Apollo 11

Apollo 11 was an Earth spacecraft which landed on the Moon on 20th July 1969. Humans regarded this as the first Moon landing.

Motivations for the landing
Around 1959, a group of aliens had landed on the Moon and sent a transmission to Earth. They requested a meeting with Humans so as to share technology. The American government intercepted the transmission and started NASA's moon project to meet them. The Silence, which controlled humanity up to that point, was also interested in the moon landing in order for the human race to produce the astronaut suit. (DW: Day of the Moon) In the popular imagination, the Moon landing had much to do with the Americans' rivalry with the Soviet Union. (WC: Blue Moon)

The mission
Coordinated by Mission Control at the Kennedy Space Center, the Apollo 11, powered by a Saturn V rocket, lifted off on 16th July. En Route to the Moon, the crew encountered unnamed aliens. Mission Control, as well as Torchwood, would know of this, but not the public. After getting locked by an overzealous secret services officer, Spencer, the Doctor ended up locked up in the Center, though gained release in enough time to greet the aliens due to land on the Moon in a flying saucer prior to the Apollo. The Doctor convinced the aliens that Humanity needed to develop on their own. The Doctor then witnessed the landing. (WC: Blue Moon)

A later incarnation of the Doctor interfered with the transmission of the landing with the help of Canton Delaware. At the crucial moment Neil Armstrong landed, they inserted footage of a Silent ordering for its kind to be killed on sight. (DW: Day of the Moon)

Public reaction
A crowd gathered to watch the takeoff from the ground. (WC: Blue Moon) With interest in the landing so intense, public places virtually emptied as people all over the world glued themselves to their televisions. (ST: One Small Step...)

Due to the nature of the Silence, the footage the Doctor added was not remembered, but left as a subliminal message for present and future human generations. Following the landing, whenever an individual saw a Silent, they would kill it, unknowingly leading to the Silence's downfall. (DW: Day of the Moon)

Minor references and mentions
The Doctor and Martha had also personally witnessed the Moon landing four times together, as opposed to watching it on television. Exactly how this was accomplished without them crossing timelines is unknown. (DW: Blink)

Behind the scenes

 * Prior to the real actual touchdown on the Moon, Moon Landing in TV Comic had already (obviously inaccurately) shown it has happening for the first time in 1970.