I come back to this thread and I see people still think "Geographical boundaries recognized by treaty, influence and/or presence" and "Planets subject to Federation law" are the same thing. Geography and politics aren't the same things. Hell, they aren't even depicted on the same type of map
But please, go on thinking the United Federation of Planets is a conquering force that subjects everyone within a defined radius around Earth to their laws regardless of whether those people have been on that planet before Earth even knew what a warp coil was.
Please proceed to throw out everything we know about how planets join the Federation too.
Edit to add: It's the United Federation of Planets
I don't want to know what alternate version of the movie you people are watching .. I want to know what franchise
you people have been watching.