Please see the picture. Red dots are stars, lines are the path that light takes, our observer is at center. Assuming that stars are somewhat uniformly spread around us, I suppose that stationary observer (left picture) sees about as many stars in every direction, but an observer moving in y-direction (right picture) sees stars concentrated on the sides due to length contraction and fewer stars up and down. Can we use this method to tell is earth moving relative to rest of the universe? If space looks same in every direction, we are not moving?