NASA's ISS live feed is center to an app that I am developing. I am wondering if it is copyright infringement to embed the live stream in my app. I think that it might be ok to use it because according to US copyright law, any US government work is not protected under copyright law. First of all, is this true? Second, because NASA is part of the US government, does that mean that NASA's ISS live stream is owned by the US government, and therefore not protected by copyright law?
It is true that any work of the US government is not subject to copyright in the United States; it may be subject to copyright abroad (the relevant law excludes US government works from US copyright protection; other countries have their own copyright laws that generally don't explicitly exclude US government works, and so the works may be copyrighted there).
A government work is defined as something produced by a government employee in the course of his official duties. It doesn't include everything released by a government agency; for instance, if a contractor makes something and the contract specifies that the government gets the copyright, the work is copyrighted (since it wasn't made by a government employee). If a foreign cosmonaut or astronaut composes and sings an original song in a livestream, then NASA may not have copyright in the livestream but the foreign astronaut would have copyright in the song.
That said, NASA has a page of guidelines for reuse of their media, where they say that their stuff normally isn't copyrighted unless otherwise noted. They don't make any sort of guarantee, but they suggest you'd probably be fine embedding it, at least as far as they're concerned.