Vanquish is set in space, on a massive cylindrical colony – an O'Neill cylinder – known as SC-01 Providence. This is actually America's 51st state. It was created in order to gather solar energy, and help alleviate the issues caused by over-population in the US by providing more living space for its citizens. The energy that it gathers in its power generation plants is converted into microwaves and beamed down to Earth, more specifically to the US.
SC-01 Providence
Providence supports a large population of colonists and has all the commodities and luxuries of any city on the surface. Providence also has a substantial garrison of US Marines, although these are largely annihilated in the Order's attack. The colony's interior holds dense urban districts as well as stretches of serene parkland and artificial lakes. The artificial gravity maintained by the station's rotation means that the entire interior of Providence can be constructed upon.
Providence fires its Microwave Energy Array
The destruction of Providence by Zaisev's tactical nuke
The station goes through a day and night cycle. This is demonstrated when Sam observes the Kreon passing overhead.
The damage inflicted on Providence by the Order of the Russian Star is extensive. It is unknown what the Order does with the colony's population during their brief occupation, as no civilians are ever seen in-game, or whether any were able to escape during the attack. If not, then the death toll resulting from the station's destruction could have been over 30 million.