Celestial latitude is just known as celestial latitude .
What you call celestial latitude is what I call declination.
Who brought the brightness of stars into the debate ? It adds nothing .
You were asking about a method of determining the distance of Polaris from Earth. Polaris is a classical cepheid so it follows that the brightness curve allows us to determine its luminosity and therefore its distance. The Cepheid law uses a method which is completely independent of the shape of Earth. So I would disagree that it 'adds nothing'. Rather it provides information based on observational evidence. You dismiss the Cepheid variable approach because it provides a result that you don't want to agree with. Instead you are looking for an experiment or method that does provide you with the answer or 'proof' that you are looking for.
If you can't grasp the significance of the survey of latitude to the Pole star , and what it tells you about the shape of the land across the survey , then you don't know the model you defend .
I'm not defending any model. I'm just trying to discuss something with you. If you are not interesting in listening to what I'm saying (because you don't want to believe it) then just say so and I won't waste any more time with you on it. Discussing things means taking into account and respecting both points of view. So far it seems you are only respecting your own point of view.
In a few thousand years Polaris won't be anywhere near the NCP any more so we will have to designate a different star to perform your latitude experiment with. But since that will be well after both yours and my lifetime you will probably regard that as irrelevant.
Reading back I can see two intriguing comments that you have made...
We know nothing about the stars - we have theory only .
I have two scopes of my own and access to three more . I think now that these are just microscopes use to observe the nearby vault of the sky . The stars are in the same place now as they were 50 yrs ago .
We actually know a lot more about the stars now that we did say a century and a half ago. Spectroscopy is now a well established branch of astronomy and I can easily create my own HR diagram using the equipment I have in my back garden. You can see spectral lines in stars directly so how is that theory only? I guess we only accept something if it tells you what you want to hear. We can match the positions of spectral absorption lines in stars with the positions of emission lines we observe from gas tubes in a lab. Direct correlation so it doesn't take a lot of genius to work out that the spectral lines in stars are caused by gases absorbing light. Equally we can use redshift to measure how far way celestial bodies are. So your claims about the ridiculously large distances predicted by RE or globe theory don't seem to be quite so ridiculous after all. Trust me, I know what I'm talking about on this subject.
Secondly I also have a couple of telescopes...well nine actually. All used for specific purposes including two specialised solar telescopes. What do you use your telescopes/microscopes for? If you are trying to use microscopes for astronomy then you are not going to see much, I can promise you that!