Sovereign in Space?

There is some rumor of the wealthy Russian businessman who is funding Asgardia, a space station project that will orbit the Earth, in low orbit (LEO), that he intends to pursue (and get) UN membership for Asgardia. The short answer is that Asgardia would likely be under the sole jurisdiction of Russia and therefore not a sovereign nation. However, if they gave up their Russian citizenship and declared themselves an independent sovereign nation, they could apply for membership; but getting past the application stage would be unlikely. What follows is the longer answer.