On the first two episodes of CBS's Extant, astronauts float inside of the show's space station. How is this possible?
Floating happens because the space station is traveling extremely fast (about 5 miles a second) while constantly falling towards the Earth due to gravity. The only force on the station is gravity towards the Earth, but its "sideways" speed of 5 miles a second is just enough so that it balances out the Earth's pull and the station remains in orbit around the planet. Since the station feels the full effect of a force (gravity), anything inside of station is free of that force. Thus, weightlessness!
As scary as it is to imagine, if you were in a falling elevator, you would also experience weightlessness! All of the force is on the elevator and you are inside of it, free of that force. Now imagine that elevator falling in space, but also being pushed at 5 miles a second and ... bingo! Space station!
For the live tweet of episode 2 of Extant, check out the Storify below.