Newtonian Celestial Mechanics has been plagued by problems from the very beginning.
Firstly, Isaac Newton [1642-1727] provided “no hypotheses” about how his hypothetical “invisible force” was mediated “instantaneously” over “vast distances”.
Newton’s theory of gravity offered no prospect of identifying any mediator of gravitational interaction.
His theory assumed that gravitation acts instantaneously, regardless of distance.
http://en.wikipedia.org/wiki/Action_at_a_distance#Gravity
Newton’s postulate of an invisible force able to act over vast distances led to him being criticised for introducing “occult agencies” into science.
Later, in the second edition of the Principia (1713), Newton firmly rejected such criticisms in a concluding General Scholium, writing that it was enough that the phenomena implied a gravitational attraction, as they did; but they did not so far indicate its cause, and it was both unnecessary and improper to frame hypotheses of things that were not implied by the phenomena.
(Here Newton used what became his famous expression “hypotheses non fingo”)https://en.wikipedia.org/wiki/Isaac_Newton#Mechanics_and_gravitation
Hypotheses non fingo (Latin for “I feign no hypotheses,” “I frame no hypotheses,” or “I contrive no hypotheses”) is a famous phrase used by Isaac Newton in an essay, General Scholium, which was appended to the second (1713) edition of the Principia.
Here is a modern translation (published 1999) of the passage containing this famous remark:
I have not as yet been able to discover the reason for these properties of gravity from phenomena, and I do not feign hypotheses.
Secondly, the Newtonian Three-Body Problem has “no general analytical solution”.
In its traditional sense, the three-body problem is the problem of taking an initial set of data that specifies the positions, masses and velocities of three bodies for some particular point in time and then determining the motions of the three bodies, in accordance with the laws of classical mechanics (Newton’s laws of motion and of universal gravitation).
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Historically, the first specific three-body problem to receive extended study was the one involving the Moon, the Earth and the Sun.
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In 1887, mathematicians Ernst Bruns and Henri Poincaré showed that there is no general analytical solution for the three-body problem given by algebraic expressions and integrals.The motion of three bodies is generally non-repeating, except in special cases.
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Lagrange, tackling the general three-body problem, considered the behaviour of the distances between the bodies, without finding a general solution.
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In 2013, physicists Milovan Šuvakov and Veljko Dmitrašinović at the Institute of Physics in Belgrade discovered 13 new families of solutions, bringing the total number of families of repetitive motion to 16.
Newton thought the mathematics of a stable Solar System required “periodic divine intervention”.
Sir Isaac Newton had published his Philosophiae Naturalis Principia Mathematica in 1687 in which he gave a derivation of Kepler’s laws, which describe the motion of the planets, from his laws of motion and his law of universal gravitation.
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Newton himself had doubted the possibility of a mathematical solution to the whole, even concluding that periodic divine intervention was necessary to guarantee the stability of the solar system.https://en.wikipedia.org/wiki/Pierre-Simon_Laplace#Stability_of_the_solar_system
Other mathematicians settled for an “approximate solution” without “divine intervention”.
Perturbation theory comprises mathematical methods for finding an approximate solution to a problem, by starting from the exact solution of a related problem.
A critical feature of the technique is a middle step that breaks the problem into “solvable” and “perturbation” parts.
Perturbation theory is applicable if the problem at hand cannot be solved exactly, but can be formulated by adding a “small” term to the mathematical description of the exactly solvable problem.
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The earliest use of what would now be called perturbation theory was to deal with the otherwise unsolvable mathematical problems of celestial mechanics: for example the orbit of the Moon, which moves noticeably differently from a simple Keplerian ellipse because of the competing gravitation of the Earth and the Sun.
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Isaac Newton is reported to have said, regarding the problem of the Moon’s orbit, that “It causeth my head to ache.”
Therefore, if you wish to retain a sense of perspective, it’s helpful to remember Newtonian Celestial Mechanics is the refined art of the Celestial Mathematical Approximation.
Pierre-Simon Laplace [1749-1827] was one of the pioneers of Perturbation Theory who strove to develop a stable mathematical solution for the Solar System without “divine intervention”.
Perturbation theory was investigated by the classical scholars – Laplace, Poisson, Gauss – as a result of which the computations could be performed with a very high accuracy.
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The development of basic perturbation theory for differential equations was fairly complete by the middle of the 19th century.https://en.wikipedia.org/wiki/Perturbation_theory#History
Dispensing with the hypothesis of divine intervention would be a major activity of Laplace’s scientific life.
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Laplace now set himself the task to write a work which should “offer a complete solution of the great mechanical problem presented by the solar system, and bring theory to coincide so closely with observation that empirical equations should no longer find a place in astronomical tables.”The result is embodied in the Exposition du système du monde and the Mécanique céleste.
https://en.wikipedia.org/wiki/Pierre-Simon_Laplace#Stability_of_the_solar_system
The modern mainstream consensus appears to be that Laplace was “not sufficiently precise” to demonstrate the stability of the Solar System.
It is now generally regarded that Laplace’s methods on their own, though vital to the development of the theory, are not sufficiently precise to demonstrate the stability of the Solar System, and indeed, the Solar System is understood to be chaotic, although it happens to be fairly stable.
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Laplace seems to have regarded analysis merely as a means of attacking physical problems, though the ability with which he invented the necessary analysis is almost phenomenal.As long as his results were true he took but little trouble to explain the steps by which he arrived at them; he never studied elegance or symmetry in his processes, and it was sufficient for him if he could by any means solve the particular question he was discussing.
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Jean-Baptiste Biot, who assisted Laplace in revising it for the press, says that Laplace himself was frequently unable to recover the details in the chain of reasoning, and, if satisfied that the conclusions were correct, he was content to insert the constantly recurring formula, “Il est aisé à voir que…” (“It is easy to see that…”).https://en.wikipedia.org/wiki/Pierre-Simon_Laplace#Celestial_mechanics
However, it appears doubtful [by definition] that a “sufficiently precise” approximation can ever be [knowingly] arrived at when the problem has “no general analytical solution”.
The modern mainstream is also less than fulsome in its praise for Laplace’s five volume tome Méchanique Céleste because many of his results were “appropriated from other writers”.
Laplace’s analytical discussion of the solar system is given in his Méchanique céleste published in five volumes.
The first two volumes, published in 1799, contain methods for calculating the motions of the planets, determining their figures, and resolving tidal problems.
The third and fourth volumes, published in 1802 and 1805, contain applications of these methods, and several astronomical tables.
The fifth volume, published in 1825, is mainly historical, but it gives as appendices the results of Laplace’s latest researches.
Laplace’s own investigations embodied in it are so numerous and valuable that it is regrettable to have to add that many results are appropriated from other writers with scanty or no acknowledgement, and the conclusions – which have been described as the organized result of a century of patient toil – are frequently mentioned as if they were due to Laplace.
Nevertheless, the publication of Méchanique Céleste demonstrated to the public that Celestial Mechanics had matured and developed some predictive Crystal Balls.
The third volume of Méchanique Céleste [1802] fired the imagination of Laplace’s readers by providing a Formula for the Obliquity of the Ecliptic.
Traité de Mécanique Céleste – Volume 3 – 1802 – Pierre-Simon Laplace
https://archive.org/details/gri_33125010895080
Retrospect of Philosophical, Mechanical, Chemical, and Agricultural Discoveries – Volume 6 – 1811
https://archive.org/details/retrospectphilo01unkngoog
In the fifth volume of Méchanique Céleste [1825] Laplace provided a refinement that limited the Formula for the Obliquity of the Ecliptic to a range of 3º 7’ 30”.
The total range of the variation of the Obliquity of the Ecliptic was calculated by Laplace, in 1825, to be limited to 3º 7’ 30”, or 1º 33’ 45” on each side of the mean value.
The Obliquity of the Ecliptic – George F. Dodwell
http://www.setterfield.org/Dodwell/Dodwell_Manuscript_1.htmlThese altitudes give 34° 17.1729 for the altitude of the pole at Loyang, a result which agrees very nearly with the mean of the observations of the Jesuit missionaries, on the latitude of that city; they give also 23° 54’.0402 for the obliquity of the ecliptic at the epoch of Tcheou- Kong, which may be fixed without sensible error, at the year 1100 before the Christian era.
By remounting to that epoch, according to a formula given in the sixth book of the Mecanique Celeste, Laplace found that the obliquity of the ecliptic ought then to have been 23° 51’.8694; and he remarks that the difference of 2′.1703 will appear very small, if we consider the uncertainty which still exists respecting the masses of the planets, as well as that which the observations of the gnomon present, arising especially from the penumbra which renders the termination of its shadow ill-defined.
The History of the Arts and Sciences of the Ancients – 1829 – Charles Rollin
https://archive.org/details/bub_gb_8w8MAQAAIAAJ
The Golden Age of European Celestial Mathematical Approximations drew to a close in the middle of the 19th century and the dawn of a new American Age was heralded by the arrival of Simon Newcomb at the U. S. Naval Observatory in 1861.
Simon Newcomb (March 12, 1835 – July 11, 1909) was a Canadian-American astronomer and mathematician.
Though he had little conventional schooling, he made important contributions to timekeeping as well as writing on economics and statistics and authoring a science fiction novel.
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In the prelude to the American Civil War, many US Navy staff of Confederate sympathies left the service and, in 1861, Newcomb took advantage of one of the ensuing vacancies to become professor of mathematics and astronomer at the United States Naval Observatory, Washington D.C..
The new American Age of Celestial Mathematical Approximations emphatically arrived in 1873 after Simon Newcomb recommended for publication the Secular Variations of the Elements of the Orbits of the Eight Principal Planets by J. N. Stockwell which included a sophisticated Formula for the Obliquity of the Ecliptic.
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Secular Variations of the Elements of the Orbits of the Eight Principal Planets
J.N. Stockwell – Smithsonian Contributions to Knowledge, Vol. 18 – 1873 – Article 3
https://archive.org/details/smithsoniancontr181873smi
Historical Notice of John Nelson Stockwell of Cleveland – 1920 – T. J. J. See
Journal: Popular Astronomy, vol. 28, pp.565-584
http://adsabs.harvard.edu/full/1920PA…..28..565S
George Dodwell studied Stockwell’s Formula for the Obliquity of the Ecliptic and produced a Curve of Obliquity which shows the last maximum [24º 12′] occurred around 7,000 B.C.
Figure 1, below, is a graph of the regular, periodic variation of the Inclination of the Earth’s Axis of Rotation, usually known as the secular, i.e., age-long, variation of the Obliquity of the Ecliptic.
It is due to the gravitational attraction of the planets upon the Earth, interacting with the attraction of the Sun and Moon on the Earth’s equatorial protuberance.
In this graph the normal curve of the Obliquity of the Ecliptic is traced for three oscillations.
The curve is derived from the comprehensive formula given by the American astronomer, J.N. Stockwell (Smithsonian Contributions to Knowledge, Vol. 18. 1873, Article 3).
This formula, Stockwell says, enables us to obtain the numerical values of the Obliquity during all past and future ages.
From the curve, we see that the obliquity, which is now (in 1954) 23º 26′ 43″, is gradually decreasing to a minimum of 22º 30′ about 13,000 A.D.; and that it was at its last maximum, 24º 12′, about 7000 B.C..
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The attractions of the planets, combined with the sun and moon, however, cause a displacement in the plane of the Ecliptic, so that it oscillates with respect to the equator in a long period, varying from 26,000 years to 53,000 years, and this produces in the obliquity a series of maximum and minimum, having a total variation of 2º 37′ 22″, namely, from an absolute maximum of 24º 35′ 38″ down to an absolute minimum of 21º 58′ 36″, according to Stockwell’s calculations.The Obliquity of the Ecliptic – George F. Dodwell
http://www.setterfield.org/Dodwell/Dodwell_Manuscript_1.html
In 1877 Simon Newcomb became director of the Nautical Almanac Office and everything appeared to be progressing perfectly for the eminence grise of Celestial Mechanics as he entered the last decade of the 19th century.
In 1877 he became director of the Nautical Almanac Office where, ably assisted by George William Hill, he embarked on a program of recalculation of all the major astronomical constants.
Then in 1894 Norman Lockyer unleashed two bombshells that threatened to undermine the very foundations of mainstream academia.
https://en.wikipedia.org/wiki/Norman_Lockyer
Chapter XI – The Age of the Temple of Amen-Ra at Karnak
If it be accepted that the arguments already put forward justify us in regarding the temple of Amen-Ra as a solstitial solar temple, we are brought face to face with the fact that if it be of any great antiquity its orientation should be such that it will no longer receive the light of the setting sun at the summer solstice along its axis.
This results from the fact that there is a slow change in what is called the obliquity of the ecliptic – that is, the angle between the plane of the earth’s equator and the plane of the ecliptic; this change is brought about by the attraction of the other planetary bodies affecting the plane of the ecliptic.
If these planes approach each other, the obliquity will be reduced; the present obliquity is something like 23° 27′; we know that 5,000 B.C. it was 24° 22′, nearly a degree more.
A difference of 1° means, then, a difference of time of about seven thousand years.
It may go down to something below 21°.
Since the obliquity has been decreasing for many thousand years, a temple directed to the rising or setting sun at the solstice some thousands of years ago had a greater amplitude than it requires now.
Taking the orientation as 26°, and taking hills and refraction into consideration, we find that the true horizon sunset amplitude would be 27° 30′.
This amplitude gives us for Thebes a declination of 24° 18′.
This was the obliquity of the ecliptic in the year 3700 B.C., and this is therefore the date of the foundation of the shrine of Amen-Ra at Karnak, so far as we can determine it astronomically with the available data; but about these there is still an element of doubt, for, so far as I learn, the recent magnetic readings have not been checked by astronomical observations.
The Dawn of Astronomy – 1894 – Sir Norman Lockyer
https://archive.org/details/dawnastronomyas00lockgoog
Ra /rɑː/ or Re /reɪ/ is the ancient Egyptian solar deity.
http://en.wikipedia.org/wiki/Ra
Amun (also Amon (/ˈɑːmən/), Amen; Ancient Greek: Ἄμμων Ámmōn, Ἅμμων Hámmōn) was a major Egyptian deity.
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After the rebellion of Thebes against the Hyksos and with the rule of Ahmose I, Amun acquired national importance, expressed in his fusion with the Sun god, Ra, as Amun-Ra.http://en.wikipedia.org/wiki/Amun
Amen (Amon) and Amen-Ra, King of the Gods, and the Triad of Thebes
Among the gods who were known to the Egyptians in very early times were Amen and his consort Ament, and their names are found in the Pyramid Texts, e.g., Unas, line 558, where they are mentioned immediately after the pair of gods Nau and Nen, and in connection with the twin Lion-gods Shu and Tefnut, who are described as the two gods who made their own bodies, and with the goddess Temt, the female counterpart of Tem.
It is evident that even in the remote period of the Vth Dynasty Amen and Ament were numbered among the primeval gods, if not as gods in chief certainly as subsidiary forms of some of them, and from the fact that they are mentioned immediately after the deities of primeval matter, Nau and Nen, who we may consider to be the equivalents of the watery abyss from which all things sprang, and immediately before Temt and Shu and Tefnut, it would seem that the writers or editors of the Pyramid Texts assigned great antiquity to their existence.
Of the attributes ascribed to Amen in the Ancient Empire nothing is known, but, if we accept the meaning “hidden” which is usually given to his name, we must conclude that he was the personification of the hidden and unknown creative power which was associated with the primeval abyss, gods in the creation of the world, and all that is in it.
The word or root amen, certainly means “what is hidden,” “what is not seen,” “what cannot be seen,” and the like, and this fact is proved by scores of examples which may be collected from texts of all periods.
In hymns to Amen we often read that he is “hidden to his children, “and “hidden to gods and men,” and it has been stated that these expressions only refer to the “hiding,” i.e., “setting” of the sun each evening, and that they are only to be understood in a physical sense, and to mean nothing more than the disappearance of the god Amen from the sight of men at the close of day.
http://www.touregypt.net/amen.htm
The first bombshell unleashed by Norman Lockyer upon the Cognigenti of Mainstream Academia was the realisation that anyone capable of resolving the Formula for the Obliquity of the Ecliptic could date any architectural alignment of their choosing.
In other words, the Cognigenti of Mainstream Academia were no longer the sole arbiters of the historical timeline.
The second bombshell unleashed by Norman Lockyer upon the Cognigenti of Mainstream Academia was the obliquity of 24° 18′ used by Lockyer to date of the Temple of Amen-Ra.
The [unthinkable] significance of 24° 18′ is that it exceeded the last obliquity maximum of 24º 12′ [about 7000 B.C] according to Stockwell’s Celestial Mathematical Approximation of 1872.
The mainstream was actually cut a break by Lockyer when he dated the Temple of Amen-Ra using Laplace’s old Formula for the Obliquity of the Ecliptic.
It may be said that this is only a statement, and that the record has been falsified; some years ago anyone who was driven by facts to come to the conclusion that any very considerable antiquity was possible in these observations met with very great difficulty. But the shortest and the longest shadows recorded (1100 years B.C.) do not really represent the true lengths at present. If anyone had forged these observations he would state such lengths as people would find to-day or to-morrow, but the lengths given were different from those which would be found to-day.
Laplace, who gave considerable attention to this matter, determined what the real obliquity was at that time, and proved that the record does represent an actual observation, and not one which had been made in later years.
The Dawn of Astronomy – 1894 – Sir Norman Lockyer
https://archive.org/details/dawnastronomyas00lockgoog
Had Lockyer used Stockwell’s 1872 Formula for the Obliquity of the Ecliptic then the dating of the Temple of Amen-Ra [with an obliquity of 24° 18′] would have been between 44,000 B.C. and 49,000 B.C.
The unthinkable [and unpublished] 50,000 year timeline based upon Stockwell’s Formula for the Obliquity of the Ecliptic panicked the Cognigenti of Mainstream Academia into action.
The task of squeezing the toothpaste back into the tube naturally fell upon Simon Newcomb [then director of the Nautical Almanac Office ] because he was responsible for promoting the publication of Stockwell’s Celestial Mathematical Approximations in 1872.
Simon Newcomb acted decisively.
The following year [1895] saw the publication of Newcomb’s Tables of the Sun and Newcomb’s simplified Formula for the Obliquity of the Ecliptic.
Newcomb’s Tables of the Sun is the short title and running head of a work by the American astronomer and mathematician Simon Newcomb entitled “Tables of the Motion of the Earth on its Axis and Around the Sun” on pages 1–169 of “Tables of the Four Inner Planets” (1895), volume VI of the serial publication Astronomical Papers prepared for the use of the American Ephemeris and Nautical Almanac.
The work contains Newcomb’s mathematical development of the position of the Earth in the Solar System, which is constructed from classical celestial mechanics as well as centuries of astronomical measurements.
The bulk of the work, however, is a collection of tabulated precomputed values that provide the position of the sun at any point in time.
https://en.wikipedia.org/wiki/Newcomb%27s_Tables_of_the_Sun
Until 1983, the Astronomical Almanac’s angular value of the obliquity for any date was calculated based on the work of Newcomb, who analyzed positions of the planets until about 1895:
ε = 23° 27′ 08.26″ − 46.845″ T − 0.0059″ T2 + 0.00181″ T3
where ε is the obliquity and T is tropical centuries from B1900.0 to the date in question.
https://en.wikipedia.org/wiki/Axial_tilt
The very next year [1896] Newcomb’s simplified Formula for the Obliquity of the Ecliptic was [miraculously] adopted by the International Astronomical Congress.
Newcomb’s Formula for the Obliquity of the Ecliptic, as adopted by the International Astronomical Congress of 1896, and used ever since then by international agreement, is:
E (1900 + T) = 23º.27’08.26 – 46”.845T – 0”.0059 T2 + 0”.00181T3
Where
E = the Obliquity of the Ecliptic
T = the number of centuries from 1900 A.D.,
taken as ‘+’ for centuries after 1900 A.D., and ‘—’ for centuries before 1900 A.D.The Obliquity of the Ecliptic – George F. Dodwell
http://www.setterfield.org/Dodwell/Dodwell_Manuscript_1.htmlBy the time he attended a standardisation conference in Paris, France, in May 1896, the international consensus was that all ephemerides should be based on Newcomb’s calculations – Newcomb’s Tables of the Sun.
Thus, in two short years, Simon Newcomb had successfully neutralised the threat that had panicked the Cognigenti of Mainstream Academia by producing a simple Formula for the Obliquity of the Ecliptic that was a mendacious masterpiece [in its time].
Newcomb’s formula contains no Celestial Mechanics.
Newcomb’s formula contains no cyclical oscillations that can be misinterpreted.
Newcomb’s formula flows smoothly and very gradually for [plus or minus] 10,000 years.
Newcomb’s formula integrates smoothly with observational data between 1750-1900 A.D.
Newcomb’s formula can be safely used for mainstream dating back to 1,000 or 2,000 B.C.
Newcomb’s formula is so simple it can even be used by Earth Scientists.
And most important of all: the mainstream agreed to adopt Newcomb’s formula in 1896.
In other words, the Cognigenti of Mainstream Academia had regained control of the historical timeline when the “international consensus” agreed to adopt Newcomb’s mendacious masterpiece as their mainstream yardstick for dating architectural alignments.
Newcomb’s Formula has been adopted by astronomers as the International Formula for the secular, or age-long, variation of the Obliquity of the Ecliptic, within the limits of time just mentioned, that is, as far back as perhaps 1000 B.C. or 2000 B.C., and that which it will follow in similar ages to come.
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It is the general belief of astronomers that Newcomb’s Formula does truly and very closely represent the Obliquity, within the time limits mentioned; and the divergences of the Ancient and Mediaeval Observations from this Formula have been consequently ascribed to errors of these observations, due, it is generally thought, to the use of simple or crude instruments and methods of observation.The Obliquity of the Ecliptic – George F. Dodwell
http://www.setterfield.org/Dodwell/Dodwell_Manuscript_1.html
Newcomb was rewarded in 1897 for quietly putting the 50,000 year old cat back in the bag.
Awards and honours
Member, and holder of several offices, of the National Academy of Sciences (1869);
Gold Medal of the Royal Astronomical Society (1874);
Elected a member of the Royal Swedish Academy of Sciences (1875);.
Fellow of the Royal Society (1877);
Huygens Medal of the Haarlem Academy of Sciences (1878);
Editor of the American Journal of Mathematics (1885–1900);
Copley Medal of the Royal Society (1890);
Chevalier of the Légion d’Honneur (1893);
President of the American Mathematical Society (1897–1898);
Bruce Medal of the Astronomical Society of the Pacific (1898); and
Founding member and first president of the American Astronomical Society (1899–1905).
Asteroid 855 Newcombia is named after him.
The crater Newcomb on the Moon is named after him.
The Royal Astronomical Society of Canada has a writing award named after him.
the TIME SERVICE Building at the US Naval Observatory is named The Simon Newcomb Laboratory
The USS Simon Newcomb YMS 263 minesweeper was launched in 1942 – decommissioned in 1949
Norman Lockyer was rewarded in 1897 for not letting the 50,000 year old cat out of the bag.
Honours and awards
Fellow of the Royal Society (1869)
Janssen Medal, Paris Academy of Sciences (1875)
Knight Commander of the Order of the Bath (1897)
President, British Association (1903 – 1904)
The crater Lockyer on the Moon and the crater Lockyer on Mars are both named after himhttps://en.wikipedia.org/wiki/Norman_Lockyer#Honours_and_awards
https://en.wikipedia.org/wiki/Knight_Commander_of_the_Order_of_the_Bath
There were, however, a few loose ends that needed to be tidied up in the public domain.
The tidying up operation began in 1911 when Nature [founded by Norman Lockyer] published a letter suggesting the Temple of Amen-Ra possibly dated from 4,000 B.C.
From observations he had taken Sir J. Norman Lockyer determined the date of the foundation of the temple as 3700 B.C.
These observations were taken in 1891, and the centre line of the temple could not be deter1nined with the desired accuracy because of the debris, etc., which had accun1ulated along the axis.
The task of digging out the temple was, however, being undertaken by the Department of Antiquities, and in 1911 Mr. Howard Payn made further observations on behalf of Sir J. Norman Lockyer.
These observations were taken under considerable difficulties, and the axis of the temple was not completely cleared.
In a letter dated October 11 and published in “Nature” of October 19, 1911, Mr. Howard Payn says: “The result of the survey in general quite confirms the data used by Sir N. Lockyer in fixing the date at which the original axis was laid down, viz. about 3700 B.C.”
When considering the effect of the altitude of the hills across the Nile Valley behind which the sun set, Mr. Howard Payn said his observations would “make the date of the foundation a little earlier, possibly … 4000 B.C.
Note on the Age of the Great Temple of Ammon at Karnak as Determined by the Orientation of its Axis – F. S. Richards – 1921 – Survey of Egypt Paper No. 38
http://www.cfeetk.cnrs.fr/fichiers/Documents/Ressources-PDF/documents/K1154-RICHARDS.pdf
This triggered a new series of investigations which closed the issue in the public domain in 1921 by simply concluding the Temple of Amen-Ra was never designed to align with the summer solstice.
There is thus no reason to suppose that the temple of Amen-Ra at Karnak was originally laid down to have any relation whatever with the position of the setting sun at the time of summer solstice.
Note on the Age of the Great Temple of Ammon at Karnak as Determined by the Orientation of its Axis – F. S. Richards – 1921 – Survey of Egypt Paper No. 38
http://www.cfeetk.cnrs.fr/fichiers/Documents/Ressources-PDF/documents/K1154-RICHARDS.pdf
Ironically, the paper from 1921 [which so smoothly sidestepped all the issues] established that if the Temple of Amen-Ra had originally been aligned with the summer solstice then the Obliquity of the Ecliptic at that time was 25° 9’ 55”.
Based upon an obliquity of 25° 9’ 55” Simon Newcomb’s formula dates the Temple of Amen-Ra around 8,650 B. C. and according to Stockwell’s formulation the angle cannot be dated because it is beyond his “limits of the obliquity”.
Let us notice here that, according to Stockwell’s formula for the long-period variation of the Obliquity of the Ecliptic, which is still more comprehensive and more far-reaching than Newcomb’s formula, the maximum value which the obliquity can ever reach, under the combined gravitational effects of the sun, moon and planets upon the earth is 24° 35’ 38”.
The Obliquity given by the solar orientation of the Temple of Karnak, 25° 9’ 55” is more than half a degree greater than this maximum.
The Obliquity of the Ecliptic – George F. Dodwell
http://www.setterfield.org/Dodwell/Dodwell_Manuscript_1.html
Note on the Age of the Great Temple of Ammon at Karnak as Determined by the Orientation of its Axis – F. S. Richards – 1921 – Survey of Egypt Paper No. 38
http://www.cfeetk.cnrs.fr/fichiers/Documents/Ressources-PDF/documents/K1154-RICHARDS.pdf
And everyone in the mainstream [except George Dodwell] lived happily ever after because the foundation of the Temple of Amen-Ra is safely and officially dated at 3,200 B.C.
Founded 3200 BC
However, in 1984 the world of Celestial Mathematical Approximations finally admitted [to themselves] that Simon Newcomb’s mendacious masterpiece no longer reflected reality.
Clearly, the world of mainstream Celestial Mathematical Approximations hasn’t a clue about the long term motion of the Obliquity of the Ecliptic or the age of the Temple of Amen-Ra.
As for Simon Newcomb the reader is left to decide for themselves whether he’s a Hero or a Villain in the pantheon of scientific luminaries.
In addition to the master criminal Adam Worth, there has been much speculation among astronomers and Sherlock Holmes enthusiasts that Doyle based his fictional character Moriarty on the American astronomer Simon Newcomb.
Newcomb was revered as a multitalented genius, with a special mastery of mathematics, and he had become internationally famous in the years before Conan Doyle began writing his stories.
More to the point, Newcomb had earned a reputation for spite and malice, apparently seeking to destroy the careers and reputations of rival scientists.
https://en.wikipedia.org/wiki/Professor_Moriarty
Sherlock Holmes and some Astronomical Connections – 1993 – B. E. Schaefer
Journal of the British Astronomical Association, Vol.103, No.1
Personally, I think Simon Newcomb was The Harry Houdini of Heuristics who enabled academia to escape from an unthinkable reality i.e. its state of prejudice and ignorance.
A heuristic technique, sometimes called simply a heuristic, is any approach to problem solving, learning, or discovery that employs a practical methodology not guaranteed to be optimal or perfect, but sufficient for the immediate goals.
Where finding an optimal solution is impossible or impractical, heuristic methods can be used to speed up the process of finding a satisfactory solution.
Heuristics can be mental shortcuts that ease the cognitive load of making a decision.
Examples of this method include using a rule of thumb, an educated guess, an intuitive judgment, stereotyping, profiling, or common sense.
MalagaBay 
The photo of the Temple of Amen-Ra immediately above, with the group of tourists strongly suggests a mismatch of scale and I would, based simply on size, equate this temple as contemporaneous with the enormous rock trilithons of the Temple of Jupiter at Baalbek in Lebanon. These constructions are too large to have been made by humans of our size but would make sense for larger sized humans. I would add the Athenian Acropolis to these gigantic constructions.
I would thus suggest that these constructions could have been made by giant sized humans living during the Jurassic Era when other giant life-forms existed. The problem is the absence of any giant human fossils apart from their inferred architectural artefacts.
The other problematical assumption is that of assuming that the Earth’s orbit around the sun, along with its rotational speed, have been constant so that retrocalculation is possible. The standard accretion cosmological model assumes the earth-sun distance etc have been constant since the beginning. The various interpretations proposed by the Thunderbolts Project suggest otherwise.
Of course if one is a devout uniformitarian and Darwinian, these musings of mine would be heresy.
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The date of this post is April 2015, so I am submitting a reply late, – by 2yrs. But first I have to say you have posted, IMHO, an excellent study of the tribulations of this particular subject.
In both this thread and an earlier one re ‘Axial tilt’, you make reference to George F Dodwell. However the main thrust of Dodwell’s efforts regarding obliquity, was his assertion that the Earth’s obliquity changed –abruptly- from a low value to what it is today; an event he dated to 2345 bce. He also attributed the changes in obliquity in the following the two millennia bce also to an exponential sort of readjustment to the new value. That was a very maverick jump from the ‘herd-pen’, and what followed was to be expected.
In 2010 I was also making enquiries on obliquity and the possibility of abrupt changes (I heard of Dodwell later). That was based on findings of ancient calendars (now dated from pre 5000bce to post 2000bce), that showed such a sudden change in obliquity in their construction/adjustment, between 3000 and 2200bce. Long story, so fast forward, it appears that the ‘constant’ in Stockwell/Newcomb formula (today epsilon suffix 0) can change – naturally, abruptly, cataclysmically, —with enough pre-historical evidence, as I have found out. What followed after that date was mild in comparison.
What I refer to gives credence not only to Dodwell, but also somehow to Plato– his reason for the periodic cataclysms was ‘a declination of the heavens’. How could he ‘guess’ or invent a reason like that? As I also found out, up to the first millennium bce ancient knowledge was still remembered quite correctly. Then the age of obfuscation set in.
Rolling back the Age of Obfuscation one step at a time.
Thank you…
I have great difficulty accepting precession at all, either the whole sky has to ‘precess’ in unison or it just doesn’t work for me. http://binaryresearchinstitute.com/bri/sirius-research-group/ click on angular momentum in the link too. Binary has a host of problems too, but what if the earth [solar system] was following a helical course through space, somethin like b. in this image http://etacar.put.poznan.pl/piotr.pieranski/IdealTwistedPair.html Lets guess a simple orbit takes 26,000y. close encounter with partner 40 odd k and the full circuit 100 odd k. I have the temple built after 1,000k bce.
An interesting link. More confirmation than illumination.
https://www.varchive.org/lec/lethbridge/amnesia.htm
This is apsidal, or orbital, precession. The animation should help to show what happens.
http://en.wikipedia.org/wiki/Apsidal_precession
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