Chapter 14: Curing Newton's headache - the Moon
To Sir Isaac Newton, the Moon’s motions were notoriously problematic and caused him much misery and sleepless nights. In an astronomy essay (dated August 2005) by S.M. Alladin and G.M. Ballabh, we may find the following amusing anecdote regarding Sir Isaac's exasperation with the seemingly intractable motions of our Moon :
“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" - by S.M. Alladin and G.M. Ballabh(2005) (opens in a new tab)
Here's how the Tychosium 3D simulator traces our Moon's motions. No wonder that they caused so much torment to poor Sir Isaac!
It is indeed 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, nearmost and most intensely studied celestial body: shouldn’t our world’s scientific community have fully settled the matter by now, after all this time? How can our own 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" - Wikipedia (opens in a new tab)
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 today's scientists are still hard at work trying to wrap their heads around the Moon’s seemingly inexplicable and 'anomalous' orbital motions, as this abstract from a scientific study (dated February 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" - by Lorenzo Iorio (2011) (opens in a new tab)
Back in the days, the Moon’s baffling motions caused much pain in Newton's brain, since they stubbornly refused to comply with his theory of universal gravitation. So let us first take a brief look at what the Moon controversy was all about, as documented in the astronomy literature:
To this day, no general consensus has been reached regarding these apparent variations of the Earth’s and the Moon’s orbital and/or rotational speeds. Astronomy literature offers only frail theories - and unending flame wars - about some “non-gravitational effects”(!) which would account for the observed phenomena. A host of other proposed effects to explain these other enigmas have been put forth over time, such as “tidal forces”, “core-mantle coupling”, assorted "turbulences" and “planetary perturbations”. 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.”
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 the Earth’s rotation rate) curtly states in the abstract:
“There are no satisfactory explanations of the accelerations. Existing theories of tidal friction are quite inadequate.”
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. In short, and the reason why I'm stressing this point, is because you shouldn't let anyone tell you otherwise - i.e. that “the old Moon controversy was eventually resolved”; it would be a bare-faced lie which flies in the face of what has been repeatedly admitted all over the past and present literature, as I am partially documenting here.
Yet, what astronomy students are taught today is that the Moon’s utterly bewildering motions were eventually “figured out” 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 add a plethora of 'terms','perturbations','non-gravitational effects' or whatnot that would supposedly account for all the observed anomalies... Eventually, a disjointed hodge-podge of assorted theories were concocted 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 deemed as 'scientific heresy' - in academic circles). However, dear reader, I'm not quite finished yet with this 'rant' of mine concerning the problems that our own Moon has posed to our scientific community over the centuries. Here’s an extract from the book “Pierre-Simon Laplace, 1749-1827: A Life in Exact Science”, by Charles Coulston Gillispie (1997):
And here’s an old piece 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 grave contradiction with Newton’s gravitational theories:
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” (as viewed from the Earth), although its orbital speed was - paradoxically enough - 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 sorry 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.”
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”, the 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 countless ad hoc “remedies" whipped up by the heliocentric disciples - in their feverish travails to patch up the cracks in their crumbling edifice. The time has truly come to clear up this sorry 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 also a Copernican disciple and is thus 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 or 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.)
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°, 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 (on average) 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 fairly 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 between its perigee and apogee amounted to 42108km (or exactly 3 X 14036km). As you may agree, the explanatory power of the TYCHOS model - what with its proposed PVP orbit - is truly astonishing.
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 are a natural consequence of) the Earth-Moon system's annual 14036-km motion around its PVP orbit.
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 will obviously affect our perceived motions of all of the bodies of our Solar System (in relation to the stars) since it will cause them to appear to alternately accelerate or decelerate. In Chapter 24, we will see how Dayton Miller's interferometer experiments go to support the MVC and its 0.8 value. In Chapter 25, we shall then see how even the minuscule parallactic behavior of our nearmost stars can by accounted for by Earth's slow progression around its PVP orbit, thus resolving the 'mystery' of the existence of BOTH positive and negative stellar parallax.
For now, what you'll need to envision and keep in mind is that we earthlings are like children eternally proceeding (along an almost 'straight line' which only curves by about 1.42° per century) around a huge merry-go-round (the PVP orbit) that slowly rotates at 1.6km/h. It is this slow - and hitherto unknown - motion of the Earth-Moon system that caused Sir Isaac Newton's so many headaches and sleepless nights...
Modern astronomers will tell you that “the Moon recedes from Earth each year by (a little less than) 4 centimeters”. We shall now see how the Tychos model can account for - and thus dismantle - the rather alarming notion that our Moon would be, slowly but surely, "waving goodbye" to Mother Earth!
“The Moon is gradually receding from the Earth, at a rate of about 4 cm per year. This is caused by a transfer of Earth's rotational momentum to the Moon's orbital momentum as tidal friction slows the Earth's rotation.” "What will be the fate of our Moon?" - Physlink.com (opens in a new tab)
“Although the moon’s distance from earth varies each month because of its eccentric orbit, the moon’s mean distance from Earth is nonetheless increasing at the rate of about 3.8 centimeters (1.5 inches) per year. That’s about the rate that fingernails grow.” "Wayward moon receding from Earth" - EarthSky.org (opens in a new tab)
According to the TYCHOS, the Moon is not receding from Earth and is not going to vanish in space; we shall now see why the Moon's "4-cm-per-year recession" is yet another illusory conclusion drawn by Copernican astronomers who are, of course, unaware of the existence of the 25344-year PVP orbit. Hence, their computations related to the Moon’s apsidal oscillations will always fail to account for this ‘secular revolution’ of the Earth-Moon system. As they measure (against the background stars) this minute “4-cm annual recession” of the Moon, they will conclude that “our Moon is slowly drifting away from Earth”.
However, we know that the Moon-Earth distance is constantly oscillating back and forth (i.e. cyclically approaching and receding from the Earth). As we saw in Chapter 13, the Moon's orbit oscillates back and forth by 42108km (a value which we shall call the "MMAO" - i.e. "the Moon's Maximal Apsidal Oscillation"). So could the secular drift of the MMAO (over a Great Year of 25344 solar years) possibly be responsible for what astronomers interpret as an annual "4-cm recession of the Moon"? Let's see if this might be the case:
If we consider that the Earth-Moon system completes a full 360° revolution in 25344 years, we may envision how the MMAO (as its spatial orientation remains 'fixed' to the Moon's orbit) will slowly revolve ONCE in relation to the Earth in 25344 years. We may thus calculate by how much the MMAO would appear to 'drift' annually (as viewed from the Earth and in relation to the stars):
42108km / 25344y = 1.66km-per-year (representing the amount that the Moon will appear to recede from us annually - due to the slow, secular 'precession' of the MMAO around Earth).
Now, astronomers will be using their grossly inflated star distances as a benchmark to gauge the fluctuating Moon-Earth distances (i.e. with instruments calibrated to the officially-estimated stellar distances). However, as will be thoroughly expounded in Chapter 23, the TYCHOS stipulates that the stars are about 42633 times closer than currently believed. So let's divide the above value by 42633 - and see what we obtain:
1.66km / 42633 = 0.0000389km = 3.89cm (i.e. the amount that astronomers reckon to be "the Moon's annual recession rate"!)
In conclusion, the Moon is - thankfully - not parting from us anytime soon. What astromomers are "seeing" is just the slow, 25344-year secular precession of the MMAO - given by the tranquil 1-mph-motion of the Earth-Moon system around the PVP orbit. In our current epoch, the MMAO's oscillation is evidently in its 'receding phase'; over time though, there will be an 'approaching phase' which will reverse the current recession and bring things back to normal - in the good tradition of the wondrously stable and reliable 'Swiss clockwork' known as our Solar System.