By Gemini to the Moon

A TL where NASA's Gemini mission evolved to include a lunar landing.

Timeline
July 5, 1959 (Point of divergence): Stanisław Jaros killed Soviet leader Nikita Khrushchev with a bomb in Poland. Georgi Malenkov wrested control of USSR afterwards.

October 24, 1960: The Nedelin disaster in Russia forced her to indefinitely suspends its fledgling space program for the time being.

May 5, 1961: USA's Alan Shepard became the first human in space.

July, 1961: After astronaut Gus Grissom went into space, USSR restarted its manned spaceflight program.

February 20, 1962: USA astronaut John Glenn became the first person to orbit the Earth.

April 12, 1962: Russia sent their cosmonaut Yuri Gagarin into orbit. In response Kennedy orders NASA to conduct a lunar landing mission by the end of the decade.

Late 1963: US Project Mercury spaceflight mission ends with Mercury-Atlas 12. They moved on to the Gemini spaceflight program afterwards.

1964: NASA astronaut Ed White became the first man to spacewalk when he exited the Gemini spacecraft. Soviet cosmonaut Alexei Leonov will follow thereafter.

1965: USA performed the first space rendezvous and docking.

1968: With a Gemini spacecraft, USA performed the world's first manned circumlunar flight mission.

1969: Neil Armstrong became the first man to step foot on the Moon. NASA deployed the first space station based on the Big Gemini design.

1970: The fundings for manned lunar program were cut due to lost of public interest so no more manned lunar missions after Armstrong's.

1972: USA sent the second space station "Manned Orbiting Laboratory" into orbit. USSR deployed their own "Zarya 1" afterwards.

1973: USSR performed a manned circumlunar flight, but stagnations will prove lethal to their ambitions to land a man on the Moon and level the playing field with the Americans.

1976: NASA sent a probe to land on Mars.

1991: Collapse of the USSR.

1996: NASA Mars probe Sojourner is launched.

2008: The Large Hadron Collider went online.

2016: Hillary Clinton won the U.S. presidential election.