THE EARLY

MODERN PERIOD:

COPERNICUS

TO

NEWTON

(1543–1726)

The Early Modern Period: From Copernicus’ De Revolvtionibvs (1543) to the Third and Final Edition of Newton’s Principia (1726)

The current philosophical and cultural predominance of heliocentrism emerged in the early modern period, being initially promulgated by Copernicus (1473–1543) in the early sixteenth century.1 The heliocentric model was further refined and promoted by Galileo (1564–1642)2,3 and Kepler (1571–1630)4 in the early seventeenth century. A late seventeenth and early eighteenth century exposition of that view incorporating (so-called) gravitation5 with the (allegedly) resultant ellipsoidicity or spheroidicity of the earth is included in the third edition of Newton’s Philosophiae Naturalis Principia Mathematica (1726). Specifically, Newton wrote the following theorem using (alleged) universal gravitation to propose (to a first degree of approximation) the (alleged) sphericity of the large-scale structure of the earth’s surface, subsequently using the (alleged) diurnal rotation of the earth to propose (to a second degree of approximation) the (alleged) ellipsoidicity or spheroidicity of the large-scale structure of the earth’s surface:

That the axes of the planets are less than the diameters drawn perpendicular to the axes.
    The equal gravitation of the parts on all sides would give a spherical figure to the planets, if it was not for their diurnal revolution in a circle. By that circular motion it comes to pass that the parts receding from the axis endeavor to ascend about the equator; and therefore if the matter is in a fluid state, by its ascent towards the equator it will enlarge the diameters there, and by its descent towards the poles it will shorten the axis. So the diameter of Jupiter (by the concurring observations of astronomers) is found shorter between pole and pole than from east to west. And, by the same argument, if our earth was not higher about the equator than at the poles, the seas would subside about the poles, and, rising towards the equator, would lay all things there under water.6

Concerning the diameter of Jupiter (by the concurring observations of astronomers), Newton states in the subsequent proposition as follows:

To find the proportion of the axis of a planet to the diameters perpendicular thereto.
    [...]
    [8th paragraph] And Cassini observed, in the year 1691, that the diameter of Jupiter reaching from east to west is greater by about a fifteenth part than the other diameter. Mr. Pound with his 123-foot telescope, and an excellent micrometer, measured the diameters of Jupiter in the year 1719, and found them as follows: […] [Newton reports Pound’s four sets of observations in a table, the average ratio of the Greatest diameter to the Lesser diameter being 12.99 to 12.01, more or less consistent with Cassini’s observation.]7

Hence, on the basis of Newton’s metaphysical precept of gravitation and the observation of a celestial entity presumed to be a spheroidal or ellipsoidal mass (that on the basis of observation, not presumption, could just as easily be a luminary) the (alleged) approximate sphere (of the earth) is mathematically modeled as an oblate spheroid or ellipsoid of revolution. In that regard, Newton addresses the following problem (see Figure 1):

To find the proportion of the axis of a planet to the diameters perpendicular thereto.
    [...]
    [5th paragraph] Therefore if APBQ represent the figure of the earth, now no longer spherical, but generated by the rotation of an ellipse about its lesser axis PQ; and ACQqca a canal full of water, reaching from the pole Qq to the centre Cc, and thence rising to the equator Aa; the weight of the water in the leg of the canal ACca will be to the weight of the water in the other leg QCcq as 289 to 288, because the centrifugal force arising from the circular motion sustains and takes off one of the 289 parts of the weight (in the one leg), and the weight of 288 in the other sustains the rest.8,9 [...]

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Figure 1. [...] the figure of the earth, now no longer spherical, but generated by the rotation of an ellipse about its lesser axis PQ […] (from Newton)10,11


The reader is advised that the above focus on Newton’s explanation of the (alleged) genesis of the (alleged) ellipsoidal or spheroidal (as opposed to spherical) large-scale structure of the earth’s surface is to point out (from the perspective of the heliocentric model) its absolute dependence upon the (alleged) diurnal rotation of the earth. In other words, heliocentrism (because it posits the (alleged) diurnal rotation of the earth) necessarily implies its (alleged) ellipsoidicity or spheroidicity. Whereas, a refined version of that model is the currently accepted paradigm,12 the adherence of many geocentrists to the ellipsoidal or spheroidal large-scale structure of the earth’s surface (allegedly shaped as a result of its alleged diurnal rotation during its allegedly naturalistic formation) is an absurdity since geocentrism necessarily implies a stationary earth. And whereas heliocentrism implies a moving, spheroidal earth with a distant cosmology,13 geocentrism must imply a stationary, planar earth with a proximate cosmology.

Hence, contemporary society is not only being deceived by centuries of heliocentrism, but also by the equally pernicious spheroidal earth geocentrism.14


— FINIS —


  1. For an English translation, see Nicolaus Copernicus, On the Revolutions of the Heavenly Spheres, translated by Charles Glenn Wallis, in Great Books of the Western World, Vol. 16, Ptolemy ∙ Copernicus ∙ Kepler, Robert Maynard Hutchins, Editor in Chief, and Mortimer J. Adler, Associate Editor, and published with the editorial advice of the faculties of The University of Chicago (Chicago: William Benton, Encyclopaedia Britannica, 1952).↩️

  2. Galileo Galilei, Il Saggiatore (The Assayer) in La Letteratura Italiana, Storia e Testi [Italian Literature, History and Texts], Vol. 34, Galileo e gli Scienziati del Seicento [Galileo and the Seventeenth Century Scientists], Tomo I [Tome I], Opere di Galileo Galilei, A Cura di Ferdinando Flora [Works of Galileo Galilei, Edited by Ferdinando Flora] (Milano: Riccardo Ricciardi Editore, 1953).↩️

  3. For an English translation of Il Saggiatore, see Galileo Galilei, The Assayer (Translated from the Italian by Stillman Drake) in The Controversy on the Comets of 1618, Translated by Stillman Drake and C.D. O’Malley (Philadelphia: University of Pennsylvania Press, 1960), pp. 151–336.↩️

  4. Johannes Kepler, Epitome of Copernican Astronomy (Translated by Charles Glenn Wallis) in Great Books of the Western World Vol. 16, Ptolemy ∙ Copernicus ∙ Kepler, Robert Maynard Hutchins, Editor in Chief, and Mortimer J. Adler, Associate Editor, and published with the editorial advice of the faculties of The University of Chicago (Chicago: William Benton, Encyclopaedia Britannica, 1952).↩️

  5. To understand the sophistry of the gravitation hypothesis, see The Cavendish Experiment (1798).↩️

  6. Sir Isaac Newton, Mathematical Principles of Natural Philosophy, Third Edition, 1726 (Translated by Andrew Motte, Revised by Florian Cajori) in Great Books of the Western World, Vol. 34, Newton ∙ Huygens, Robert Maynard Hutchins, Editor in Chief, and Mortimer J. Adler, Associate Editor, and published with the editorial advice of the faculties of The University of Chicago (Chicago: William Benton, Encyclopaedia Britannica, 1952). See Book III. The System of the World (In Mathematical Treatment), Propositions (Proposition 18, Theorem 16), p. 288.↩️

  7. Ibid., Proposition 19, Problem 3, p. 291.↩️

  8. Ibid., pp. 288-289, 5th paragraph. Oddly, in Figure 1, the (allegedly greater) equatorial axis is represented by the vertical line AB, whereas the (allegedly lesser) polar axis is represented by the horizontal line PQ.↩️

  9. Lest the reader think that there is some mistake, it should be noted that it is just coincidental that the page numbers associated with the above two citations in respect of Newton, specifically p. 288 (Proposition 18) and p. 289 (Proposition 19), are the same as the numbers (288 and 289) used by Newton to characterize the allegedly spheroidal shape of the large-scale structure of the earth’s surface in terms of the ratio of the minor and major diameters.↩️

  10. Loc. cit. Figure 1 is a reproduction of an unnumbered, untitled drawing included with p. 289, 5thparagraph.↩️

  11. For practical reasons, Figure 1 has been drawn as a perfect circle (as in the referenced drawing) but in reality is slightly elliptical representing an ellipse of rotation having major and minor axes differing by 1 part in 289.↩️

  12. Cf. National Geospatial-Intelligence Agency (NGA) Standardization Document (Office of Geomatics), Department of Defense World Geodetic System 1984: Its Definition and Relationships with Local Geodetic Systems (NGA.STND.0036_1.0.0_WGS84), Version 1.0.0, 2014-07-08, Table 3.1 WGS 84 Defining Parameters, page 3-4.↩️

  13. The distant cosmology subsumed by spheroidal earth geocentrism raises another absurdity, that of the (allegedly) distant stars orbiting a stationary earth at (allegedly) superluminal velocities. On the other hand, the proximate cosmology subsumed by planar earth geocentrism precludes any absurdity wherein the proximate luminaries orbit (the proximate) Polaris diurnally at velocities many orders of magnitude lower.↩️

  14. To understand the reason for the recent re-emergence of this fallacy, see Nota Bene: The Fallacy of Spheroidal Earth Geocentrism.↩️


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