Would the arms of a rotating ice skater still move outwards if there was no other object in the universe? If there is no other object in the universe apart from a rotating ice skater, then nothing can be used as a reference frame. Would it make any sense to say that the skater is rotating? If so, rotating with respect to what? 
Would she feel an outward pull on her arms?
Does rotation makes sense if there is no background reference frame? 
 A: There is a substantial literature on this positivist point of view. The key to looking it up is "Mach's principle". Wikipedia has a page on it and the Stanford Encyclopedia of Philosophy discusses the question amongst other issues on a page on "Early Philosophical Interpretations of General Relativity". If you want to go to the opera on the question the SEP has the page "Absolute and Relational Theories of Space and Motion".
A: We know that the Earth is in motion (thanks to Copernicus and Galileu the entire Universe is not revolving around the Earth in 24hs).
In motion in relation to the distant stars or in relation to the background (the absolute physical space) ?   
As you say : 'Switch off the stars' --
I am still in motion because nothing happened to the Earth and it keeps spinning and evolving in direction to were the Leo constelation used to be. I assume here that the net effect of all the matter in the universe is null because the universe appears to be isotropic and homogeneous.   
Then, I'will have to exclude: 'In motion in relation to the distant stars'.  
Let's explore the notion 'In motion in relation to the background' because it seems to be the only option available.  
There are unbelievers because they were told that the motions are only relative to other bodies, and some dont know the past history of the motion of the Earth when the motion was clearly visible.  
Do we have a Foucault pendulum at hand? It will show that the Earth is spinning.  Some will argue that we dont know if the Foucault still give the same result. Use the same reasoning and I know that it will have to work, the same.  
For those that remain unbelievers that the motion is in relation to the background I will have to say:  
I'm using an antenna tunned to the CMB radiation and it clearly shows that:
The Earth is rotating and the Earth is in motion in direction ... Leo...
OR
the entire universe is revolving around the Earth in 24hs (the time lapse for one rotation) AND the world is not isotropic.  
Some will argue: it is in motion in relation to the CMB (considered as a body) and not in relation to the background.  
Finally I say:  'Swich off the CMB' ... Now there are no references left in the sky.  
Beleive it or not I'm still in motion.   
In motion in relation to the absolute physical space.  
