Moonbase Laika

A moonbase was established on the Moon around 2050.

By 2070, it was used to control Earth's weather with a gravitron. The Cybermen attempted to take it over in 2070, but were stopped by the Second Doctor. (TV: The Moonbase)

Alternate timeline
In an alternate timeline where the Cybermen allied with Rassilon and began rewriting history, (COMIC: Supremacy of the Cybermen) the Second Doctor was partially converted while on the Moonbase. (COMIC: Prologue: The Second Doctor)