Chapter 22: Deconstructing Bradley and Einstein
If there were some sort of posthumous "Nobel prize" dedicated to the preservation of the heliocentric theory, the award would probably have to be conferred to James Bradley and Albert Einstein. The latter, of course, needs no introduction - although most people may not know that his initial claim to fame was that of having 'convincingly resolved the anomalous precession of Mercury's perihelion' (which threatened to falsify & invalidate the all-important Newtonian physics). In this chapter we shall see how these two 'science superstars' deluded themselves and the world with their ill-conceived attempts to salvage the doomed, unphysical Copernican / Keplerian model.
I would firstly like to share with you the strange tale behind a supposed phenomenon that astronomers refer to as "stellar aberration" - a term coined by Sir James Bradley (the Royal Astronomer between 1742 and 1762). Bradley is universally celebrated as the man who provided definitive proof of Earth’s alleged motion around the Sun - as it supposedly hurtles at breakneck speed (90X the speed of sound!) along a 300 Mkm-wide orbit.
“James Bradley’s discovery of stellar aberration, published 1729, eventually gave direct evidence excluding the possibility of all forms of geocentrism including Tycho Brahe's.”
Back in 1725, the soon-to-become Astronomer Royal James Bradley was looking at a star called "Gamma Draconis" with his state-of-the-art telescope crafted by George Graham, London's leading instrument maker. The telescope was fitted into his chimney, for this northern star he chose to observe happened to regularly transit just above London where he lived. At 33 years of age, Bradley was already an experienced astronomer and he had duly calculated just how his chosen star should move against the more distant stars. He looked and looked, for several weeks - but the star didn't seem to move much in relation to the background stars. However, after a month or so, he finally saw that the star had moved a tiddly weeny bit. As he checked his calculations however, he realized - to his dismay - that the star had moved very oddly and in an entirely unexpected manner and direction! Together with his assistant Molyneux (a wealthy man who had financed their ambitious star-watching project), they feverishly checked and re-checked their equipment - but couldn't find anything amiss with it.
The two inquisitive men were vexed and baffled. So they decided to undertake a massive survey of the skies, over several years. In all, they eventually looked at the motions of 200 other nearby stars and, to their growing consternation and distress, they found that ALL those stars were moving in the same strange manner as Gamma Draconis. Sadly, Molyneux soon passed away - stepping into his grave without an answer to the upsetting mystery. The task to resolve the pesky puzzle was thus left to Bradley. As the story goes, the solution to the riddle came to him during a boat trip on the river Thames. Here's how astronomy historian Thony Christie (of the "Renaissance Mathematicus" blog) recounts Bradley's "Eureka Moment":
"Molyneux died in 1728 before Bradley solved the puzzle. The solution is said to have come to Bradley during a boat trip on the Thames. When the boat changed direction, he noticed that the windvane on the mast also changed direction. This appeared to Bradley to be irrational, as the direction of the wind had not changed. He discussed the phenomenon with one of the sailors, who confirmed that this was always the case. The explanation is that the direction of the wind vane is a combination of the prevailing wind and the headwind created by the movement of the boat, so when the direction of the headwind changes the direction of the windvane also changes." "The emergence of modern astronomy – a complex mosaic: Part XLV" - by Thony Christie (2020) (opens in a new tab)
One could sum up in one sentence Bradley's fantastical theory as follows: "The stars are seen to move in the 'wrong' directions (i.e. unlike one might expect if Earth revolved around the Sun) because the light particles they emit are just like raindrops slanting at an angle towards the face of a walking man". Incredibly enough, this extravagant theory has been widely embraced as 'definitive proof' of the Earth's supposed revolution around the Sun. But let me quote again from Thony Christie's "Renaissance Mathematicus" blog:
"Bradley realised that the direction of the light coming from the stars was affected in the same way by the movement of the Earth orbiting the Sun. He and Molyneux had discovered stellar aberration and the first empirical evidence of the Earth’s orbit around the Sun. The more common phenomenon used to explain aberration uses rain. When one is standing still the rain appears to fall vertically but when one in walking the rain appears to slant into one’s face at an angle. The same happens to starlight falling onto the moving Earth."
Here follows another description of Bradley's arcane concept of 'stellar aberration'. Note for later what is described as 'the most puzzling fact', i.e. that the observed star displacements are 'exactly three months out of phase':
“The aberration of starlight was discovered in 1727 by the astronomer James Bradley while he was searching for evidence of stellar parallax, which in principle ought to be observable if the Copernican theory of the solar system is correct. He succeeded in detecting an annual variation in the apparent positions of stars, but the variation was not consistent with parallax. The observed displacement was greatest for stars in the direction perpendicular to the orbital plane of the Earth, and most puzzling was the fact that the displacement was exactly three months (i.e., 90 degrees) out of phase with the effect that would result from parallax due to the annual change in the Earth’s position in orbit around the Sun.”
An here’s an extract from a book titled "The Sky at Einstein’s Feet" (2006).
The below excerpt of another article neatly sums up Bradley’s puzzling observations, which had astronomers scratching their heads. As you read it, keep in mind my Chapter 21 diagram titled "A Man's Yearly Path"; Sir James Bradley was, of course, wholly unaware of our yearly trochoidal motion and therefore had no chance of comprehending why the stars were moving in such peculiar manner.
Quoting the above paper:
“For instance Polaris, the pole star, seemed to travel annually around an ellipse whose width was 40”, 40 seconds of arc. As discussed in the section on parallax, that might suggest that the distance to Polaris was 1/40 of a parsec or 0.1 light year. However, the shifts in position did not occur at the times they were expected. The greatest shift of Polaris in any given direction occurred not when the Earth’s was at the opposite end of its orbit, as it should have been, but 3 months later. For instance, in the drawing above, the apparent position of Polaris should have been shifted the furthest in the direction of ‘December’ when Earth was in its ‘June’ position, which is far as it can go in the opposite direction. Instead, it happened in September, when the Earth had moved 90° from its position in June.” "The Aberration of Starlight" - by Dr. David P. Stern (2006) (opens in a new tab)
That’s right: Bradley found, to his amazement, that the maximal annual elongation of Polaris from an earthly observer does not occur over the expected six-month time period but will, in fact, occur three months later - i.e. nine months after the start of a year-long observation. This most recent article (February 2023) published on the "All the Science" website makes a succinct summary of Bradley's 'puzzling' observations:
"The greatest apparent displacement of the star being observed should have been found between observations six months apart, when the locations of the observations were furthest apart. The actual displacements, however, followed a completely different pattern and were clearly not due to parallax. The Pole Star, Polaris, for example, was found to follow a roughly circular path, with a diameter of about 40 arc seconds (40”)." "What is the Aberration of Light?" - by Phil Riddel (2023) (opens in a new tab)
My below graphic conceptually illustrates why any circumpolar star will reach its maximum elongation, as viewed by an earthly observer, over a 9-month period, rather than a 6-month period. Presumably, Bradley’s rough estimate of 40” was based on the vector D2 which, for an earthly observer, represents about 40”. Vector D1 represents 51.136”, i.e. the observed annual precession of the starfield which Bradley, however, could not reconcile with the ‘lunisolar wobble’ theory (see Ch.10) since it doesn’t imply that stars would revolve around trochoidal paths.
The obscure 'stellar aberration' concept (which Bradley concocted in his urge to justify otherwise inexplicable observations) has to be among the most contorted attempts at rescuing the Copernican model from its inevitable demise. As a matter of fact, Bradley's theory was subsequently falsified by his illustrious colleague George Airy who filled a telescope with water and showed that - contrary to expectations - no variation of the 'aberration' could be observed (viz. "Airy's Failure"). In spite of this setback, Bradley's thesis has somehow survived to this day - and is still widely held as valid in astronomy circles. In hindsight, it is ironic that Bradley’s laborious enterprises very nearly ended up demolishing heliocentrism 'from within', so-to-speak, since his own empirical observations contradicted the Copernically-expected motions of our stars.
Here are some interesting and curious statements we may read at the 'Explaining Science' website:
"In trying to explain his observations Bradley discovered an entirely different effect which came to be known as stellar aberration. His discovery not only confirmed the heliocentric theory but allowed an accurate measurement of the speed of light. (...) The shift in position of a nearby star caused by parallax proved to be very much smaller than the position shift due to stellar aberration, which unlike parallax does not vary with a star’s distance." "Stellar aberration" - Explainingscience.org (opens in a new tab)
Huh? If 'stellar aberration' does not vary with a star's distance, how then could it have any correlation with the speed of light? The logic of this, you may agree, would seem to be rather flimsy. At the end of the day, the only rational conclusion to draw from Bradley's 'unexpected' observations is that they revealed a local / terrestrial motion which affects all the stars equally; namely, the ever-looping frame of reference that we earthly observers are subjected to - as we revolve around our perpetual, trochoidal path (see Chapter 21).
Albert Einstein's Special Relativity Theory (SRT) proposed a different explanation for the 'stellar aberration phenomenon'. However - as pointed out in later years by various authors - when applying the SRT's tenets and algebraic formulae to stellar aberration, they simply fail to account for what is actually observed! In the abstract of his below-linked paper, Daniele Russo spells out the embarrassing problem right from the start:
"Abstract: The classical and relativistic explanations of the stellar aberration are compared, on the basis of the physical models implied by the two interpretations. Our analysis shows that the physical model required by the Special Relativity theory is inconsistent with the observed effect." "Stellar Aberration: the Contradiction between Einstein and Bradley" (2007) (opens in a new tab)
In his conclusions, Russo justly highlights the SRT's "lack of adequate physical explanations" for the observed 'stellar aberration':
"In classical Physics, a mathematical description of a phenomenon always lays on a physical model. In the case of the SRT, in spite of the simple mathematical model involved, the contrary to experience consequences of the light postulate make it often difficult to conceive adequate physical models for the various relativistic effects. Probably because of this reason, most expositions of the SRT are based on algebraic demonstrations, but lack adequate “physical” explanations that should instead be the basis of every physical theory about the macrocosmic world, as well as an indispensable element to any possible analysis or confutation. The case of the stellar aberration is emblematic. The algebraic route, consisting in the application of the SRT transformation to the system of the star and to that of the observer, does not apparently lead to contradictions. But the underlying physical model, based on a radial light radiation (light clock model), turns out to be incompatible with the parallel starlight irradiation actually reaching the Earth."
So much for Einstein's Special Relativity : as expounded by Russo in his paper (which I recommend to read in its entirety), SRT is "inconsistent with the observed (empirically-verifiable) effect" and "incompatible with the parallel starlight irradiation actually reaching the Earth". Therefore, I would tersely state that the SRT doesn't merit much attention here in this book which, of course, prioritises empirically verifiable observation over algebraic abstraction. Let's now take a look at Einstein's famed General Relativity theory (GR) - and see how it fares within the TYCHOS paradigm. Not everyone may know that Einstein’s GR theory got kick-started by his acclaimed “resolution” of the purportedly anomalous advance of Mercury’s perihelion. It was, in fact, considered as one of the most compelling proofs of GR, as stated in the Wikipedia:
“Einstein showed that general relativity agrees closely with the observed amount of (Mercury’s) perihelion shift. This was a powerful factor motivating the adoption of general relativity.” "Tests of General Relativity" - Wikipedia (opens in a new tab)
However, numerous authors have since then pointed out innumerable problems with Einstein’s equations and computational methods, as well as with his highly questionable determinations of Mercury’s supposedly anomalous apsidal precession. As it is, Einstein himself eventually distanced his subsequent GR research from the dubious argumentations surrounding the supposedly 'anomalous' advance of Mercury's perihelion.
“Einstein’s paper devoted to the GR prediction of Mercury’s perihelion advance, is the only one among his publications that contains the explanation of the GR effect. (...) Since then, to our knowledge, he never returned to the methodology of the GR perihelion advance problem. […] As a matter of fact, the GR foundational premises have been subjected to changes and reinterpretations (optional, alternative, or claimed ‘correct’ ones) by Einstein himself, his advocates as well as today’s GR specialists and self-proclaimed ‘experts’.” "Einstein Paper on the Perihelion Motion of Mercury from GRT" - by A.A. Vankov (2011) (opens in a new tab)
“It is thus proven that Einstein’s Mercury correction is completely false, and fails for planets as well as black holes! (...) The only possible conclusion to be made is that the Einstein GR correction is completely false. Thus, one of the only proofs that GR is valid has been shown to be incorrect, and invites GR to be discarded as a valid theory!” "The Incorrect Theory of Mercury’s Anomalous Precession" - by Roger Rydin (2010) (opens in a new tab)
I will hereby do my best to summarize in simple layman’s terms and maths this historically crucial, worldwide scientific debate, namely “the mystery of the anomalous precession of Mercury’s perihelion”. In this raging debate, no less than Newton’s sacrosanct laws were at stake since Mercury was observed to disobey the same. Eventually, the “victory” went to Mr. Albert Einstein, thus rocketing the little-known patent clerk (and proven plagiarist) to universal stardom literally overnight. By most (academic) accounts, Einstein’s fledgling Theory of General Relativity was then gloriously confirmed by his dreadfully convoluted “explanation” of Mercury’s seemingly anomalous behavior. The whole issue revolved around a small 43″ (arcseconds) discrepancy in Mercury’s precessional motion around the Sun: Mercury had been observed by Urbain Le Verrier to precess by an 'excess amount' of 38″ per century (later re-estimated at 43″ by Simon Newcomb in 1882), a fact which contradicted Newton’s laws.
"In 1859, Urbain Le Verrier discovered that the orbital precession of the planet Mercury was not quite what it should be; the ellipse of its orbit was rotating (precessing) slightly faster than predicted by the traditional theory of Newtonian gravity, even after all the effects of the other planets had been accounted for. The effect is small (roughly 43 arcseconds of rotation per century), but well above the measurement error (roughly 0.1 arcseconds per century). Le Verrier realized the importance of his discovery immediately, and challenged astronomers and physicists alike to account for it." "Anomalous precession of Mercury" - Hand Wiki (opens in a new tab)
At the time of the vivid debate set off by Le Verrier, the General Precession was observed to be about 5026” (arcsecsonds) per century. Since Mercury’s perihelion was observed to precess by 5600” per century - i.e. 43" more than the 5557" value that astronomers expected and could account for - the whole controversy revolved around these observed (yet supposedly anomalous) 43 'extra' arcseconds-per-century exhibited by Mercury. The below extract from a 2017 paper by Kevin Brown neatly summarizes the issues surrounding Mercury's hotly-debated 'anomaly' - in a nutshell:
"When we observe the axis of the elliptical orbit of a planet such as Mercury (for example) over a long period of time, referenced to our equinox line, we must expect to find an apparent precession of about 0.01396 degrees per year, which equals 5025 arc seconds per century, assuming Mercury's orbital axis is actually stationary. However, astronomers have actually observed a precession rate of 5600 arc seconds per century for the axis of Mercury's orbit, so evidently the axis is not truly stationary. This might seem like a problem for Newtonian gravity, until we remember that Newton predicted stable elliptical orbits only for the idealized two-body case. When analyzing the actual orbit of Mercury we must also take into account the gravitational pull of the other planets, especially Venus and Earth (because of their proximity) and Jupiter (because of its size). It isn't simple to work out these effects, and unfortunately there is no simple analytical solution to the n-body problem in Newtonian mechanics, but using the calculational techniques developed by Lagrange, Laplace, and others, it is possible to determine that the effects of all the other planets should contribute an additional 532 arc seconds per century to the precession of Mercury's orbit. Combined with the precession of our equinox reference line, this accounts for 5557 arc seconds per century, which is close to the observed value of 5600, but still short by 43 arc seconds per century." "Anomalous Precessions from Reflections on Relativity" - by Kevin Brown (2017) (opens in a new tab)
Well, we shall now see how the TYCHOS model can readily account for these allegedly 'anomalous' 43" of Mercury's precession. As we go along, keep in mind the obvious and fundamental fact that the COPERNICAN model has Earth revolving around Mercury once every year - whereas the TYCHOS model has Mercury revolving around Earth once every year. Hence, since Copernicans assume that Earth revolves yearly around the Sun (and its junior moon Mercury), they will expect Mercury to return to its perihelion earlier than it does in reality; this, because if the Earth truly revolved around the Sun, it would be "subtracting" annually from Mercury an amount corresponding to "1 unit of spatial revolution" (or, if you will, '1 Earth-vs-Mercury rotation'). In the TYCHOS, of course, no such subtraction occurs. Now, since we know that Mercury's synodic period is 116.88 days (which is the interval between two Sun-Mercury conjunctions - as viewed from the Earth) - we see that:
0.43" X 116.88 days = 50.2584" (or near-precisely the annual General Precession rate of 50.26" that was observed back in those days)
Evidently, Mercury's perihelion precession just reflects the General Precession of our Solar System - and those "anomalous 0.43 arcseconds" simply represent "1 Mercurian day" (i.e. the aforementioned "1 unit" which the Earth would subtract from Mercury IF we were revolving around the Sun). Yet, Copernican astronomers will be baffled by what they'll interpret as an 'anomalous, excess 0.43" annual precession rate' (or 43" per century)! So, to recapitulate:
The allegedly 'anomalous' precession of Mercury was 43” per century.
The allegedly 'anomalous' precession of Venus was 8.6” per century. (Yes, even Venus was thought to precess in anomalous fashion!).
As already mentioned, the observed equinoctial precession was, at the time of Einstein's ruminations, 5026” per century.
As we divide 5026" by Mercury’s synodic period we obtain Mercury's specific precession rate:
5026” / 116.88 days ≈ 43” (i.e. the perceived 'anomaly' under the heliocentric paradigm)
And if we divide 5026" by Venus’ synodic period we obtain Venus's specific precession rate:
5026” / 584.4 days ≈ 8.6” (i.e. the perceived 'anomaly' under the heliocentric paradigm)
In other words, the perceived "anomalies" were nothing but the natural / specific precession rates of Mercury and Venus, as related to their revolutions around the Sun - and commensurate to our system's General Precession. The (heliocentric) astronomers' computations erroneously account for 'one extra unit' of Mercury's and Venus' precessional motions since they believe that the Earth revolves around the Sun.
Let's verify this once more from another 'mathematical perspective': the Sun revolves once around Earth in ca. 365.25 days. One century thus contains 36525 days. The DAILY equinoctial precession (back in the early 1900’s) would thus have amounted to:
5026” / 36525 ≈ 0.1376”
Since Mercury, a moon of the Sun, revolves 3.125 X around the Sun every year (116.88 X 3.125 = 365.25), we see that:
3.125 X 0.1376” = 0.43”
1/100th of the alleged 43”-per-century “anomaly”
Similarly, since Venus is a moon of the Sun and revolves 0.625 X around the Sun every year (584.4 X 0.625 = 365.25), we see that:
0.625 X 0.1376” = 0.086”
1/100th of the alleged 8.6”-per-century “anomaly”
As you may admit, this is the simplest falsification of Einstein's theories ever performed. In what must be the funniest twist of this whole affair, it can be rightly remarked that these purported 'anomalies' actually proved that the Sun, Mercury and Venus all revolve around the Earth, and not the other way round. Once this is realized and accounted for, these 'vexing anomalies' simply disappear!
To be sure, I am by no means the first person to have concluded that the 'anomalous' precession of Mercury's perihelion was spurious (i.e. non-existent) and that, consequently, Einstein's very first "proof" of his nebulous theory of General Relativity was based on thin air. For instance, here is what the eminent professor Roger A. Rydin wrote about the subject:
“There are significant arguments that General Relativity has not been proven experimentally, and that it contains mathematical errors that invalidate its predictions. Vankov has analyzed Einstein’s 1915 derivation and concludes that when an inconsistency is corrected, there is no perihelion shift at all!” "The Theory of Mercury’s Anomalous Precession" - by Roger A. Rydin (2011) (opens in a new tab)
I will spare you the full account of the two 1919 expeditions (to Africa and South America) led by Sir Arthur Eddington to photograph a solar eclipse which purportedly provided the "ultimate proof" of Einstein's GR theory. Suffice to say that, as incredible as it may sound, this proclaimed "victory" of the Theory of General Relativity was founded upon only two out of three data sets (one of which was discarded as 'defective'). In any case, the observational data collected by Eddington's 1919 expeditions have been shown to be anything but conclusive by numerous subsequent analytical reviews.
"Einstein became world famous on 7 November 1919, following press publication of a meeting held in London on 6 November 1919 where the results were announced of two British expeditions led by Eddington, Dyson and Davidson to measure how much background starlight is bent as it passes the Sun. Three data sets were obtained: two showed the measured deflection matched the theoretical prediction of Einstein's 1915 Theory of General Relativity, and became the official result; the third was discarded as defective. At the time, the experimental result was accepted by the expert astronomical community. However, in 1980 a study by philosophers of science Earman and Glymour claimed that the data selection in the 1919 analysis was flawed and that the discarded data set was fully valid and was not consistent with the Einstein prediction, and that, therefore, the overall result did not verify General Relativity." "The 1919 eclipse results that verified general relativity and their later detractors: a story re-told" - by Gerard Gilmore and Gudrun Tausch-Pebody (2021) (opens in a new tab)
All the same, these highly questionable experimental results established Albert Einstein as the ‘champion scientist’ of our times, though not without substantial help from the solicitous media.
In conclusion, there never were any anomalies in either Mercury’s or Venus’ precessional motions, They are simply a by-product of the erroneous belief that the Earth revolves around the Sun. Likewise, there never was any ‘aberration of starlight’. Bradley’s and Einstein’s proposed explications thereof were not only contradictory: they were both flawed at their core and must be definitively abandoned.
In the next chapter, we shall see why the stars may well be considerably closer to us than posited by mainstream astronomers―just as Tycho Brahe steadfastly maintained throughout his lifetime, and with very good reason.