Simon, can you elaborate on this crop from Ch. 19 of your book? Specifically your choice of 2hrs 56 minutes and 44 days of the sun’s motion as your basis for the PVP orbit’s diameter.
Dear Schoepffer,
That crop you posted is from the 1st Edition of my TYCHOS book (2018),
I have since elaborated about this subject in Chapter 11 of the 2nd Edition (due for printing very soon).
Doh! 
In this other conceptual graphic, I show how the Sun would ‘visually’ employ ca. 44 days to cover the distance between Polaris and Vega
I see it now.
Simon,
I came across your theory and found it’s interesting.
But I have some difficulty understanding some specific parts of your theory.
In Chapter11, the diameter of the Earth’s PVP orbit is calculated as follows:
Sun would ‘visually’ employ ca. 44 days to cover the distance between Polaris and Vega (as viewed under an imaginary circumpolar orbit of the Sun).
We may therefore perform a simple calculation to estimate the diameter of our PVP orbit. Assuming the Sun travels at 107226 km/h, in 1056 hours (i.e. 44 days) the Sun would cover the distance of:
107226 km/h X 1056h = 113 230 656 km (the diameter of our PVP orbit)
My question is, why does the geometry of solar orbit have something to do with the geometry of earth’s PVP orbit? It seems arbitrary to assign the length of a ~44° chord along sun’s orbit, to the diameter of PVP orbit. Why we cannot assign the length of a ~44° chord along the orbit of another planet (e.g. Jupiter) to the diameter of PVP orbit?
This determination of the size of PVP orbit seems geometerically invalid.
I’m very confused.
Could you provide some detailed explanation for this?
Hello mizusato and welcome to the forum.
I have moved your question to this relevant topic titled “Estimating the PVP orbit”.
Please spend a little time reading the above posts - and if you still have questions I’ll be happy to answer them. Make sure you first understand what that 44° ‘chord’ represents; it has nothing to do with Jupiter (or any other planet) but only with the angle / distance that the Sun would cover - if it were to revolve around a hypothetical circumpolar orbit: If this were the case, the Sun would employ ca. 44 days to move from Polaris to Vega - as viewed from Earth.
Thank you for your reply.
Actually I have read this post before asking my question.
Yet I still have trouble connecting the dots.
Yes, the sun employs ~44d to move from Polaris to Vega as viewed from Earth and covers a specific distance. However, how could that specific distance equal to the size of PVP orbit?
According to your reasoning process, if the sun’s orbit were bigger, the derived PVP orbit size would be bigger accordingly; if the sun’s orbit were smaller, the derived PVP orbit size would be smaller accordingly.
That is saying, there is a causal link between the size of solar orbit and the size of PVP orbit.
However, I (maybe wrongly) think they are totally independent sizes.
If the diameter of PVP orbit were 10x smaller or 10x larger, we could still see north celestial pole move ~44 degrees from Polaris to Vega in half of a 25000y cycle because the earth’s axis always points outward the orbit. Is this correct?
Dear mizusato, I fully understand your question - since it was one that had me scratching my head for a long while when (or before) determining the 113.2-Mkm diameter of the PVP orbit. At one time, I was actually stuck with the idea that the PVP might not need to exist at all : all that was needed (apparently) was for the Earth’s axis to flip by 50° in order to have Vega as our North star in about 11500 years from today.
In fact, Polaris is today at 89° of declination - and Vega is at 39° (at the opposite side of our celestial sphere). Ergo, a 50° separation.
However, I then realized that - as of official calculations - Earth’s axis is expected to be tilted at 22.9°. in about 11500 years time. As explained in Chapter 11 of my book:
In about 11500 years Earth’s axis will then be tilted (as officially predicted) by 22.9° - as opposed to the current 23.4° - for a total axial rotation (in relation to our 180° Northern celestial hemisphere) of 46.3°. This 3.7° difference (between 50° and 46.3°) can be accounted for by Earth’s 113.2 Mkm displacement along its PVP orbit. This, because in the TYCHOS (as we shall see later on) the Earth-Vega distance is estimated to be ≈37AU. The PVP orbit’s diameter of 113.2 Mkm (or 0.757AU) amounts to ca. 2.05% of 37AU - and that aforementioned 3.7° difference amounts to ca. 2.05% of 180.°.
Hope this clears it up! 
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