Simple and Irrefutable Proof that Earth is a Sphere

Simple and Irrefutable Proof that Earth is a Sphere

This is the simplest way I know to prove the shape of the Earth. It does not involve any physics or mathematics and does not rely on the type of observations that flat earthers like to dismiss by invoking perspective or other subjects that they don't understand. If there is no error in this proof then ALL flat earth arguments are wrong. There is no error.

Absolute proof that Earth is not flat: 

The stars appear to revolve anti-clockwise around the North Pole with the Pole Star, or Polaris, appearing virtually motionless. Everyone agrees about that, but there is problem for flat earth. The star trails are always circular, which means that the apparent motion of each star is on a plane perpendicular to the observer's line of sight to Polaris. That fits the globe model perfectly, but on a flat earth the star trails should only be circular at the North Pole and should become increasingly elliptical as the observer moves south. Circular trails would mean that the stars are moving in different planes for different observers.
Another problem for flat earth is that if you turn round and head due south you will find a second celestial pole straight ahead. Travelling south from anywhere on Earth will take you to a place where the stars revolve clockwise around a point above your head, and there can only be one place where that happens. That is the South Pole, which does not exist on the flat earth. There the apparent movement of the stars is clockwise, because the rotation is still the same but you have gone to the other side of the globe so you are looking in the opposite direction. 
North Star (STAR TRAILS) Time-lapse HD! 
https://www.youtube.com/watch?v=tp6UkqIwVfk 
Where do we see the South Celestial Pole by looking straight up?  
https://www.youtube.com/watch?v=BGD3lhDCgpY 
The observed motion of the stars is not possible on a flat earth. 
All straight routes going north lead to one point, the North Pole, and all straight routes going south lead to the South Pole. That is not possible on a flat earth. 

Absolute proof that Earth is spherical: 

The angle of elevation of Polaris is equal to the observer's latitude in the Northern Hemisphere and increases by 9° for every 1,000km from the Equator. That is not possible on a flat earth but works perfectly on a globe with Polaris at a distance many times greater than the diameter of the Earth. The same is true of the Southern Hemisphere except that there is no pole star in the south. For those who want to quibble and say that it would be possible to create a curved shape which fits the measured angles with Polaris much closer – it would be, but that would mean that it would not curve 90° from the poles to the Equator, resulting in a flying saucer shape which definitely does not match reality.