I know that.  We've known that since we understood "line of sight".

If I can't pick up your rocket across the planet, then the world is not flat.  

I like your pictures showing the rocket moving into space over the curvature of the earth though.  Thanks.

Bonus for bozos:  The shortest distance on a flat plane is a straight line.  The shortest distance on a sphere is a curved line.  What type of line do your pretty pictures show?