Why 365.25 days - and not 360?

WHY 365.25 DAYS - AND NOT 360?

The question is certainly worth investigating: since the Sun appears to move by near-exactly 1° per day (against the stars), why doesn’t our calendar year last for 360 days? In astronomy textbooks you will find many attempts at explaining why this is the case – but there seems to be no firm, general consensus about this thorny matter. To be precise, each day the Sun is observed to move eastwards vis-à-vis the stars by 3.93 min of RA (1° being equal to 4 min of RA).

Once more, the TYCHOS model ‘comes to the rescue’ - let me illustrate how, in a few easy steps.

The below graphic from Chapter 12 of my book shows why the solar day is 4 minutes longer than the sidereal day. Quite simply, as Earth rotates once around its axis (and slowly moves around its PVP orbit), the Sun will have moved, in the meantime, a bit eastwards (between day 1 and day2). We will thus return facing a given star “X” in 1436 minutes – yet another 4 minutes will be needed for our meridian (which determines the Sun’s zenith) to return facing the Sun.

Hence:

Sidereal DAY = 1436 min (Earth having rotated by 360°)

Solar DAY = 1440 min (Earth having rotated by 361°)

Further on in Chapter 12, I then show why the solar YEAR – on the other hand – is shorter than the sidereal YEAR. This is because our earthly observer “Joe”, having moved by 14036km (in one year) along its PVP orbit, will return facing the Sun about 20.4 minutes before he returns facing the star he faced the previous year. Hence:

Solar YEAR ≈ 365.24219 days - or 525948.753 min

Sidereal YEAR ≈ 365.256363 days - or 525969.163 min

(i.e. a difference of ≈ 20.4 min)

Before we get on, it is important to remind the reader that, in one sidereal year, the Earth actually spins around its axis 366.256363 times. This, because as the Sun circles around us each year (‘counter-clockwise’), it will “subtract” one (‘counter-clockwise’) rotation of the Earth’s axis.

Now, we just saw that one sidereal DAY lasts for 1436 min. We also saw that 20.4 min is the extra time needed for our “Joe” to return facing the same star – following the completion of one solar YEAR. This is what is empirically observed and is thus beyond dispute.

This convenient percentage calculator tells us that 20.4 min is approximately 1.42% of 1436 min (representing a 360° rotation of Earth’s axis)

Well, 1.42% of 366.256363 days is just about 5.2 days. And in fact, 20.4 min / 3.93min (the amount that the Sun moves against the stars each day) ≈ 5.2. This is why a solar / calendar year doesn’t last for 360 days (as in 360°) but more like 365.2(…) days.

In other words, what causes these 5.2 ‘extra days’ is simply the Earth’s motion around its PVP orbit, thus requiring the Sun-Earth rotational relationship an extra 1.42% to remain synchronized over a full sidereal year, during which the Earth moves ‘westwards’ by 14036km – as stipulated by the TYCHOS model.

But let’s see if we can find further corroboration in support of the above statement. Let’s imagine for a moment that Earth does NOT move around its PVP orbit – but remains immobile in the middle of the Sun’s orbit. The Sun, however, still employs 25344 years (as of the TYCHOS calculations) to complete a “Great Year” – while Earth’s axis only “ticks” by 20.4 min annually.

In 25344 years, the Earth’s axis would therefore “tick” for a total of : 20.4 min x 25344 = 517017.6 min

As we divide this value by 1436 min (as we should, since a sidereal day only involves a 360° rotation of Earth’s axis), we obtain:

517017.6 min / 1436 min = 360.04011142 (or practically 360!) “axial rotations”

To be sure, this result would not have been obtained if the “Great Year” lasted for any other period than 25344 years – i.e. the duration of the “Great Year” (and of a 360° “equinoctial precession”) as proposed by the TYCHOS model. Likewise, none of the above maths would ‘check out’ with the observed reality if the Earth moved at any other speed or annual distance (respectively 1.6km/h and 14036km) - or any different relative Earth-Sun velocities - than those propounded in the TYCHOS.

Q.E.D. :slight_smile:

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ABDUL RAZZAQ’S EXCELLENT QUESTIONS

In January 2022, Prof. Abdul Razzaq released his 136-page book titled:

“The Sun and the Stars are set in motion - New Model of Solar System: Legitimate Refutation of Heliocentric Model”. https://septclues.com/Abdul_Razzaq_BOOK.pdf

Below is a short extract from his book which contains 8 excellent questions - each one of which finds sound and logical answers in the TYCHOS model - as expounded and illustrated in my above post. I shall be contacting Prof. Razzaq by e-mail in the next few days - in the hope that he might consider joining this forum and share his views, thoughts and knowledge with us all. :slight_smile:

1.3 Questions lacking mathematical and logical answers in heliocentric model

There are several questions which have no logical and mathematical answers in the
heliocentric model. Several assumptions have to be made to answer these questions.
However, these assumptions cannot be validated logically and mathematically keeping
in view the established facts and realities. These questions are listed below for
perusal and philosophical thinking of the reader to comprehend the flaws of the heliocentric
model and the purpose of writing this manuscript:

1- What is the actual time taken by the earth to revolve 360° in the orbit? Whether
sidereal year or tropical year?

2- What revolution period (tropical or sidereal) can justify the generation of 24 hour day
with 23.9345 hour rotation period of the earth?

3- The sun and the stars are assumed stationary but the earth meets the same star
earlier during rotation and aligns with the same star later than the sun during
revolution in the orbit. Why?

4- Sidereal year is 1224.51 seconds (about 20.4 minutes) longer than tropical year.
How is this difference created while the sun and stars relative to the earth are
stationary?

5- Axial Precession (precession of equator) is considered responsible for the 1224.51
seconds difference in tropical and sidereal years. How can axial precession
create this difference? Does the earth fall back in the orbit due to precession and
takes more time to reach at its initial position in the orbit? How can this difference
be validated mathematically?

6- Circular displacement of observer on the earth causes a change in angle of view
of the reference star but circular displacement of the earth in orbit does not
change angle of view of the reference star. How is this possible?

7- Tilted axis of the earth always keeps pointing to the pole star throughout the
orbital motion. How can this be proved geometrically and logically?

8- Meridians of tilted earth will not have same alignment to the radiation from the
sun during autumnal/vernal equinoxes and summer/winter solstices. How is
uniform time observed on meridians while the earth revolves in orbit with tilted
axis?

Really enjoying these recent posts as, by sheer coincidence, I happen to have just reached page 105 and the ‘unobservable arc seconds’ the day that Simon posted on such.
It’s one thing to have something like retrograde motion simply mislabeled but to have something ‘unobservable’ is sublime indeed. It is well worth doing the work, studying the Tychos just to arrive at this point.
I have a request, maybe there are some ‘real’ astronomers lurking, uncommitted on this forum. What exactly is meant by Tropical Year and is it connected to the fact that only in the tropics is the sun directly overhead at some time each day?

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I believe this is Simon’s concept of “Man’s Yearly Path”.

It cannot and that is why the internet is replete with cartoon-ish animations and diagrams instead of simulations like Patrik’s.

This is an interesting paper so far…

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Dear Schoepffer, I have now finished reading it. In the first part of his book Prof. Razzaq indeed raised a great many valid and legitimate questions as to the impossible geometry & configuration of the heliocentric model, mainly with regards to its grave problems related to the observed sidereal and tropical days and years (as treated in Chapter 12 of my TYCHOS book). It truly looked like a promising affair - as his arguments were quite similar to mine in that respect.

As I proceeded through the chapters (nodding at many of its excellent arguments) I kept wondering where he was heading and what his conclusions would be - as to the relative motions of our solar system’s bodies and the stars. It turned out to be quite a disappointment…

In short, Prof. Razzaq has “revived” the ancient idea of ALL of the stars (which he calls ‘the celestial sphere’) revolving in unison around the Earth - while still retaining a daily, anti-clockwise rotation of our planet. In his proposed model, he has the Sun and the stars orbiting clockwise around us - the latter slightly faster than the Sun. Now, the mathematics and geometrics of his system may possibly even turn out to be correct - and I’d say that they are, in any event, superior to those of the heliocentric model.

However, the notion that all the bodies comprised in the ‘celestial sphere’ (i.e. ALL the stars in the universe) revolve clockwise around the Earth - and that all would do so at a slightly faster rate than the Sun - is simply beyond any rational thought and plausibility. Firstly, because every star in the sky is observed to have its own proper motion (i.e. slowly moves in every imaginable ‘x-y-z’ direction over time) and thus there appears to be no uniform / common motion of the entire ‘celestial sphere’. Secondly, because even though Prof. Razzaq’s model nicely accounts for the apparently ‘fix’ position of our current North star Polaris over our north pole, it ultimately fails to account for the observed alternation of our north stars - and thus, for the all-important ‘equinoctial precession’ which brings us from Polaris to Vega - and back again to Polaris in 25344 years. And this is when we get to the strangest (incorrect) statement to be found in Prof. Razzaq’s book, namely:

“Nonetheless, as seen from the earth, the angle between Polaris and Vega is not 46.90° but is less than 1°.”

Not so! As seen from Earth, Polaris and Vega are - respectively - at about 89° and 39° of declination - i.e. roughly 50° apart, as illustrated in this conceptual graphic from Chapter 11 of my book:


Nonetheless, I would like to conclude this post by warmly commending Prof. Razzaq for his evidently earnest efforts to disprove the utterly unphysical heliocentric model. His own model is, in spite of its flaws and implausible star motions, geometrically superior to the Copernican contraption that we have all been taught in school. :slight_smile:

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For what it’s worth, I just finished Ch. 12 this morning…. eminently readable! I got it in one pass.

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Simon,

With the talk of 365 vs 360, and 365 vs 365.25 (or 365.2425) I’m wondering what, if any, implications there would be for calendars and time-keeping within the Tychos? This is a bit of a divergence from the main points you posted, however, I’m wondering if your calculation in any way improve the accurate calculation of days per year. Also, I’m curious to hear opinions you may have regarding the necessity of leap years?

Can you comment at all on the “leap day” concept which was used in Roman times?

A fun fact: when calculating using “365” days for ordinary years and “366” for every fourth leap year, in 100 years, there will be “36,525” days: “365.25.”

Also, it seems the Julian and Gregorian calendars and previously Hebrew calendars observe a “solar cycle.” Do you know if this cycle is referring to the sun’s activity, or is it a cycle determined by the type of calendar and frequency of leap years? And again, if the Tychos provides more accurate measurements, could this mean fewer leap years?

Very interesting post!
Thanks