reference
20 July

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20 July 1966 was the day that the First Doctor started travelling with Polly and Ben — and the day the Second Doctor stopped. Though it was an apparent accident, it was nevertheless the first occasion on which the Doctor was able to pick up his companions on the same date and at the same city to which he ultimately returned them. (TV: The War Machines, The Faceless Ones)

Three years later, Apollo 11 landed on the Moon and Neil Armstrong became, as far as the majority of humanity was aware, the first man to walk on the Moon. (TV: Day of the Moon, PROSE: Who Killed Kennedy, Time Traveller's Diary)

The Second Doctor, Jamie McCrimmon and Zoe Heriot played on the beach on the Isle of Wight while most people were inside watching the moon landing. (PROSE: One Small Step)

The Eleventh Doctor interfered with the transmission of the Moon landing with the help of the former FBI agent Canton Everett Delaware III. At the crucial moment that Armstrong set foot on the Moon, they inserted footage of a Silent ordering for its kind to be killed on sight. (TV: Day of the Moon)

Meanwhile, the Tenth Doctor escaped his imprisonment inside Mission Control at the Kennedy Space Center with the help of Mission Commander Cliff Boxworth. The Doctor created a visualisation of the alien language, in which an alien species had been transmitting to contact humanity and share its knowledge, and use the symbols the TARDIS translated to get the species' attention. Before the Apollo 11 landing, the Doctor asked the aliens not to contact humanity, telling them that humanity needed to find their own way. Afterwards, the Doctor watched from a distance as Neil put his first steps on the Moon. (PROSE: Blue Moon)

In 1970, another Moon landing took place, with the First Doctor, John and Gillian watching on the Moon. (COMIC: Moon Landing)