Chapters
Chapter 13 — Our system's 'central driveshaft': the Moon

# Chapter 13: Our system's 'central driveshaft': the Moon

The very fact that our lunar satellite – the Moon – appears to be some sort of “central driveshaft” of our entire system should, all by itself, undo the Copernican theory. In the heliocentric model it simply makes no conceivable sense that our Moon would have such a central role in our Solar System. Instead, if we envision our Moon as a body revolving around Earth at the center of our Sun-Mars binary system, then the central role of our Moon becomes evident.

In the TYCHOS, our Moon turns out to have the most revealing average synodic period of 29.22 days.

(Note: the more precise value would be 29.2194 - but for simplicity's sake, we shall use the rounded figure of 29.22)

I will henceforth call this 29.22-day period the Moon’s TMSP(True Mean Synodic Period).

This period provides us with the spectacular indication that our Moon plays a central role in our Sun-Mars binary system. This stands in stark contrast to the Copernican notion that the Moon is just some 'random' peripheral appendage circling around Earth. If that were the case, why would all of our system’s celestial bodies in the Copernican scenario exhibit exact multiples of Moon’s synodic period? Here are the facts:

The Moon, Mercury, Venus and Mars exhibit an orbital resonance pattern of:

### 1 : 4 : 20 : 25

1 TMSP : Average orbital period of our Moon: 29.22 days (29.22 X 1)

4 TMSP's : Average orbital period of Mercury: 116.88 days (29.22 X 4)

20 TMSP's: Average orbital period of Venus: 584.4 days (29.22 X 20)

25 TMSP's: Average orbital period of Mars: 730.5 days (29.22 X 25)

The average orbital period of the Sun is 365.25 days (29.22 X 12.5)

Note that: 1 + 4 + 20 + 25 = 50

Divide 50 by 4 (the number of ratios) and you arrive at 12.5 - i.e. the "Sun-Moon resonance".

Indeed, this lunar orbital resonance rule also applies to all of our so-called “outer” planets:

150 TMSP's : Average orbital period of Jupiter: 4383 days (29.22 X 150) – or 12 solar years

375 TMSP's: Average orbital period of Saturn: 10957.5days (29.22 X 375) – or 30 solar years

1050 TMSP's: Average orbital period of Uranus: 30681 days (29.22 X 1050) – or 84 solar years

2062.5 TMSP's : Average orbital period of Neptune: 60266.25 days (29.22 X 2062.5) – or 165 solar years

3100 TMSP's : Average orbital period of Pluto: 90582 days (29.22 X 3100) – or 248 solar years

As we shall see, the only reason why this perfect clockwork (featuring all of our system’s celestial bodies revolving at exact multiples of the Moon’s true mean synodic period) has gone unnoticed by astronomers throughout the ages is, essentially, due to Earth’s previously unimagined “snail-paced” motion around its own orbit. Of course, unless one is aware of this motion, all earthly determinations of the orbital periods of our system’s celestial bodies will be ever-so-slightly in error. However, as it logically puts all the pieces together, the TYCHOS model gently unveils our universe’s breathtaking cosmic harmony.

In other words, the periods of all of the bodies in our Solar System are 'round' multiples of the Moon's TMSP of 29.22 days!

Our Moon is manifestly at the center of our system in the capacity of some 'central driveshaft' for its cosmic companions.

Now, I can hear an objection like, “Hold it! Why 29.22 days? Isn’t the known synodic period of the moon 29.53 days?”

Yes, that is indeed what an earthly observer may hastily conclude. Yet, that value will depend on the particular time-window chosen to compute the Moon’s average / long-term synodic period. Therefore, only by spending centuries of careful observations will a correct average value of the Moon’s synodic period be obtained. That is just what the meticulous Aztecs appear to have done, as their famed Toltec Sunstone suggests.

“To summarize, then, the Toltec Sunstone is an image of the motion of Venus, consisting of two hundred sixty, 8-year, periods, divided up into forty 52 year periods, as encoded in the ring of 40 quincunxes surrounding the ring of 20-day names. Each 8-year period of 2922 days is counted by a rotation of the 20 day-sign ring, where each day-sign actually represents one month of 29.22 days. Therefore, one complete revolution of the day-sign ring counts 20 x 29.22 days, or the average Venus year of 584.4 days. Five of these revolutions, each uniquely named in the center quincunx, counts 100 x 29.22 = 2922 days, or five Venus years of 584.4 days each, which is equivalent to eight years of 365.25 days each. By assigning the 20 day-sign symbols to a lunar month of 29.22 days, each month of the Venus year has a unique name, just as the twelve months of our Earth year has, making it easy for the public to mark the months, or ‘moons,’ as they went by.”

For instance, if you choose a time-window of 65 years (+/- 2 days) - a little-known interval at both ends of which the Moon will realign with the Sun - you would conclude that the Moon’s average synodic period is “29.53 days”, because 65 X 365.25 days (+ 2 days) ≈ 23743 days.

If we divide 23743 days by 67 (the number of possible integer Lunar years in 65 solar years), we obtain 354.373 days.

Therefore, one average “Long ESI” (Empiric Synodic Interval) of the Moon will compute to:

354.373 days / 12 ≈ 29.53 days

Whereas if you choose a time window of 19 years (a well-known time interval, the Metonic cycle, at both ends of which the Moon will realign with the Sun), you would conclude that moon’s average period is 28.91 days.

19 X 365.25 days = 6939.75 days

If we divide 6939.75 days by 20 (the number of possible/ integer Lunar years in 19 solar years) we obtain 346.98 days.
Therefore, one average “short ESI” (Empiric Synodic Interval) of the Moon will compute to :

346.98 days / 12 = 28.915 days

But the smart Aztecs probably knew better to average the Long and Short ESIs in order to obtain the more accurate (over longer time periods) True Mean Synodic Period:

(29.53 + 28.915 = 58.445) / 2 ≈ 29.22 days (our TMSP)

The Moon also has a little-known 8-year cycle in which it very nearly realigns with the Sun every 2922 (+/-1.5) days.

This number can be obtained from: 100 revolutions X 29.22 = 2922 days = 8 solar years

Notably, the Moon’s 8-year cycle mirrors Venus’ 8-year cycle of 2922 days (5 Venus synodic periods of 584.4 days).

Thus, our TMSP of 29.22 days can be considered as the "Master Period" of our entire Solar System. The higher and lower observed values of those periods (29.53 days and 28.91 days) are just long-term fluctuations caused by the eccentricity of the Moon's orbit - and the joint 1-mph-motion of Earth-Moon system as it proceeds along the PVP orbit. Since the Earth-Moon system revolves in the opposite direction of the Sun, their respective revolutions will be opposed or co-directional, depending on the time of year. The illusion of the Moon's “acceleration/deceleration” - and its (only apparent) variable synodic periods - are thus created.

### THE MOON-SUN "SYNCHRONICITIES"

A string of remarkable 'synchronicities' emerge when comparing the respective rotations and revolutions of Earth, the Sun and the Moon. They are remarkable in the sense that, if viewed through the Copernican paradigm, it becomes extremely difficult to fathom why those multiple and apparently coincidental synchronicities would exist. After all, if Earth (along with our Moon) is just one of several planets circling the Sun, it would seem to be a quite quaint circumstance that these three separate celestial bodies would have such 'commensurate' or 'resonant' gyrational periods.

Firstly, one has to wonder why the Sun rotates around its axis in just about the same amount of time(≈27.3 days) that our Moon revolves around its orbit.

“The Carrington rotation number identifies the solar rotation as a mean period of 27.28 days, each new rotation beginning when 0° of solar longitude crosses the central meridian of the Sun as seen from Earth.”

Figure 1: The Sun and Moon's 27.3-days synchronicity - as viewed in the TYCHOS model:

Note that, as far as I can tell, this remarkable synchronicity between the Sun's rotation and the Moon's sidereal revolution has never been pointed out nor debated in astronomy literature. In any case, I have personally failed to find any studies broaching this particular 'coincidence'. Let me now illustrate how this would look like - under the Copernican model's configuration of our Solar System:

Figure 2: The Sun and Moon’s 27.3-day synchronicity, as viewed in the Copernican model.

To wit, if our Moon were just one among hundreds of moons (Jupiter’s moons, Saturn’s moons, etc.) circling the Sun, why would only one of these lunar satellites (our own Moon) have such an “intimate relationship” with the Sun? Conversely, if our Moon were instead central to the Sun’s orbit, as posited by the Tychos model (Figure 1), you may agree that this fact would suddenly appear to make far more 'intuitive sense' - and not only philosophically speaking.

Let us now compare the respective rotational speeds of the Sun, Earth and the Moon.

-Rotational speed of Sun: 6675 km/h

-Rotational speed of Earth: 1670 km/h

-Rotational speed of Moon: 16.68 km/h

We see that:

-The Sun’s rotational speed is near-exactly 4 times the Earth’s rotational speed (6675/1670 ≈ 4)

-The Sun’s rotational speed is near-exactly 400 times our Moon’s rotational speed (6675/16.68 ≈ 400)

-Earth’s rotational speed is near-exactly 100 times our Moon’s rotational speed (1670/16.68 ≈100)

Moreover,

-In the TYCHOS, the Moon’s rotational speed is approximately 10 times the orbital speed of Earth (16.68/1.601669 ≈10).

One truly has to wonder: Why would our Earth and Moon exhibit such multiple 'resonances and synchronicities' with the Sun (in terms of both rotational and orbital speeds) if our planet were just one of several bodies circling (in the "3d lane") around the Sun - as proposed by the Copernican heliocentric model?

On the other hand, if our Earth and Moon are circling in the middle of the Sun’s orbit (as proposed by the TYCHOS model), all of this becomes a decidedly less mysterious affair: our Earth and Moon revolve within the Sun's orbit - and thus enjoy a special and 'privileged' place in our Solar System (i.e. its 'barycenter'). I trust that this train of thought & logic makes sound sense - and will gradually become apparent to even the most skeptical readers of this book.

### The heliocentric model’s “lunatic” sidereal period

For this next argumentation (dismantling the Copernican theory), please keep in mind that if the Earth-Moon system truly traveled around the Sun at 107226 km/h it would move by about 70 Million kilometers every 27.3 days. Yet, in observation, our Moon lines up with the very same star each and every 27.3-day-period!

As we take a good look at the Moon’s sidereal period (of 27.3 days) through the lens of the Copernican model (which has Earth and the Moon circling the Sun around a 300 Mkm-wide orbit) we see that, once again, it miserably fails the reality test.

Let us compare its premise to an imaginary 'real world' situation that we can easily relate to:

Imagine a prisoner held on a ship which perpetually travels around a huge, circular route. It takes 365 calendar days for the ship to complete this circle (the poor prisoner can sense that the ship is circling at a certain speed). His only equipment is a magnetic compass. One night, our man sees through his porthole a distant lighthouse and estimates its location as being due North of the middle of this ship’s circular path. He really wants to figure out how long it takes for the ship to complete its circular journey. So he raises his forefinger in front of his nose and patiently starts counting the days needed for the lighthouse to align again with his forefinger.

The question is:

Should we expect our sailor to see that lighthouse regularly lining up with his finger every 27.322 days?

Of course not. Yet, this is exactly what is implied by the heliocentric theory! My below diagram depicts how our Moon is meant to align (in the Copernican model) with a given star every 27.322 days - in spite of the Earth's (supposed) orbital motion around the Sun:

To further illustrate this Copernican aberration of optical perspective, here is how the SCOPE Solar System simulator depicts the solar eclipse of March 20, 2015 at 10:00 UTC (which I personally viewed from Rome) compared to a subsequent position of the Earth-Moon pair (27.3 days later, on 16 April, 2015 at 17:00:00 UTC). On both of these dates, the Moon conjuncted - in reality - with the star Vernalis:

In fact, the entire Copernican theory relies on the misconception that “very distant objects (stars) will not be affected by parallax.”

Allow me now to state the obvious with regards to the basic laws of perspective regulating the very concept of parallax:

YES: Very little parallax will occur between two very distant objects (such as two unequally distant stars).

NO: A relatively nearby object (such as the Moon) cannot possibly remain aligned with any distant star whilst an earthly observer and the nearby object (in this case, our Moon) both drift laterally (and perpendicularly to that star's location) for several million kilometers. It is truly astonishing that the Copernican theory has survived, largely unchallenged, for as long as 400+ years!

### ABOUT THE SAROS AND EXELIGMOS CYCLES

“The saros is a period of approximately 223 synodic months (approximately 6585.3211 days, or 18 years, 11 days, 8 hours), that can be used to predict eclipses of the Sun and Moon.” "Saros astronomy" - Wikipedia (opens in a new tab)

Note that the Saros cycle of 6585.3211 days is nearly equal to 16 Full Moon cycles of 411.78433 days:

6585.3211 / 16 ≈ 411.5825 days Source: "Full moon cycle" - Wikipedia (opens in a new tab)

Now, the 18-year Saros cycle is just part of a longer and more complete triple Saros cycle known as the 'Exeligmos'. The Exeligmos comprises ca. 19756 days, into which one can find nearly 48 Full Moon cycle lengths.

19756 / 411.78433 days (a Full Moon cycle) ≈ 48 (or 3 X 16)

Here’s how the Wikipedia describes the Exeligmos (opens in a new tab):

“An exeligmos (Greek: ἐξέλιγμος — turning of the wheel) is a period of 54 years + 33 days that can be used to predict successive eclipses with similar properties and location. For a solar eclipse, after every exeligmos a solar eclipse of similar characteristics will occur in a location close to the eclipse before it. For a lunar eclipse the same part of the earth will view an eclipse that is very similar to the one that occurred one exeligmos before it.”

As a 54.1-year Exeligmos is completed, a lunar or solar eclipse will recur close to the same geographic region as it did 54 years earlier. However, at the completion of one Exeligmos the eclipse will be positioned 90 minutes earlier in our celestial sphere.

1440 minutes / 90 minutes = 16 (ergo, the Moon will 'precess' by 1/16th of our celestial sphere).

In other words, one could say that the Exeligmos is the “master cycle” of the Moon’s complex dance around Earth, at the completion of which the Moon returns to the same position with respect to the Sun. No one really knows exactly why this 54.1-year cycle exists, nor much less what causes it. Copernican astronomers can only acknowledge the Exeligmos' existence as a matter of fact - since it has been observed for millennia; yet. no attempt to explain the actual cause for its recurrence is to be found in the astronomy literature.

We shall now see how the TYCHOS model accounts for the peculiar kinematics responsible for the Exeligmos cycle - and for its very existence.

As we consider the Earth’s 1.6km/h motion (thus proceeding daily by 38.428km) we see that the distance covered by the Earth-Moon system in the course of a 19756-day Exeligmos cycle turns out to be very close to the orbital diameter of our Moon (ca. 763000 km).

19756 days X 38.428 km ≈ 759184 km

This is only about 3816 km less than the Moon’s orbital diameter. However, one may reasonably assume that this discrepancy can be accounted for by the diameter of the Moon itself (3476 km). In short, it would seem intuitively logical that an Exeligmos cycle will be completed when Earth and the Moon have together covered a distance almost equal to the Moon’s orbital diameter of 763000 km.

Let's see how this 54.1-year period would look like in the TYCHOS model. As ever, an image speaks more than a thousand words:

One can thus readily envision why the exeligmos cycle exists: it is a natural consequence of the Earth-Moon system’s 1.6 km/h motion. Every 54.1 years, the system will cover a distance equal to the Moon’s orbital diameter and, therefore, the Moon will return to an Earth-Moon-Sun alignment similar to the one 54.1 years (or 19756 days earlier). Simple as that!

To verify the exactitude of the Exeligmos' 19756-day period you may wish to test it out in the Tychosium simulator. For instance, the solar eclipse that I witnessed in Rome on March 20, 2015 (at 10:00UTC) will recur exactly 19756 days later, i.e. on April 21, 2069 (at 10:00 UTC)!

Lastly, let us verify whether the Tychos model can mathematically reconcile the Exeligmos cycle with the proposed duration of the Tychos Great Year (25344 solar years). The estimated circumference of the PVP orbit is 355 724 597 km - and in the TYCHOS, the distance covered by the Earth-Moon system over one Exeligmos is an estimated 759184 km. So let's see how this computes:

355 724 597 km / 759184 km ≈ 468.5 (i.e. the number of Exeligmoi completed by the Moon in one Great Year).

And in fact: 468.5 X 54.1 = 25345.85 - or almost precisely 25344 years, i.e. the duration of the Great Year as computed in the TYCHOS! Hence, the Exeligmos cycle turns out to be in perfect concordance with the Earth-Moon system's joint orbital speed of ≈1.6km/h. The odds of all this being entirely coincidental are, you may admit, 'astronomical'.

And thusly, the TYCHOS model elucidates the reasons for the existence of the Moon's "master cycle", the 54.1-year Exeligmos period.

### THE MOON'S 76-YEAR “CALLIPPIC CYCLE”

The Greek astronomer Callippus (ca. 330BC) gave his name to the Moon's “Callippic” cycle of 76 years (or 27759 days). It was an improvement (in terms of long-term / secular accuracy) over the so-called Metonic lunar cycle of 19 years. The Moon has indeed a most reliable 76-year cycle (or 27759 days) in which it returns to almost the exact same celestial longitude in the sky. For instance, as may be verified in the Tychosium simulator, the Moon will return - near-exactly - to just around 6h of RA on both of the below dates (separated by 27759 days):

2001-06-21 (12:00:00 UTC) and 2077-06-20 (14:00:00 UTC) = a 27759-day period

We see that 27759 days are equal to 950 TMSP's* of 29.22 days: 27759 / 29.22 = 950

Hence, there are exactly 950 TMSP's (of 29.22 days) in a Callippic cycle.

Another interesting aspect of our Moon’s Callippic cycle is its officially estimated ‘error rate’ of 1 day for every 553 years.

“The (Callippic) cycle's error has been computed as one full day in 553 years.” Callippic cycle - Wikipedia (opens in a new tab)

When viewed in the TYCHOS model, this Callippic ‘error rate’ may be interpreted as follows: As will be expounded in Chapter 21, the Sun’s annual ‘error rate’ in relation to our earthly clocks amounts to about 31.4 min, as the Sun is empirically observed to oscillate from east to west around its ‘mean zenith’ by a little more than half an hour every year. However, thanks to the ingenious gimmick known as the Equation of Time, our clocks, which tick at a constant rate, are nonetheless able to give us a useful approximation of the passage of time—accurate enough for our daily purposes.

Now, we see that 31.4 min amounts to 2.18% of 1440 min (the complete celestial sphere). Similarly, 553 years amounts to about 2.18% of 25344 years (The duration of 1 TYCHOS Great Year). It would therefore be reasonable to assume that the ‘error rate’ of the Callippic cycle is actually the lunar equivalent of the annual ‘error rate’ of the Sun.

### TESTING THE MOON'S PERIGEE PRECESSION - IN THE TYCHOS

The above graphic depicts the current astronomical understanding of the Moon’s perigee precession (a.k.a. the Moon’s “apsidal precession”). It is observed that our Moon’s perigee precesses by 0.1114° per day:

“The lunar perigee precesses in the direction of the moon’s orbital motion at the rate of n−n˜ = 0.1114 ◦ per day, or 360◦ in 8.85 years.”

A Modern Almagest: An Updated Version of Ptolemy’s Model of the Solar System (opens in a new tab) by Richard Fitzpatrick (2010)

Since our Moon’s perigee precesses by 0.1114° daily, it will complete one full 360° revolution in 8.8476327 years - or 3231.5978 days.

In fact: 0.1114° X 3231.5978 days ≈ 360°

The Moon’s perigee thus precesses annually by

0.1114° X 365.25 = 40.68885° (or ≈ 146480" arcseconds)

As we compare this empirically-observed annual precession of Moon’s perigee with our ACP (Annual Constant of Precession) of 51.136”, we see that the Moon’s perigee precesses 2864.5 X faster than the stars (i.e. our entire firmament).

146480" / 51.136" ≈ 2864.5

(Remember that our ACP of 51.136" x 25344 y adds up to a full 360° precession of our firmament - i.e. our "Great Year").

3231.5978 days / 29.22 days(the TMSP) ≈ 110.5954

There are 110.5954 TMSPs in 3231.5978 days (i.e. one full perigee precession of the Moon around Earth).

110.5954 X 2864.5 ≈ 316800 (i.e. the number of TMSP's completed by our Moon in 25344 years)

In other words, the Moon’s empirically-observed perigeal precession is in agreement with the TYCHOS-computed duration of a "Great Year" (25344 solar years).

### The MOON'S APSIDAL PRECESSION 'MIRRORS' THE EAM

What follows is nothing short of astounding: under the TYCHOS, our Moon's apsidal precession can be shown to "mirror" the EAM (Earth's Annual Motion) of 14036 km! In simple words, the so-called apsidal precession is the gradual rotation of the line connecting the apsides (line of apsides) of an astronomical body's orbit. The apsides of the Moon are the orbital points closest (perigee) and farthest (apogee) from Earth. "Apsidal precession" - Wikipedia (opens in a new tab)

We just saw that the observed angular rate of the Moon's perigee precession nicely agrees with the TYCHOS' Great Year of 25344 solar years. We shall now look at two other aspects of the Moon's oscillations. Namely, the observed magnitude (in km) of the Moon's perigee precession - and the observed magnitude (in km) of its full apsidal precession (from perigee to apogee). The Moon completes a full apsidal precession in ≈8.85 years.

Let us first have a look at how the Moon's perigee and apogee is conventionally illustrated. Here is a classic diagram one may find in astronomy books depicting the minimal and maximal Earth-Moon distances (perigee versus apogee):

The Astro Pixels database features annual charts of the Moon-Earth distances for the lunar perigee and apogee transits. Let's see if those distances might be of interest to the Tychos model. As I consulted their detailed chart of the Moon’s perigee transits, my attention was naturally drawn to this statement regarding the long-term (i.e. secular) average minimal and maximal lunar perigee distances:

“Over the 5000-year period from -1999 to 3000 (2000 BCE to 3000 CE), the distance of the Moon’s perigee varies from 356,355 to 370,399 km.” AstroPixels.com (opens in a new tab)

So let’s see: difference between 356355 km - 370399 km = 14044 km.

How interesting: this distance is almost identical to the EAM (Earth's Annual Motion) of 14036km! In fact, by carefully consulting these lunar perigee charts, one can easily verify that the Moon’s perigee regularly oscillates back and forth every solar year by an average distance of approximately 14000 km.

Here is a conceptual graphic of how the Moon's perigee will oscillate (radially) by about 14000km - "in harmony" with Earth's EAM of 14036km :

But it gets better: here’s what we can read at the Astro Pixels website about the mean variations between the lunar perigee and apogee:

“The Moon’s distance from Earth (center-to-center) varies with mean values of 363,396 km at perigee (closest) to 405,504 km at apogee (most distant).” Astropixels.com (opens in a new tab)

So let’s see: 405504km - 363396km = 42108 km - i.e. exactly 3 EAM's (14036 X 3 = 42108)!

This leads us to a most sensational realization: our Moon's apsidal precession is a perfect "reflection" of the EAM (Earth's annual 14036km motion - as proposed by the TYCHOS)! Since the Moon revolves around Earth (while Earth itself advances in space) the lunar trajectory will be a looping geometrical curve known as a 'prolate trochoid' (opens in a new tab). The longer and shorter sections of such trochoids 'operate' at a 3:1 ratio, much like that exhibited by the Moon's apogee and perigee (42108km versus 14036km). One truly couldn't wish for a better confirmation of the TYCHOS' proposed earthly rate of motion. Please make a mental note of that trochoidal 3:1 ratio - as we will encounter it again, further on in this book.

My below conceptual graphic illustrates the basic geometry of Moon's apsidal precession. Of course, the Moon doesn't complete just one such trochoid in 8.85 years - but the diagram should hopefully help envisioning the peculiar geometrics at play - particularly with respect to the above-mentioned 3:1 ratio.

I was then curious to see whether this trochoidal curve could somehow be reproduced in the Tychosium 3D simulator (over an extended length / time period which would thus plot a hypothetical time-lapse "picture" of our Moon's long-term orbital progression). I figured that, in order to "see it", I needed to increase Earth's speed in the simulator by a few orders of magnitude. This was the result:

In this chapter I have highlighted a number of aspects concerning our lunar satellite, the Moon:

• Its role as the 'central driveshaft' of our Solar System

• The synchronicity of its orbital revolutions with the Sun's axial rotations (≈27.3 days)

• The absurdity of its supposed sidereal period - as viewed within the heliocentric model

• The concordance of its Exeligmos cycle with the TYCHOS' proposed orbital speed of the Earth-Moon system

• The concordance of its Callippic cycle with the TYCHOS' proposed TMSP (of 29.22 days)

• The most remarkable commensurability (at a 3:1 ratio) between its apsidal precession and the TYCHOS' EAM of 14036km

As for our Moon's so-called 'librations' (in longitude and latitude), these are also accounted for by the TYCHOS model's geometry, what with the Moon's eccentric (yet not elliptical) orbit and the 6.7° inclination between the Moon's axis of rotation and the normal to the plane of its orbit around Earth. This is why we can actually observe up to 59% of the lunar surface - an undisputed, empirically observable fact:

"Over time, slightly more than half (about 59% in total) of the Moon's surface is seen from Earth due to libration." "Libration" - Wikipedia (opens in a new tab)

However, the complex orbital behaviour of our Moon has never been fully understood nor 'justified' - in spite of being the closest body orbiting our planet. The next chapter will therefore take a closer look at the subtler aspects of our Moon's long-term motions which, notoriously, caused Sir Isaac Newton's many a headache. As we shall see, the TYCHOS model can elucidate further aspects of its puzzling behaviour which, as famously stated by Pierre-Simon Laplace, "failed to conform in all respects with the laws of universal gravity".