If i have understood the pvp orbit correctly, the orbits consists of two separate motions:
1: the earth moves around the pvp orbit in 25344 years and
2: the earths rotation axis makes one turn (or revolution?, my english is not so good) every 25344 year.
(As opposed to, for example, the copernican solar year, where the earths rotation axis does not, allegedly, rotate at all, in relation to the sun)
This means that the axis will point in the same direction all the time relative to the center point of the circle that constitutes the pvp orbit. So in what direction does it point? As i understand it, it can vary from that the axis points along the “tangent” of the pvp orbit to that the axis points towards the center of the pvp orbit.
Im sorry for my not so sophisticated english.
Let me try another way to ask: if there was a sun in the middle of the pvp orbit circle, would we then have constant winter (or summer) or constant spring (or fall)?
With kind regards, Gunnar
I’ll take that last question of yours, dear Gunnar - as it’s the easiest one to answer 
If there were a Sun in the middle of the Earth’s PVP orbit, we would have constant winter in the Northern Hemisphere and constant summer in the Southern Hemisphere.
Tomorrow I will further elaborate on this particular subject - need some sleep right now!
DOES THE EARTH’S AXIAL TILT CHANGE OVER TIME?
I’ve had some fun today with the question of the Earth’s supposedly variable axial tilt. Here’s what we are told about it at this official Nasa observatory webpage :
“Today, the Earth’s axis is tilted 23.5 degrees from the plane of its orbit around the sun. But this tilt changes. During a cycle that averages about 40,000 years, the tilt of the axis varies between 22.1 and 24.5 degrees.”
So let’s see: that would amount to a 2.4° variation of Earth’s axial tilt over a period of 40000 years.
Now, before we get on, you must know that - in the TYCHOS model - the true / ideal duration of a solar year is slightly shorter (by a mere 0.006%) than the officially-accepted duration of the solar year, namely:
365.22057 days instead of 365.2425 days (i.e. a 0.006% difference)
As expounded and illustrated in Chapter 19 of my book, this faulty figure of 365.2425 (adopted by our current Gregorian calendar) will ultimately cause the Sun and the Earth to ‘slip out of synch’ with each other – and thus ruinously “flip our seasons upside down” in relation to our current Gregorian / civil calendar. In 25344 years (the TYCHOS Great Year), the Sun and Earth’s positions around their respective orbits will be offset by a factor of 1.5, meaning that our summers and winters will be inverted! These 180° inversions would actually happen every 8448 years (i.e. 25344 / 3 ) - if we should keep using the Gregorian calendar count…
To be more precise, this factor amounts to 1.52064, because:
0.006% of 25344 amounts to 1.52064 (meaning that the Sun and Earth will be ‘offset’ by 1.52064 revolutions 25344 years from now, due to the faulty Gregorian calendar’s solar year count).
Now, we just saw that - as NASA tells us – the Earth’s axial tilt is believed to oscillate by 2.4° every 40000 years. With a simple calculation, we may find out how long it would take (according to NASA) for the axis of Earth to change by 1°:
40000 / 2.4 = 16666.6666666 (periodic) years
Well, ‘funnily enough’, as we divide 25344 by 16666.6666666 we obtain exactly 1.52064 !
In conclusion, the current / official reckoning (that the Earth’s axial tilt would oscillate by 2.4° every 40000 years) is entirely spurious: it is based on the faulty solar year count implemented by the Gregorian calendar which currently lets the Sun slowly drift eastwards of its habitual position on, say, the June 21 summer solstice, This is why we are told that the Earth’s axial tilt is currently diminishing (since the Sun is thus allowed to drift ahead towards its habitual July position which, of course, has the Sun lower in the sky than in June).
Once more, the TYCHOS model shows that our Solar System is wondrously stable and non-chaotic! In any case, we may rule out that the purportedly variable axial tilt of Earth has played a role or been responsible for climatic changes or whatever cataclysmic events have occurred in the distant past.
Simon,
In reviewing Ch. 19, I would like to quote this sentence, “In a TYCHOS Great Year, the Sun revolves 25344 times around Earth, while Earth rotates 9 256 706 times.”
Now 9,256,706 / 25344 = 365.242503156
Prior to that you write, " * Proposed TYCHOS solar year count: 365.22057 days (or 31.44 min shorter)"
Now, 365.22057 x 25344 = 9,256,150
“Current Gregorian solar year count: 365.2424. days”
365.2424 x 25344 = 9,256,703
I am unable to derive your number of days for the Tychos Great Yr. of 9,256,706 using either the Gregorian figure or your figure of 365.22057
Is this simply a typo?
Wow - that’s some incredible ‘synchronicity’, dear Schoepffer! Today I was just thinking of updating the online version of Chapter 19 which - as I noticed a few weeks ago - needed some revision. You see, I’m currently refining the definitive manuscript of the 2nd Edition of the TYCHOS book, but I’m a bit lazy with the immediate updating of the online version !
In any case, please know that there isn’t really any general consensus about the EXACT duration of the solar / tropical year (depending on which sources you read, it is either 365.2424, 365.2425 or 365.24219…)
Dear Schoepffer, I think I owe you some due clarification regarding your last post - where you correctly pointed out what was actually a typo (i.e. that 9 256 706-day figure, which was a ‘remnant’ from the 1st Edition of my TYCHOS book). In the TYCHOS, a Great Year would in fact amount to 9 256 150 days as you rightly noted (whereas the Gregorian calendar count of the solar year would yield a Great Year of 9 256 706 days). I have now amended this in Chapter 19 of the online version of the 2nd Edition of the book.
So that’s a 556-day difference (or roughly 1.52 years) between the Gregorian and my proposed TYCHOS adjustment of our solar year count. Not much, you might say (over such a long 25344-year-or-so period) but enough to gradually offset the solar synchrony with our calendar & clocks and mess up our seasons. Needless to say, I do not pretend that my estimate is absolutely correct, to the day! However, I shall stick to my 365.22057 figure as representing the ideal year count, that is, under the current calibration of our clocks. To wit, our clocks have been somewhat ‘arbitrarily’ calibrated (around the Gregorian calendar computations) so as to serve at best our civil / daily purposes - and so far it has worked out pretty well. As you know though, our clocks are almost always out of synch with the Sun’s motions (see Chapter 21 ) (oscillating by as many as 31.44 minutes in the course of the year) and will only ‘agree’ with the Sun’s “true noon position” on 4 occasions each year (December 24, April 15, June 16 and August 29). Seen under this perspective, my proposed “5-second-per-day” adjustment of our clocks’ speed should hardly have a noticeable impact on our lives! Yet, it would ensure for all future generations that, for instance, the (Northern Hemisphere’s) summer solstice keeps occurring around June 21.
Let me now anticipate another question that I expect will be submitted sooner or later with regards to the Tychosium simulator. As Patrik and I started constructing the simulator, we opted to go with the Gregorian calendar’s count of 365.2425 days. The reason for this might not seem immediately obvious but should become clear in all its logic once you consider that all other (conventional / heliocentric) simulators have been ‘calibrated’ around the Gregorian solar year count. Hence, in order to compare our planets’ ephemerides (celestial postions) in the Tychosium with those shown on all other simulators, this was our obligatory choice. Well, the Tychosium is now in excellent agreement with conventional simulators - with regards to all of our Solar System’s PLANETARY positions (over many centuries back in time), but this doesn’t mean that they necessarily agree with the exact / relative STELLAR positions of ancient times. For instance, we don’t really have any reliable records going back, say, 1000 years ago, of precisely where Mars was positioned in relation to the background stars.
So, hoping that you’ve followed my reasoning thus far, I will now make an important statement with regards to the Tychosium simulator - and how it should be interpreted:
In spite of using a 365.2425 day count for the solar year (instead of the TYCHOS model’s proposed / ideal 365.22057 day count), I believe that the Tychosium does in fact correctly simulate our Solar System’s rotation - and relative positions against the stars - over the centuries. However, in order for this to be fully understood, one must imagine that the Tychosium actually ‘embeds’ (computationally-speaking) that 5-seconds-per-day adjustment of our current clocks’ “Gregorian calibration”. To be sure, the International Astronomical Union (IAU) regularly holds meetings where they discuss (and vividly debate) minor adjustments of our world clocks - since they appear to be slowly ‘slipping out of synch’ with the Sun…
Hope this makes sound sense, folks - and that your brains won’t explode in the process !
Dear Schoepffer,
In these last few days I’ve had what I would call a “belated (or retarded 
) Eureka moment’ – while often slapping my forehead for not having realized - to this day - what I will presently expound. And yes, I’ve been eating some humble pie too – and deservedly so.
Firstly though, I would like to express my gratitude for the questions that you (and others) have submitted on this forum which is turning out to be a great stimulus and lubrification for my slightly worn-out brain cogs which have been spinning non-stop for the best part of this last decade… In fact, this is just what I hoped this forum would become: a collective thought-machine powered by genuine, non-artificial human intelligence.
But let me get straight to the matter of my recent aha-moment (and forehead slaps). In short, what I wrote in the above post is all wrong – and I hereby retract it. See, my 365.22057-day estimation for the solar year (i.e. some 31.5 minutes shorter than the Gregorian solar year’s 365.2425-day figure) would be mathematically correct only IF the Earth didn’t spin around its axis – but only advanced at 1mph along its PVP orbit. However, as I had so meticulously demonstrated in my very own Chapter 21 (…for crying out loud!):
-
An earthly observer will revolve around a trochoidal path in the course of a year
-
The Sun and Earth alternately move in the same or opposite orbital directions
-
The Sun-Earth distances vary by about 3.4% in the course of a year
-
The analemma shows a 31.44-min annual east-west oscillation of the Sun
-
All the above factors combine to determine our need for the Equation of Time
Now, surely the fact that my early solar year estimation was 31.5 minutes shorter than the Gregorian one cannot be a random coincidence – or wholly unrelated to the 31.44-minute oscillation of the Sun! Here I was, staring at the analemma evidence (highlighted by myself years ago) without making the obvious connection between it - and my separate solar year estimation! Talk about not seeing the forest for the trees! 
To wit, that 31.5-min discrepancy between the Gregorian solar year count and my own is precisely what causes our clocks to slip out of synch (by the same amount) vis-à-vis the Sun each year. Paradoxically (and this is the best part of this whole affair) this means that my early “error” has thus confirmed the exactitude of the size of my proposed PVP orbit and of the TYCHOS Great Year of 25344 solar years. All I did, after all, was to calculate the TYCHOS solar year without accounting for the variables (all described in my own Chapter 21) which determine our need for the Equation of Time – in order to ‘compensate for’ the annual 31.44-min oscillation of our “master time-keeper”, the Sun !
I have now amended accordingly Chapter 19 of my upcoming 2nd Edition of the TYCHOS book (whose design and layout of its printed version is fortunately proceeding at snail-pace): Chapter 19: Understanding the TYCHOS Great Year
Phew!
Dear Simon,
Wow! If I have been of any assistance in your Eureka moment then I consider it high praise indeed and I am wearing a large grin right now!
I am going to have to go and read the revised chapter right now! I want to get my head wrapped completely around it! I have not idea what caused me to check the maths that a.m., it was just on a lark…
OK! Now I see what you mean! Since the Anelemma is “composed” so to speak, of photos taken every day at the same time, RELATIVE TO OUR CLOCKS, it gets out of sync and makes the wonky shape.
In reality, if we had some stationary object to reference the sun by instead of the time we could then snap a picture of the sun in the same location daily and then add or subtract the minutes on our watches to determine the actual amount that THEY are off! The sun is not out of synch, the clocks are! I get it! 