Two comets that appeared in November and December of 1680 (the latter was visible till early March 1681) marked a turning point in the history of comets. As the observation of the comet of 1577 established a new era in cometology by placing comets in the supralunar region, observation of the comets of 1680/1 opened the modern epoch of cometology by introducing comets as members of our solar system. The comets of 1680/1 were in fact a single comet observed before and after perihelion, a situation that hindsight reveals as critical in the determination of the cometary trajectory. The data collected finally established that comets move around the sun, though in different types of orbits.
The comet of 1680 and the role of Flamsteed and Newton in calculating its orbit have been the topic of several studies. In this chapter, however, we shall focus mainly on the physical and chemical constitution of comets in Newton’s theory of comets as it appeared in Newton’s main publications, Principia and Opticks. Thus, it seems appropriate to give first a brief account of the introduction of Newton to cometary studies and contemporary cometary ideas.
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References
For example see: Ruffner, The Background, 239–301; Yeomans, Comets, 95–109; Richard S. Westfall, Never at Rest, A Biography of Isaac Newton (Cambridge: Cambridge University Press, 1980), pp. 391–397; Eric G. Forbes, “The Comet of 1680–1681”, in Norman J. W. Thrower, ed., Standing on the Shoulders of Giants: A Longer View of Newton and Halley (Berkeley: University of California Press, 1990), pp. 312–323; Forbes, The Gresham Lectures, pp. 28–34; D. W. Hughes, “The Principia and Comets”, Notes and Records of the Royal Society of London, 42 (1988), 53–74; Curtis Wilson, “The Newtonian achievement in astronomy”, in The General History of Astronomy: Planetary astronomy from the Renaissance to the rise of astrophysics, vol. 2A: Tycho Brahe to Newton, R. Taton and C. Wilson (eds.) (Cambridge: Cambridge University Press, 1995), pp. 231–274, Simon Schaffer, “Newton and the Transformation of Astrology”, in Patrick Curry, ed., Astrology, Science and Society, Historical Essays (Woodbridge, Suffolk: Boydell Press, 1987), pp. 219–243.
For Newton’s involvement with cometary theories before 1680 see: Ruffner, The Background, pp. 205–238; D. T. Whiteside, “Before the Principia: the Maturing of Newton’s Thoughts on Dynamical Astronomy, 1664–1684”, Journal of History of Astronomy, I (1970), pp. 5–19.
Ibid., pp. 215–224.
In Descartes’ theory, comets are considered as dead stars – bodies denser and more agitated than the planets – that can not pass the dividing ring. This ring is assumed to be a strip in a vortex which has the slowest revolutionary motion and separates the planetary region from the outer parts of the vortex. In the solar system the trajectory of Saturn marks the dividing ring and all comets are moving beyond that. See “Comets in Descartes’ Cosmos”, in chapter three (above).
The Correspondence of Isaac Newton, 7 vols., H. W. Turnbull (ed.) (Cambridge: Cambridge University Press, 1960), vol. 2, pp. 338–339. For Flamsteed’s idea about the cometary tails also see: Forbes, The Gresham Lectures, p. 116.
Forbes, The Gresham Lectures, p. 115.
Newton, Correspondence, 2: 337–338.
Robert Hooke, Lectures and Collections Made by Robert Hooke, Secretary of the Royal Society. Cometa. … Microscopium (London, 1678), reprinted in R. T. Gunther, Early Science in Oxford, 15 vols. (Oxford: Printed for the author, 1931) vol. VIII, pp. 227–228.
Newton, Correspondence, 2: p. 231.
Newton received extracts of three letters that Flamsteed sent to James Crompton, a fellow of Jesus College, about his theory of comets on 15 December 1680, 3 January and 12 February 1681. He also received a copy of Flamsteed’s theory sometimes in February 1681. See: Westfall, Never at Rest, pp. 391–398. The letters are printed in Newton, Correspondence, 2, 315, 319–320, 336.
Newton, Correspondence, 2, 342. In response, Flamsteed proposed that the magnetic property of the sun might be different from that of a loadstone, or the sun might not be a mass of red hot iron but “a Solid globe of grosse matter encompassed with a spirituous liquid which by its violent motion stirring the particles of our aire causes the heat wee feele from him” (Ibid., p. 351). Newton rejected the first idea emphasizing that the only known attraction and repulsion of this type is the magnetic property of loadstones which vanishes by heat. To refute Flamsteed’s theory of the sun’s structure, Newton calculated the relative surface temperature of the sun and concluded that a body with a hot surface can not sustain a cold interior. Thus, the sun’s interior also should be hot which would destroy the magnetic property. Ibid., p. 359.
Hooke blamed Newton for his neglect of Hooke’s priority in discovery of the inverse square law and the influence of a central gravitating body. For a brief review of debates on this issue see: Yeomans, Comets, pp. 78–82; Westfall, Never at Rest, pp. 382–388, 402–403; A. Rupert Hall, Isaac Newton, Adventurer in Thought (Cambridge: Cambridge University Press, 1992), pp. 162–165, 202–207; Alfred Bork, “Newton and Comets”, American Journal of Physics 55(1987), pp. 1089–1095.
Georg Samuel Dörffel (1643–1688), a German astronomer and mathematician had already calculated the trajectory of the comet of 1680/1 as a parabola with the sun at the focus. Dörffel assumed that the earth was revolving on a circle around the sun (he originally believed in a geocentric system and used the Copernican idea of a moving earth only as a tool to solve the problem of cometary motion) and tried to find the angles between the comet and the sun while observing from a moving earth. Although he fitted a parabolic path to the comet, his measurements of angles between the comet and the sun were not accurate. Dörffel published his results in a tract entitled Astronomische Betrachtung des Grossen Kometen, welcher in ausgehenden 1680, und angehenden 1681 Jahr hochst verwunderlich und entsetzlich erschienen (Plauen, 1681). See Forbes, “The Comet of 1680–1681”, pp. 312–313; Yeomans, Comets, pp. 96–99.
For a complete guide to Newton’s Principia, its history, structure and fundamental concepts, see I. B. Cohen’s “ A Guide to Newton’s Principia” in Isaac Newton, The Principia, Mathematical Principles of Natural Philosophy, trans. I. Bernard Cohen, Anne Whitman, assisted by Julia Budenz (Berkeley: The University of California Press, 1999), pp. 3–370; Newton’s revisions on the Principia is discussed in pp. 11–25, however, the details of changes in the three editions are given as footnotes in related pages.
Ibid., p. 888. All references to the Principia are from I. B. Cohen’s translation (above), which is based on the third and final edition of Newton’s Principia.
Ibid., pp. 891–894.
Ibid., p. 895. This important statement had already been stated in proposition 10 of book 3. There, Newton says that “the motions of the planets can continue in the heavens for a very long time”, and referring to the scholium to proposition 22 of book 2, calculates that at a height of two hundred miles above the earth the density of air is 75,000,000,000,000 less than the density on the surface of the earth. Assuming that the medium in which Jupiter (or any other planet) is revolving has the same density as the uppermost part of the air, Newton concludes that the planet would not lose a millionth of its motion in a million years. Thus, “ the planets and comets, encountering no sensible resistance, will move through those spaces for a very long time”. See Ibid., pp. 815–816.
For example, Hevelius’s illustrations of the heads of the comets of 1664 and 1665 shows changes in their appearances.
Ibid., p. 895.
In proposition 8, corollary 4 of book 3, Newton gives a different ratio: “I have found with a thermometer that water boils at seven times the heat of the summer sun”, (Ibid., pp. 814–815). This ratio, which lowers the temperature of the summer sun to around 14–15°C, is far from the actual figure.
Newton’s figure for red hot iron is at least 100°C off. As judged visually, iron is seen red between 500°C and1000 °C (incipient red: 500–550°C, dark red: 650–750°C, bright red: yellowish red: 1050–1150°C). For Newton’s thermometry see: Hall, Isaac Newton, pp. 297–298.
Ibid., p. 918.
This last calculation is not done by Newton. However, since he assumes that an earth-size globe of iron with a temperature of red hot iron cools down after 50, 000 years, the same globe when is 2, 000 times hotter than red hot iron need 2, 000 times more time to lose its heat. It has to be noted that for Newton the cooling time was a linear function of the surface area of the heated object. It is important to mention that Newton did not explicitly claim that a typical comet was as large as the earth, however, his analogy implies his inclination to compare comets with earth-like planets.
Ibid., p. 919.
Ibid., pp. 920–921.
Ibid., pp. 921–922.
Ibid., p. 922.
Ibid., pp. 922–923. Newton, in proposition 22 (and its scholium), explains how the density of air in our atmosphere decreases by the altitude (Ibid., pp. 694–696). Also, in query 27 of the Opticks he gives a comparative scale of density of air versus altitude. According to this scale, at the height of 7½ English mile from the surface of the earth the density of air decreases to one fourth of its original quantity, and at the heights of 22½, 30, 38, 76, 152 and 228 miles, the density is respectively 64, 256, 1, 024, 106, 1012 and 1018 times rarer. See Isaac Newton, Opticks, 4th ed. (New York: Dover, 1979), pp. 367, 353. For an aid to comprehend Newton’s calculations see: David Gregory, The Elements of Physical and Geometrical Astronomy, 2 vols. (London: 1726), vol. 2, pp. 702–707.
Newton, Principia, p. 924. In all tables in the Principia the first appearance of the comet after its perihelion is December 12.
Ibid., p. 925. It has to be noted that Newton accepted that heat was not a substance but was an increase in the vibration of the particles of the matter. Therefore, reflection of the sun’s rays from the atmospheric particles of the comet can increase their vibration and consequently the vibration of the adjacent ethereal particles. Newton in queries 5, 8 and 18 of the Opticks mentions the mutual action of bodies and the light.
Ibid.
Ibid., pp. 926–927.
Newton admits that the sun is also encompassed by an atmosphere which sometimes comets, in their closest approach, can pass through it. See below: “A General Assessment of Newton’s Theory of Comets.”
Ibid., p. 926.
Ibid., p. 938.
Ibid., pp. 937–938. Newton introduces a different cause for the phenomena of variable stars: “But fixed stars that alternately appear and disappear, and increase little by little, and are hardly ever brighter than fixed stars of the third magnitude, seem to be another kind and, in revolving, seem to show alternatively a bright side and a dark side”. See Ibid., p. 938. Newton does not elaborate on the notion of ‘bright side and dark side’ of a star.
Ibid., pp. 939–940.
Newton, Opticks, p. 402. This query was numbered 23 in the first edition of the Opticks (1706).
One of the occasions that Newton states his ideas about the physical constitution of comets is in his first letter to Bentley where he rejects Descartes’ hypothesis of transformation of stars to comets, and classifies stars and comets in different categories. See Isaac Newton, The Correspondence of Isaac Newton, ed. H. W. Turnbull, 7 vols. (Cambridge: Cambridge University Press, 1961), vol. III, p. 234. Also available in I. Bernard Cohen, Robert E. Schofield, ed. Isaac Newton’s Papers and Letters on Natural Philosophy and Related Documents, 2 ed. (Cambridge, MA: Harvard University Press, 1978), pp. 283–284. Since our aim does not include tracing out the development of Newton’s physical theory of comets before the publication of the Principia, here we consider only correspondence and papers which Newton drafted after the Principia and influenced the subsequent cometary theories.
John Conduitt, the husband of Newton’s niece, composed his memoirs of Newton which are one of the main sources for the biography of Newton.
Memorandum by Conduitt, Kings College, Cambridge MS, Keynes 130, no. 11, as quoted in David Kubrin, “Newton and the Cyclical Cosmos: Providence and the Mechanical Philosophy”, Journal of the History of Ideas, 28 (1967), 340. In the same document Newton states that the fixed stars also could be replenished by comets falling on them. When Conduitt asked Newton why he did not publish these ideas, Newton replied that “I do not deal in conjectures”. See above. p. 343.
Newton, Correspondence, III, p. 316.
Ibid., III, p. 336.
Ibid., IV, p. 277.
MS. Add. 4005, fols. 23–5, published in: A. Rupert Hall, Marie Boas Hall (eds.), Unpublished Scientific Papers of Isaac Newton, A Selection from the Portsmouth Collection in the University Library, Cambridge (Cambridge: The University Press, 1962), pp. 165–169.
In a paper written after 1684, Newton states that “the Universe consists of three sorts of great bodies, Fixed Stars, Planets, & Comets”. However, in all of his published works, he is not explicit about the physical differences between the planets and comets. It is also interesting that in this paper, Newton explains the fixed stars and the planets, but leaves comets unexplained. See Ibid., pp. 374–377.
For example in proposition 41 he says: “…the bodies of comets are solid, compact, fixed, and durable, like the bodies of planets”, or at the end of the same proposition: “ We said that comets are a kind of planet revolving about the sun in very eccentric orbits”. See Newton, Principia, pp. 918, 928.
Newton, Principia, p. 928.
Ibid., p. 937.
Ibid., p. 814.
Ibid.
For example, the centripetal force acting on the moon is F = m m (4π 2R m /T m 2), where m m is the mass of the moon, R m is its mean distance from the earth, and T m is its period of revolution. If this force is equivalent to the gravitational force which is given by F = G m m m e /R m 2 (G is the constant of gravitation and m e is the earth’s mass) then we will have G m m m e / R m 2 = m m (4π 2 R m /T m 2) or T m 2 = (4π 2/G m e ) R m 3 which is the derivation of Kepler’s third law from Newton’s gravitational law. To have a quantitative example, lets denote the orbital periods of the earth by T e , the mean distance of the earth from the sun by R e and the sun’s mass by M. Then: T e 2 = (4π 2/G M) R e 3 and T m 2 = (4π 2/G m e ) R m 3 or T e 2/T m 2 = (R e 3/R m 3) (m e /M) or m e /M = (T e 2/T m 2) (R m 3/R e 3). Since T e = 365 d, T m = 27 d, R m = 384, 000 km and R e = 150, 000, 000 km, then m e /M ≈ 1/330, 000. The ratio of densities also can be calculated by knowing the apparent diameter of the bodies and their distances (which makes their true diameters computable). Newton’s figures were erroneous because of his incorrect number for the solar parallax. For the details of Newton’s calculations and his different results in different editions of the Principia see I. B. Cohen’s guide to the Principia, Ibid., pp. 218–231, and Dana Densmore, Newton’s Principia: The Central Argument (Santa Fe: Green Lion Press, 1995), pp. 382–394.
Ibid., pp. 813–814. For Newton’s figure for the solar parallax and its influence on the Newtonian planetary data see Van Helden, Measuring the Universe, pp. 144–149. Newton’s errors in his planetary calculations are analyzed in Robert Garisto, “An Error in Isaac Newton’s Determination of Planetary Properties”, American Journal of Physics 59 (1990), 42–48.
Ibid., p. 878. In the first edition of the Principia, where Newton’s figure for the solar parallax was about 20˝, densities of the earth and moon were calculated as 387 and 700 respectively. Obviously, the distance of the moon from the sun is not so different from the distance of the earth from the sun, and both receive almost the same amount of heat from the sun. Therefore, it is difficult to relate the higher density of the moon to the amount of heat it absorbs. If it is related to the smallness of the moon, then one can assume that while the earth’s diameter is about 3.5 times of the moon’s diameter, it is 1.2 less dense than the moon.
Ibid., p. 918. The accurate value is 612.5 to 10, 000, as Halley reports in his table of cometary data. See Edmund Halley, A Synopsis of the Astronomy of Comets (London: 1705), p. 7.
Ibid., p. 937. Newton believed that the sun is encompassed by a huge atmosphere. In an unfinished paper written after 1710 he wrote: “That the Sun is indeed surrounded by a huge Atmosphere appears from eclipses of the sun, in which the Moon where it covers the whole Sun appears as a black circle, surrounded by a shining corona like a halo. […] Imagine that the atmosphere of the Sun does not end where it ceases to be visible but that it extends as far as the orb of Mercury and far beyond as a more tenuous medium. It is also conductive to the ascent of vapours…. [sic]”. See Hall, Unpublished Scientific Papers of Newton, p. 319. Also in query 11 of the Opticks he refers to the great weight of the atmosphere of the sun. See: Newton, Opticks, p. 344. The solar atmosphere is so dense that it retards comets’ motion when they approach the sun. See: Newton, Principia, p. 937.
Van Helden, Measuring the Universe, pp. 151–152. Newton in the second edition of the Opticks adopts 70, 000, 000 English miles for the earth-sun distance, which is equal to a solar parallax of 12”. See Isaac Newton, Opticks: or a Treatise of the Reflections, Refractions, Inflections and Colours of Light, 2 ed. (London: 1718), p. 325 (or p. 351 in the fourth edition of the Opticks, published by Dover in 1979). Newton’s adoption of different values for the solar parallax and planetary data in different editions of the Principia is given in Garisto, “An Error in Newton’s Determination of Planetary Properties”, p. 44. In 1715, William Whiston (1667–1752), Newton’s successor in the Lucasian chair at Cambridge, published his results for the size and distances of the sun and planets, based on a solar parallax of 10”. His figures (which I have used in my calculations when the needed value was not in the Principia) are as follows:.
In the Principia, Newton simply says that the distance of the comet from the sun was less than one sixth of the sun’s diameter. Since usually all distances between the celestial objects are given as distances between their centers, Newton’s account should be read as ‘comet’s distance from the surface of the sun. If the comet’s distance was less than a sixth of the sun’s diameter from the sun’s center, then the sun’s diameter would be around 2, 800, 000 Em and the comet would pass directly through the body of the sun in a distance of one third of solar radius from the sun’s center.
Newton, Principia, p. 814. The ratio of 1 to 66 which is yielded from William Whiston’s table (above) is approximately in agreement with Newton’s figures. Newton calculated that the sun’s heat on the comet was 28, 000 denser than its heat on the earth, and Mercury was 7 times as hot as the earth. The square of 66 multiplied by 7 is about 30, 000.
For example, he maintains that the tail of comets is finally scattered and “attracted towards the planets by its gravity and mixed with their atmospheres”. (my emphasis). See: Ibid., p. 926; or “it’s necessary to empty the Heavens of all Matter, except perhaps some very thin Vapours, Steams, or Effluvia, arising from the Atmospheres of the Earth, Planets, and Comets, ” (my emphasis). See: Newton, Opticks, p. 368.
Ibid., p. 920. Also, at the end of proposition 41 of book 3 of the Principia he declares that the planets have no tails. See: Ibid, p. 928.
Recalling Conduitt’s memorandum that Newton suggested a sort of revolution in the celestial bodies (wherein bodies by attracting more and more vapor and light emitted from the sun grow sufficiently and become a moon then a comet), and Gregory’s report of Newton’s idea that “Satellites of Jupiter and Saturn can take the place of the Earth, Venus, Mars if they destroyed”, it seems that the denser bodies (or the more close ones to the sun) are the most potential planets to evolve to a comet. Was Newton thinking that the planets, one by one, gain more light and vapor from the sun and turn into a comet?.
Newton in a letter to Flamsteed, which is written before the Principia, admits that Jupiter, Mars and Venus are encompassed in fine and thin atmospheres which allow their limbs to appear distinct. See: Newton, Correspondence, II, p. 345.
Ibid., p. 816. Since the coma of a comet – with a diameter approximately ten times larger than the comet’s diameter – is observable, it means that its density in this entire large volume is higher than the density of the ether. Newton’s calculations, however, show that the density of the terrestrial atmosphere at an altitude of 200 miles is the same as the density of the ether, which implies that an alien observer would see our atmosphere with a maximum thickness of 200 miles. In other words, the thickness of the atmosphere of the earth is 200 times less than of a typical comet at an equal distance from the sun.
Based on Newton’s theory of orientation of cometary tails, if the earth had a tail, its extremities might have been observed from the earth. In other words, the end parts of the tail – raised a few days earlier – would have enough distance from the earth to reflect the sun’s rays and be distinguished as patches of light.
David Gregory also refers to a similar fact in his discussion of the possibility of rotation of comets: “It is not known whether a Comet revolves about itself, but it is probable that, like all the other great bodies of the World, it turns all its Faces towards the Sun […] If the Nucleus be turn’d about […] that Vapour, which, going out of the Comet, makes the Tail, is not so much to be look’d upon, as the Atmosphere of the Comet join’d with it (as the denser Atmosphere of the Earth is join’d with it) and making Part of it;” See Gregory, The Elements, vol. 2, pp. 851–852.
Newton, Principia, p. 926, emphasis is mine.
Newton in an unpublished paper (MS. Add. 4005, fols. 45–9) discusses the motion of the planets and stars about “their several axes”. See: Hall, Unpublished Scientific Papers of Newton, p. 380. In his fourth letter to Bentley, Newton affirms that “the diurnal Rotations of the Planets could not be derived from Gravity, but required a divine Arm to impress them”. See: Newton, Correspondence, III, p. 244.
Newton, Principia, pp. 926–927.
Newton, Opticks, p. 340.
Ibid., pp. 343–344.
According to Newton, the corpuscles that make the black color are smaller than any other particles which exhibit colors, and “Fire, and the more subtile dissolver Putrefaction, by dividing the Particles of Substances, turn them to black” (Ibid., p. 260). On the other hand, Newton, in query 6 of the Opticks says that “black Bodies conceive heat more easily from Light than those of other Colours do” (Ibid., p. 339). Therefore, the black particles of the smoke on the surface of the nucleus must have the strongest vibrations.
Ibid., pp. 341–342.
Newton in a letter to Flamsteed in February 1681 says “that ye atmosphere about ye head [of the comet] shines also by the suns light, though perhaps not altogether by it”. (Newton, Correspondence, II, p. 346, my emphasis). Why he emphasized on not altogether by it is not known, but is interesting.
Newton developed several theories of the ether, most of them unfinished. However, he proposed two major concepts of the ether in two different periods of his life. In the 1670s he thought the ether to be a subtle air capable of penetrating the pores of glass, crystal and other terrestrial matters. This mechanical ether, acting by impact, was responsible for gravity and action at a distance. However, after 1710, Newton adopted a new definition in which the ether consisted of very small particles that repelled one another and were repelled by particles of the gross matter. The particles of this ether are rarer in the stars, planets and comets than the space between them. Therefore, gravity is the force that pushes bodies from the denser parts of the medium to the rarer parts. For Newton’s theory of ether see: Drake Gjertsen, The Newtonian Handbook (New York: Routledge Press, 1986), pp. 190–192; G. N. Cantor, M. J. S. Hodge, “Introduction: major themes in the development of ether theories from the ancients to 1900”, in G. N. Cantor, M. J. S. Hodge (eds.), Conceptions of Ether, Studies in the History of Ether Theories, 1740–1900 (Cambridge: Cambridge University Press, 1981), pp. 1–60; B. J. T. Dobbs, “Newton’s Rejection of the Mechanical Aether: Empirical Difficulties and Guiding Assumptions”, in Arthur Donovan, et al, eds. Scrutinizing Science: Empirical Studies of Scientific Change (Dordrecht: Kluwer Academics, 1988), pp. 69–83.
Newton, Principia, p. 925.
Ibid., p. 922.
Newton, Opticks, p. 350.
One of the reasons that comets may fall on the sun is their retardation in the solar atmosphere: “…and also because the atmosphere of the sun has some density, the comet must have encountered some resistence and must have been somewhat slowed down and must have approached closer to the sun”. See: Newton, Principia, p. 937.
Newton, Principia, p. 926.
See: David Kubrin, “Newton and the Cyclic Cosmos: Providence and the Mechanical Philosophy”, Journal of History of Ideas, 28 (1967), 325–346; Sara Schechner Genuth, “Comets, Theology, and the Relationship of Chemistry to Cosmology in Newton’s Thought”, Annali dell’Instituto e Mouseo di Storia della Scientza di Firenze, 10, pt. 2 (1985), 31–65; Idem, “Newton and the Ongoing Teleological Role of Comets”, in Norman J. W. Thrower, ed., Standing on the Shoulder of Giants (Berkeley: University of California Press, 1990), pp. 299–311. Pierre Kerszberg, “The Cosmological Question in Newton’s Science”, Osiris, 2 (1986), 69–106.
Newton, Correspondence, III, p. 233. Richard Bentley (1662–1742), delivered a series of lectures in 1692, entitled “A Confutation of Atheism from the Origin and Frame of the World”, and before publishing his work consulted Newton to correct his teachings of Newton’s ideas. They exchanged four letters, discussing mainly philosophical aspects of universal gravity, mechanical philosophy and deity. The four letters and also Bentley’s work can be found in Isaac Newton’s Papers and Letters on Natural Philosophy and Related Documents, I Bernard Cohen (ed.), with Robert E. Schofield (Cambridge: Harvard University Press, 1978), pp. 279–312, 313–394.
Conduitt memorandum on March 7, 1724/5, concerning Newton’s idea about the fate of the comet of 1680, from Turnor, Collections, p. 172.
Once when Newton was explaining his ideas about the reconstitution of the earth by comets, Conduitt asked him why he did not publish his ideas and Newton replied “I do not deal in conjectures”. Kings College, Cambridge MS, Keynes 130, no. 11; cited from Kubrin, “Newton and Cyclic cosmos”, p. 343.
Edmund Halley was very interested to calculate the amount of vaporization of the waters of the earth and the heat of the sun which the earth receives in various latitudes. He also tried to calculate the rate by which the bulk of the earth was growing through attraction of particles from the space. From 1692 to 1714, Halley published at least five studies as follows: “An Account of the Circulation of Watery Vapours of the Sea, and the Cause of Springs”, Philosophical Transactions, 16 (1686–1692), pp. 468–473; “An Estimate of the Quantity of Vapour Raised out of the Sea by the Warmth of the Sun…”, passim, 16 (1686–1692), 366–370; “A Discourse concerning the Proportional Heat of the Sun in all Latitudes…”, passim, 17 (1693), 878–885; “An Account of the Evaporation of Water, as it was Experimented in Gresham College in the Year 1693. With Some Observations Thereon”, passim, 18 (1694), 183–190; “A Short Account of the Cause of the Saltness of the Ocean…With a Proposal …to Discover the Age of the World”, passim, 29 (1714–1716), 183–190.
David Gregory in his memorandum of 20 February 1697 wrote: “In drawing up the table of refraction of the stars he [Newton] does not consider that the height of the atmosphere extends further than 40 or 50 miles”. See: Newton, Correspondence, IV, p. 267.
Newton’s data are: at the height of 7½ English mile from the surface of the earth the density of air decreases to one fourth of its original quantity, and at the heights of 22½, 30, 38, 76, 152 and 228 miles, the density is respectively 64, 256, 1, 024, 106, 1012 and 1018 times rarer (Newton, Opticks, p. 367); the air is 860 times lighter than water (Newton, Principia, p. 816; the same ratio is given 850 in proposition 41 of book 3, see: Ibid., p. 922); the density of the earth is five or six times greater than the density of water (proposition 10 of book 3, Ibid., p. 815). Based on these information one can calculate the mass of the atmosphere as: ρ r = ρ 0 [−a(r−r’)] where ρ 0 is the air density at the surface of the earth, ρ r is the air density at any point from the center of the earth, a is the ratio by which – as Newton stated – the density of air decreases by the increase of the altitude, and r’ is the radius of the earth. Therefore, M (mass of the atmosphere) will be the integral of ρ r .4π.r2 dr from r’ to 10 r’ (it does not make a difference if we extend the limit of integration to infinity). Solving this integral equation based on r’ ≈ 4, 000 English mile (≈6, 400 km) and ρ water = 850 ρ air (or ρ air = 1.2 kg/m3), the mass of the atmosphere will be about 5 × 1018 kg. This value (based on Newton’s data) is very close to modern value for the mass of the atmosphere.
Newton, in the first edition of the Principia, suggested that the bulk of the solid earth is continually increased. In 1694 he told Halley that “there was reason to Conclude That the bulk of the Earth did grow and increase … by the perpetuall Accession of New particles attracted out of the Ether by its Gravitating power, and he [Halley] Supposed … That this Encrease of the Moles of the Earth would occasion an Acceleration of the Moons Motion, she being at this time Attracted by a Stronger Vis Centripeta than in remote Ages”. From Journal Book of the Royal Society, Oct. 31, 1694. cited from Kubrin, “Newton and Cyclic Cosmos”, p. 337. Newton omitted the idea of increase of the mass of the earth in the second edition of the Principia.
“ But because of the great number of comets, and the great distance of their aphelia from the sun […] they should be disturbed somewhat by their gravities toward one another”. See: Newton, Principia, p. 936.
As already noted, Newton at the end of the last proposition of the Principia, summarizes the cycle of transformation of the cometary exhalations and vapors as follows: “And the vapors that arise from the sun and the fixed stars and the tails of comets can fall by their gravity into the atmospheres of the planets and there be condensed and converted into water and humid spirits, and then – by a slow heat – be transformed gradually into salts, sulphurs, tinctures, slime, mud, clay, sand, stones, corals, and other earthly substances”. See: Newton, Principia, p. 938.
The history of the development of Newtonian celestial mechanics has a close relationship with Newton’s study of comets. In Ruffner’s words, Newton’s theory of comets “was not an afterthought in the Principia, nor was it a casual deduction after the principles had been established. The theory of comets was an essential part of the Principia, which would have been incomplete without it”. See Ruffner, The Background, pp. 352–353.
Application of the micrometer in sighting tools, either in the focal plane of a telescope (as used by Picard, Newton and Kirch) or in the eyepiece of a telescopic quadrant (as used by Flamsteed, Cassini, Picard and others) produced highly precise and reliable data which reduced the errors of the calculated path. At the same time, use of Huygens’s pendulum clock in observatories helped astronomers to correct their solar and planetary data, and also calculate the position of reference stars accurately.
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(2008). Comets in Newtonian Physics. In: A History of Physical Theories of Comets, From Aristotle to Whipple. Archimedes: New Studies In The History And Philosophy Of Science And Technology, vol 19. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-8323-5_4
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