Chapter 14: Curing Newton's headache - the Moon

To poor Sir Isaac Newton, the Moon’s motions were notoriously problematic - and caused him much misery and sleepless nights :

“The motion of the Moon is very complicated. Sir Isaac Newton is supposed to have told his friend Halley that lunar theory ‘made his head ache and kept him awake so often that he would think of it no more."

Dynamics of the Sun-Earth-Moon system

Here's how the Tychosium 3D simulator traces our Moon's motions. No wonder that they caused so much misery to Sir Isaac!

It is quite ironic that the greatest - and still ongoing - astronomical controversy of all times revolves around our own Moon’s motions. After all, the Moon is our largest, nearest and thus most intensely studied celestial body: shouldn’t our world’s scientific community have fully settled the matter by now, after all these centuries? How can the Moon’s motions still be such a hotly debated question? Here’s what we can read today at Wikipedia:

“Lunar theory attempts to account for the motions of the Moon. There are many small variations (or perturbations) in the Moon’s motion, and many attempts have been made to account for them.” Lunar Theory

Attempts. Just attempts. The “lunar theory” Wikipedia page goes on saying that “after centuries of being problematic, lunar motion is now modeled to a very high degree of accuracy.” Well, that is simply untrue since modern scientists are still looking to solve the Moon’s seemingly inexplicable and 'anomalous' orbital motions, as this abstract from a scientific study dated 2011 concludes:

“Thus, the issue of finding a satisfactory explanation for the anomalous behavior of the Moon’s eccentricity remains open.” On the anomalous secular increase of the eccentricity of the orbit of the Moon

No wonder the Moon’s baffling motions caused much pain in poor Sir Isaac’s brain: they stubbornly refused to comply with his gravitational theories! But let us have a brief look at what the Moon controversy was all about, as documented in the astronomy literature:

The controversy surrounding the secular acceleration of the moon's mean motion

No firm explanation has been put forth for what causes these apparent variations of the Earth’s and the Moon’s orbital and/or rotational speeds. Astronomy literature offers very frail theories (and unending flame wars) about the so-called “non-gravitational effects” which would account for the observed phenomena. Astronomy historian John Phillips Britton remarked in a 1992 essay that the Moon’s acceleration...

...“was proving an embarrassment to theoretical astronomers, since no gravitational explanation for this phenomenon could be found.”

— p. 153, “Appendix I. Secular accelerations of the Sun and Moon”, Models and Precision: The Quality of Ptolemy’s Observations and Parameters by John Phillips Britton (Garland, 1992)

Eventually, astronomers turned to geologists for assistance and - for a while - some sort of mad consensus was reached that it all had to do with “tidal friction forces” that would somehow slow down Earth’s rotation as well as speed up the lunar motion! However, in the introduction to his academic paper “Non-gravitational Forces in the Earth-Moon System”(1972), Robert Russell Newton (famed for his extensive work on the apparent changes of Earth’s rotation rate and expertise about lunar eclipses) curtly states in the abstract:

“There are no satisfactory explanations of the accelerations. Existing theories of tidal friction are quite inadequate.”

— p.179, Astronomical Evidence concerning Non-gravitational Forces in the Earth-Moon System by R.R. Newton (1972) for Astrophysics and Space Science, Volume 16, Issue 2, pp.179-200

Further on in his paper, R.R. Newton concludes:

“We are seriously lacking in mechanisms to explain the non-gravitational forces. The only mechanism of tidal friction (the ‘shallow seas’ model) that has been evaluated quantitatively provides only one-fourth of the necessary amount of friction, and it does not provide for much change with time within a period as short as historic times.”

In fact, the Moon’s motions were - and still are - in serious conflict with Newton’s gravitational laws. It is a matter of historical record that his theories were contradicted by the Moon’s “inexplicable, renegade behavior”, and that this plain fact ignited a humongous, endless controversy among our world’s scientific community which, incredibly enough, remains unresolved to this day. Now, don’t let any smartass astronomer tell you otherwise (i.e. that “the Moon controversy was eventually resolved”) for it would be a bare-faced lie which flies in the face of what has been repeatedly admitted all over the astronomy literature, as I am partially documenting here.

Yet, what astronomy students are taught today is that the Moon’s utterly bewildering motions were successively “resolved” by some of the most revered scientists of our times (e.g., Euler, Horrocks, Lagrange, Laplace, Clairaut, Dunthorne, Mayer, Einstein, to name but a few), all of whom contributed to constructing a vast number of “terms” and “perturbations” that would supposedly account for the Moon’s 'anomalous' motions. Eventually, a veritable hodge-podge of theories were formulated in order to rescue Newton’s sacrosanct gravitational laws. Here’s what we can read today at the Wikipedia's Lunar Theory entry (as linked above):

“The analysts of the mid-18th century expressed the perturbations of the Moon’s position in longitude using about 25-30 trigonometrical terms. However, work in the nineteenth and twentieth century led to very different formulations of the theory so these terms are no longer current. The number of terms needed to express the Moon’s position with the accuracy sought at the beginning of the twentieth century was over 1400; and the number of terms needed to emulate the accuracy of modern numerical integrations based on laser-ranging observations is in the tens of thousands: there is no limit to the increase in number of terms needed as requirements of accuracy increase.”

As you can see, there is apparently no limit to the increase of terms needed to explain the Moon’s motions. The numbers of these terms keep growing year by year, with no end in sight; and most assuredly, astronomy students are not encouraged to question the validity of the same (to do so would be 'scientific heresy' - in the world of academia). But let me submit a few more excerpts from the astronomy literature to back up and document my previous assertion (that most astronomers, back in the days, agreed at least upon one thing: i.e. that the Moon’s motions gravely contradicted Newton’s gravitational laws). Here’s an extract from the book “Pierre-Simon Laplace, 1749-1827: A Life in Exact Science”, by Charles Coulston Gillispie (1997):

A Life in Exact Science

And here’s an extract from the “Edinburgh Review or Critical Journal”, again highlighting the fact that the Moon’s observed motions (what with its so-called “anomalies and inequalities”) were in stark contradiction with Newton’s gravitational theories:

The Edinburgh review or Critical Journal

The problems with the Moon’s motions ranged from its observed periodic (short-term) motions and all the way to its secular (long-term) motions over the centuries. The latter triggered a gigantic (and still unsettled) debate as studies of the ancient solar/lunar eclipses suggested that over time the Moon was continually “accelerating”, although - paradoxically enough - its orbital speed was thought to be slowing down. Other theories proposed that it was actually Earth’s rotation that was decelerating! In short, and to put it bluntly - it was all a big mess.

“Astronomers who studied the timing of eclipses over many centuries found that the Moon seemed to be accelerating in its orbit, but what was actually happening was that the Earth’s rotation was slowing down. The effect was first noticed by Edmund Halley in 1695, and first measured by Richard Dunthorne in 1748, though neither one really understood what they were seeing.” Is the Moon moving away from Earth?

A host of other proposed effects to explain the baffling motions of our Moon have been put forth over the centuries, such as “tidal forces”, “core-mantle coupling”, assorted "turbulences" and “planetary perturbations”. All these various gravitational or non-gravitational “disturbances” had to be imagined / invented by our most eminent astronomers, physicists and mathema[g]icians since the Moon’s observed motions obstinately refused to obey Newton’s laws. The theories kept piling up, yet none of them succeeded at attaining any sort of plausible, let alone precise, answer to the puzzling motions of the Moon.

Perhaps the most cringeworthy attempt to salvage Newton’s 'inviolable laws' was that of Paul Dirac, hailed as “one of the most significant physicists of the 20th century”. Here’s what we may read in a paper by F. R. Stephenson published in the Journal of the British Astronomical Association:

“The most plausible cause of a non-tidal acceleration is a possible time rate of change of G, as was first proposed by Dirac. Such a change would affect the planets as well as the Moon, producing accelerations (or decelerations) in the exact ratio of the mean motions.”

Huh? A “time rate of change of G”, that all-important 'gravitational constant'? Oh well, so... " Hey, gentlemen, let’s just tweak that “constant” and make it a “non-constant”, et voilà: Newton wins again!" It is quite comical to read about the many ad hoc “remedies" concocted by the heliocentric disciples - in their feverish travails to patch up the cracks in their crumbling edifice. In short, the time has come to clear up this messy state of affairs. I shall start with these supposed secular “accelerations” and/or "decelerations" of the Moon and demonstrate how the TYCHOS can account for them in the simplest imaginable manner. My below graphics should hopefully help visualize what has caused so much confusion and controversy around our Moon's observed motions.


Isaac Newton credited his own mentor and sponsor Edmond Halley for having first discovered the "secular acceleration of the Moon". Interestingly, in the below book extract we can read that Halley was spurred by "a perceived need to prove that the universe was not eternal"...

My below diagram illustrates how and why the Moon will indeed appear to accelerate over the centuries, yet it is only an illusion caused by the Earth-Moon system circling around the PVP orbit - as proposed by the TYCHOS model :

As you can see, once you know that Earth is slowly moving around its PVP orbit, the illusory "accelerations" and/or "decelerations" of the Moon (and/or of Earth's rate of rotation) simply disappear. Our Solar System is an extremely stable and reliable 'clockwork'- and all of our celestial bodies travel around their circular orbits (and rotate around their axes) at constant / invariable speeds. I trust that this will be welcomed as comforting news to this planet's population! So, is the universe eternal? Perhaps not - but it's probably not going to drift apart (or grind to a halt) anytime soon.

I shall now further clarify the fact that the apparent accelerations and decelerations of our Moon (or of Earth's rotation) are completely illusory.

We are told (by Copernican astronomers) that the Earth's rate of rotation is gradually decelerating or, in other words, that its axial spin is slowing down. On the other hand, we are also told that the Moon's orbital motion is slowly speeding up (in relation to Earth) and yet - at the same time - slowing down (in relation to the stars). Yes, it certainly sounds terribly confusing! However, everything can be readily explained by the gradually changing perspectives naturally caused by Earth-Moon system's slow, clockwise revolution around the PVP orbit.

Imagine a man in London always looking in the direction of Earth's 1.6km/h-motion around its PVP orbit (the man is a medium and is - magically - able to sense this direction at all times (the man is a Copernican believer and, of course, unaware of Earth's PVP orbit). For 6336 odd years, our immortal man carefully monitors the Moon's celestial positions as it moves against the background stars:

As shown in my above diagram, by the end of that 6336-year period, our man in London will find himself at a 90° angle (in relation to the Universe) from where he started (at “year 0”). Now, 90° is of course ¼ of 360° - and ¼ of Earth's circumference (40075km) amounts to 10018.75km. This means that our man in London has been, so-to-speak, 'slipping out of synch with the Moon' annually by about 1.6 kilometers (of planet Earth's circumference):

10018.75km / 6336 = 1.58124km (per year)

Well, this is very interesting, because 1.58124km equals 0.0039457% of 40075km (the circumference of planet Earth). As we saw in Chapter 12, Earth moves annually by 14036km (i.e. by 0.0039457% of its PVP orbit circumference of 355 724 597km); this motion makes us 'meet up' with the Sun at a slightly earlier point of its own orbit (in fact, 37087km 'earlier' - which is 0.0039457% of the solar orbit of 939 943 910km). And remember, 1 solar year equals 0.0039457% of 25344 years (i.e. the exact duration of one Great Year - as computed in the TYCHOS model).

At the end of these 6336 years of patient observation, our man in London will probably conclude that Earth's rotation has decelerated by 6 hours (of RA) - in relation to the Moon. As he scratches his head, he may also speculate that the Moon's orbital motion might instead have accelerated - in relation to Earth. However, to his growing puzzlement and distress, this speculation will clash with the fact that the Moon has, on the other hand, appeared to decelerate in relation to the background stars!...

One may easily imagine why our man in London will remain forever stumped at his own observations – unless he should come to realize the TYCHOS model's geometric configuration - what with the existence of the PVP orbit (and Earth's slow advancement around it). To be sure, under the heliocentric paradigm (what with Earth circling around the Sun), the observed secular motions of our Moon are not only bewildering: they are utterly inexplicable from any rational, optical, geometrical and physical perspectives.

In conclusion, and as my above diagrams should have clarified, the apparent accelerations and/or decelerations of Earth and the Moon are completely illusory. They both proceed at constant speeds around circular (albeit somewhat eccentric) orbits – much like all the other bodies in our Solar System.

(Note: In Chapter 23, I will also show why our Moon is NOT receding from Earth at about 4cm per year as currently believed. Ideally, I would have included this topic in the present chapter - but as you will realize, I must first expound why the stars are far closer to us than currently believed.)

THE MOON'S EVECTION" - explained by the TYCHOS

We shall now examine what astronomers define as "the largest observed inequality” (or "anomaly") of the lunar motion: namely, the Moon’s so-called EVECTION. In the Wikipedia we read:

“In astronomy, evection (Latin for “carrying away”) is the largest inequality produced by the action of the Sun in the monthly revolution of the Moon around the Earth. The evection, formerly called the Moon’s second anomaly, was approximately known in ancient times, and its discovery is attributed to Ptolemy. Evection causes the Moon’s ecliptic longitude to vary by approximately ± 1.274° (or ± 4586.45″ seconds of arc), with a period of about 31.8 days. The evection in longitude is given by the expression +4586.45''\ sin(2D-L), where D is the mean angular distance of the Moon from the Sun (its elongation), and L is the mean angular distance of the moon from its perigee (mean anomaly). It arises from an approximately six-monthly periodic variation of the eccentricity of the Moon’s orbit and a libration of similar period in the position of the Moon’s perigee, caused by the action of the Sun.”

Evection causes the Moon’s ecliptic longitude to vary by approximately ± 1.274° [or ± 4586.45″ seconds of arc], with a period of about 31.8 days

Now, 31.8 days is more than ONE revolution of the Moon around Earth. However, we wish to know how much the Moon oscillates during just ONE of its orbits around Earth (so as to compare it with ONE revolution of the Sun around Earth). One lunar sidereal period is 27.3 days (or 0.8585 X 31.8 days).

This means that the Moon (in the course of ONE revolution around the celestial sphere) will appear to oscillate back and forth by about:

1.274° X 0.8585 = ± 1.09373° (for a total East-West longitudinal oscillation of 1.09373°X 2 = 2.18746°)

The Moon - as viewed from Earth - subtends about 0.54° in the sky.

We see that 2.18746 / 0.54 = 4.05

The diameter of our Moon is 3474km. Hence, the total East-West displacement (“evection”) of the Moon will add up to:

3474km X 4.05 ≈ 14070km (or very close to our EAM of 14036km - representing Earth's annual motion around its PVP orbit!)

Once more, the TYCHOS (with its annual earthly motion of 14036km) accounts for yet another "inequality" of the Moon's observed motions - and this time it has to do with its longitudinal oscillation. In the previous chapter, we saw that the radial oscillation of the Moon's perigee amounted to about 14044km - and that the radial oscillation of its apogee amounted to exactly 3 X 14036km. As you may agree, the explanatory power of the PVP orbit is truly astounding.

We may thus confidently assert that the major, apparent "inequalities, irregularities and anomalies" of the Moon's spatial motions are, once more, all directly related to (and a natural consequence of) the Earth-Moon system's annual 14036-km motion around its PVP orbit.

Computing the apparent velocity variation of the Moon

As we just saw, the Moon’s evection (i.e. its longitudinal oscillation) amounts almost precisely to 14036km.

Let us now verify whether this oscillation (that Kepler ascribed to periodic variations of the Moon’s orbital speed – and its orbit’s supposed ellipticity) may be related to Earth's orbital speed of ≈1.6km/h.

Knowing that Moon’s orbital speed is 3656km/h, this is how much time the Moon will employ to cover a distance of 14036km.

14036 / 3656 = 3.839hours – or 230.35 minutes

Our civil calendar year is made of 365 days – or 525600 min. This is the timespan against which we gauge the annual lunar motions.

230.35min = 0.043826% of 525600min

We have thus obtained the percentage value of the Moon’s orbital velocity responsible for the apparent speed fluctuations (i.e. the East-to-West oscillation known as the ‘evection’)of our lunar satellite:

0.043826% of 3656km/h(the Moon’s orbital velocity) = 1.6022km/h

This is in excellent agreement with Earth’s orbital speed of 1.601169km/h (as of the Tychos model).

The below graphic should help visualize why Kepler (et al) fell for the apparent yet illusory velocity variations of our Moon’s orbital motions around Earth:

Note that at the March & September equinoxes, there will be "0" variation; at the June & December solstices the variation amplitudes will be 1.6; at mid-seasons, the variation amplitudes will be 0.8. Hence, the "mean variation coefficient" of the Moon's orbital speed will be:

0 + 0.8 + 1.6 + 0.8 + 0 + 0.8 + 1.6 + 0.8 = 6.4 ÷ 8 = 0.8

This "Mean Variation Coefficient" (henceforth "MVC") of 0.8 km/h will obviously affect our perceived motions of all of the bodies of our Solar System (in relation to the stars) since they will alternately travel in the same - or in the opposite - direction of Earth. In Chapter 25, we shall see how even the minuscule motions of the stars (and their 'mysterious' parallactic behaviors) can by accounted for by Earth's 1.6km/h motion and thus, by our "MVC".

What you need to keep in mind is that we earhtlings are like children eternally spinning around a carousel (a.k.a. "merry-go-round"). Yet, this carousel is also slowly advancing at about 1mph, almost 'on a straight line'. It is this slow (and hitherto unknown) advancement that caused Sir Isaac Newton's headaches and sleepless nights.