How do we know that the Earth is in outer space and not inner space?

We don't.  

Maybe you should have put this under Games.  

We are in inner space. Inner space was created around earth to make room for the air we breathe. There is no air in outer space. 

Did you see that photo of Earth NASA published a while ago, taken from far out in the Solar System, near Saturn, was it? It was actually a test photograph, not originally intended for publishing until the staff realised the tiny blue dot in a vast blackness sprinkled with stars, is the Earth...