Brahe died in the first year of the seventeenth century and left astronomers and natural philosophers with a number of crucial questions regarding comets. These questions, however, arose from a single fundamental philosophical inquiry related to the nature of comets. Cometology, during almost the entire seventeenth century, was a struggle to answer this basic question, which finally was resolved in Newton’s Principia.
The seventeenth century was, to say the least, a productive period in the history of astronomy: the heliocentric system of Copernicus was recast in the more elaborate Keplerian system, which finally was demonstrated and proved by Newtonian celestial mechanics; telescopic observations, besides many other discoveries, enabled scientists to deal with the surface features of the celestial bodies and consequently to discuss their nature based on observational facts; a concept of central force, acting at a distance and governing all motions in the solar system, was developed; a new mathematics made it possible to calculate motions of the celestial bodies caused by their mutual attractions; and finally, the application of the micrometer in observation increased the angular resolving power up to 15 arc-seconds by 1700, an increase by a factor of four compared to the early decades of the seventeenth century.128 Benefiting from all these achievements, cometary theories drastically changed at the end of the seventeenth century, a time when the physics and kinematics of comets became two independent subjects of study.
For almost the entire seventeenth century, the nature and motion of comets were assumed to be the two sides of one coin: it was generally accepted that a transient object had to move on a straight or curvilinear line and a permanent body had to travel on a circular path periodically. This presumption was based on a kind of Aristotelian interpretation of the newly discovered phenomena. In the Aristotelian supra-lunar region, motion on a straight line was not allowed. However, when transient objects were discovered in the ethereal region, they were assumed not to move perpetually like permanent objects. In other words, comets could be celestial but would not perform circular motions. Therefore, the most secure criterion to infer the nature of a comet was its trajectory. Consequently, until the introduction of the Newtonian theory of comets in 1687, any theory about the physics of comets was dependent on their kinematics.
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References
Allan Chapman, “The Accuracy of Angular Measuring”, p. 134.
The original title is De tribus cometis anni MDCXVIII disputatio astronomica. An English translation of this treatise along with Guiducci’s answer (Discourse on Comets), Grassi’s reply to Guiducci (The Astronomical Balance), Guiducci’s Letter to Tarquinio Galluzzi, Galileo’s The Assayer, and Kepler’s Appendix to the Hyperaspistes, is in Stillman Drake and C. D. O’Malley, trans., The Controversy on the Comets of 1618 (Philadelphia: University of Pennsylvania Press, 1960).
See n. 106, Chapter 2.
Drake, The Controversy, p. 13.
Ibid., p. 14. Grassi admits that the instruments he used were not as accurate as those used by Brahe.
Ibid., p. 15. Based on the early seventeenth century commonly used figures for the radius of the earth and the moon, Grassi’s volume for the comet was about and of the volumes of the earth and the moon respectively.
Grassi’s idea about telescopic magnification was erroneous, which caused a bitter reply of Galileo through his student Guiducci. Grassi claims that the magnification power of a telescope decreases by the distance of the observed object, in such a way that the fixed stars receive no magnification from the telescope. Since the comet’s (the third comet of 1618) magnification through a telescope was not considerable, then it was assumed to be located at a great distance. In the first decade of telescopic observations, there was not a clear technical idea about the magnification powers of the telescope. A telescope may increase light gathering power, or angular size, or resolution power. A typical telescope may not magnify the angular size of a star perceptible, but it resolves the foggy Milky Way into individual stars. On the other hand, the optical quality of the objective and ocular lenses made in the early seventeenth century was too poor to reveal details of comets. It should be noted that even with modern telescopes (of the same size used by Galileo, for instance) the cloudy feature of comets can not be resolved into more details. For the history of the telescope, see pp. 111–116.
Kepler changed his theory of comets in several later publications. We will discuss this in the section devoted to Kepler’s cometary theory.
This is not exactly the middle of the distance between the moon and the sun. Grassi’s value for the earth’s radius is 3, 579 miles; therefore, he locates the comet at a distance of 160 Er from the earth’s center. In Tycho’s system, the moon and the sun are located at 60 and 1, 150 Er from the earth respectively. Thus, the comet is much closer to the moon than the sun.
Based on Brahe’s scheme of sizes and distances for the planets, this value is about on third of the diameter of the moon. See Van Helden, Measuring the Universe, p. 50.
Grassi’s calculations are confusing. If the comet is at the distance of 572, 728 miles from the center of the earth, the circumference of its circle will be 1.02997412 miles and 60 degrees of it equals to 1.71662411 miles.
Drake, The Controversy, p. 18.
The debate on the comets of 1618 has been the subject of many studies. See Drake, The Controversy, pp. vii–xxv; William Shea, “The Challenge of the Comets”, Galileo’s Intellectual Revolution (New York: Science History Publications, 1977), pp. 75–108; Pietro Redondi, Galileo Heretic (Princeton: Princeton University Press, 1987), pp. 28–67; Mario Biagioli, Galileo Courtier (Chicago: The University of Chicago Press, 1993), pp. 267–311; Richard R. Westfall, “Galileo and the Jesuits”, in Essays on the Trial of Galileo (Vatican City: Vatican Observatory, 1989), pp. 31–57, Ruffner, The Background, pp. 72–93, Yeomans; Comets, pp. 57–62. Here, we concentrate mainly on the ideas and theories exchanged between both sides on the physics of comets.
Mario Guiducci, Discorso delle comete (Florence, 1619); An English translation is in Drake, The Controversy, pp. 21–65. The original manuscript of the book is largely in Galileo’s own handwriting, and the sections drafted by Guiducci are edited and signed by Galileo. See Shea, “The Challenge of the Comets”, pp. 75–76.
The inner planets are seen in their greatest brilliancy when they are at quadrature.
This assumption, based on the information that Galileo gives a few pages later, could not be valid. Galileo says that the inclination of the circle of the comet of 1577 was less than 30 degrees, while that of 1618 was 60 degrees. Furthermore, the comet of 1577 moved in the order of signs, but the comet of 1618 moved against the signs. See Drake, The Controversy, p. 49.
Drake, The Controversy, p. 27.
Ibid., pp. 28–35.
Ibid., p. 35.
Ibid., pp. 36–37.
Ibid., pp. 53–54. Galileo imagines that the aurora borealis is seen most frequently in the summer and says that since in the summer the sun is at the north of the celestial equator, the shadow cone tilts towards the south and the vapor needs to rise only a short distance to reflect the sun’s rays from the outside of the shadow cone.
Galileo states this idea more clearly in his Dialogue: “… Neither do I feel any reluctance to believe that their [comets] matter is elemental, and that they may rise as they please without encountering any obstacle from the impenetrability of the Peripatetic heavens, which I hold to be far more tenuous, yielding and subtle than our air”. See Galileo Galilei, Dialogue Concerning the Two Chief World Systems, trans. Stillman Drake (Los Angeles: University of California Press, 1967), p. 52.
Drake, The Controversy, pp. 56–62.
Galileo’s ideas about comets are scattered in his various writings. After Guiducci published the Discourse, Grassi, under the pseudonym of Lothario Sarsi, replied to Galileo directly by writing a treatise entitled Libra astronomica (The Astronomical Balance, see Drake, The Controversy, pp. 67–132). The debate was continued by Guiducci’s letter to Father Tarquinio Galluzzi (Ibid., pp. 133–150), and finally, in 1623, Galileo published one of his masterpieces named Il saggiatore (The Assayer, Ibid., pp. 151–336) in which, along with many other topics in physics and astronomy, he expanded and explained parts of his cometary theory that had been rejected or misunderstood by Grassi and the Jesuits. Furthermore, Galileo in the Dialogue explains his cometary theory briefly. See Galileo, Dialogue, p. 52, 218.
An English translation of this appendix is in Drake, The Controversy, pp. 337–355.
The complete title of Kepler’s work is Ad Vitellionem Paralipomena, quibus Astronomiae pars Optica traditur (Frankfurt, 1604). For an English translation see: William H. Donahue, trans., Optics: Paralipomena to Witelo and Optical Part of Astronomy (Santa Fe: Green Lion Press, 2000). For the development of Kepler’s optical theory of comets see Barker, “The Optical Theory”, pp. 18–25. A brief account of Kepler’s cometary theory and a list of Kepler’s works on comets is in C. Doris Hellman, “Kepler and Comets”, in Arthur Beer, Peter Beer, ed., Kepler, Proceedings of Conferences held in honour of Johannes Kepler, Vistas in Astronomy, 18 (1975), 789–796. For Kepler’s treatment of cometary motion see Ruffner, The Background, pp. 94–118; Ruffner, “The Curved and the Straight”, 178–183; Westman, “The Comet and the Cosmos”.
Kepler, Appendix to the Hyperaspistas, in Drake, The Controversy, p. 346. From 1604 to 1625, Kepler published several works devoted partially or totally to his cometary theory. His De Cometis libelli tres (Augsburg, 1619) contains his mature version of theory of comets. A brief summary of it can be found in the Appendix to the Hyperaspistas, Ibid.
Rothmann also pointed this problem in a letter to Brahe in 1588. See Barker, “The Optical Theory”, p. 22.
Kepler, Appendix to the Hyperaspistas, in Drake, The Controversy, p. 347.
Although the concept of light pressure was proposed before the mid-nineteenth century (for example, Descartes defined light as a pressure transmitted through the subtle matter of vortices, or Newton theorized that light consist of particles possessing momentum) it was James Clerk Maxwell (1831–1879) who showed that transverse electromagnetic waves should exert a force. Maxwell’s theory was experimentally verified in 1901 after developments made by Pëtr Lebedev (1866–1912), Ernest Nichols (1869–1924) and Gordon Hull (1870–1956). See Morton L. Schagrin, “Early Observations and Calculations on Light Pressure”, American Journal of Physics 42 (1974), 927–940.
Johann Kepler, Aussführlicher Bericht von dem newlich im Monat Septembri und Octobri diss 1607. Jahrs erschienenen Haarsten oder Comten und seinen Bedeutungen (Halle in Saxony, 1608), Aijr or Christian Frisch, ed. Johannis Kepleri Astronomi opra omnia, 8 vols. (Frankfurt: Heyder & Zimmer, 1858–1871), vol. 7, p. 25. In the 1670s, Pierre Petit in a similar way thought of comets as universal garbage collectors. See Yeomans, Comets, p. 73.
Johann Kepler, Optics: Paralipomena to Witelo and Optical Part of Astronomy, trans. William H. Donahue (Santa Fe: Green Lion Press, 2000), p. 278.
Johannes Kepler, Gesammelte Werke (Munich: C. H. Beck, 1937-), 7: 281, cited from Van Helden, Measuring the Universe, p. 84.
If they were spherical, there would be void spaces between the spheres. Vacuum is not admitted in Descartes’ cosmos as that of Aristotle. Descartes developed his theory of elements mainly in Le monde, ou Traité de la Lumière (1633) and Les Principes de la Philosophie (1647), and mentioned it briefly in Dioptrique (1637) and Météores (1637). Because of the Church’s condemnation of Galileo in 1633, Descartes did not publish Le monde (The World), in which he had adopted a heliocentric model of the world. But, parts of the Le monde published by 1637 and some of it was published posthumously. The theory of elements discussed here is taken from: René Descartes, Principles of Philosophy, trans. Valentine Rodger Miller and Reese P. Miller (London: D. Reidel Publishing Company, 1983). To trace the development of Descartes’ theory of elements see John W. Lynes, “Descartes’ Theory of Elements: From Le Monde to the Principles”, Journal of History of Ideas 43 (1982), 55–72.
Descartes, Principles, III, 46.
The particles of the second element are not equal in size; their sizes gradually increase from the vicinity of the central star to the outer parts of the vortices. Their agitation, however, decreases from the center of the vortices towards the outer parts. See ibid., III, 82.
Ibid., III, pp. 49–54. The three elements of Descartes, in fact, are three manifestations or forms of a single primary matter, which based on their different shapes, sizes and motions, have different functions in the universe. Similarly, the three different kinds of celestial bodies known for Descartes (stars, planets, and comets) have a single origin.
Descartes, Principles, III, pp. 58–60, 62.
Ibid., III, pp. 87–92.
Ibid., III, p. 69. The vortices are arranged in such a way that two vortices cannot touch at their poles. Therefore, particles that are flowing out from the equatorial parts of a vortex can easily enter the polar region of a vortex above or below, see Fig. 3.10.
Ibid., III, pp. 93–94.
Besides the dispute about the priority of discovery, a heated debate was going on over the nature of the sunspots, which lasted even till the end of the seventeenth century. Galileo and his followers believed that the spots were located on the sun, but Christopher Scheiner, Jean Tarde, Athanasius Kircher and others (mostly Jesuits) assumed the spots to be external bodies. For a detailed account of the debate between Galileo and Scheiner see: William R. Shea, “Galileo, Scheiner, and the Interpretation of Sunspots”, Isis 61 (1970), 498–519. Tarde’s argument is discussed in Frederic J. Baumgartner, “Sunspots or Sun’s Planets: Jean Tarde and the Sunspots Controversy of the Early Seventeenth Century”, Journal of History of Astronomy xviii (1987), 44–54. In 1640, William Crabtrie in an interesting letter to William Gascoigne (the inventor of the micrometer) gives all evidence then available to prove that the spots are not external bodies. See William Derham, “Observations upon the Spots that have been upon the Sun, from the Year 1703 to 1711. With a Letter of Mr. Crabtrie, in the Year 1640. upon the same Subject. By the Reverend Mr William Derham, F. R. S.”, Philosophical Transactions of the Royal Society of London, 27 (1710–1712), 270–290.
Descartes, Principles, III, p. 95. Descartes mentions the equatorial appearance of the sunspots, their irregular shapes, and their motion around the axis of the sun.
Ibid., III, pp. 59–62.
Ibid., III, pp. 55, 64.
Ibid., III, p. 99.
Any star whose brightness is changing, periodically or irregularly, is a variable star, including cataclysmic variable stars (novae and supernovae). Although the latter phenomena had already been observed, by the mid seventeenth century only one star (Mira or omicron Ceti) was discovered to have a changing magnitude. David Fabricius observed Mira in 1596 and 1609 and found a considerable difference between the observed magnitudes. In 1638 Phocylides Holwarda of Holland ascertained its periodicity, but it was Ismael Boulliau who established the period of 333 days for the star in 1667 (the modern value is 331 days and the magnitude of the star changes from 1.7 to 9.5). See Allen, Star Names, pp. 164–165, and N. T. Bobrovinkoff, “The Discovery of Variable Stars”, Isis 33 (1942), 687–689. Descartes, however, claimed that the sun was variable too. See Descartes, Principles, III, p. 103.
Ibid., III, pp. 110–119. In other words, the density of comets is higher than the density of planets.
Ibid., III, p. 121.
Ibid., III, p. 119.
Descartes is not explicit about the distance between the boundaries of a typical vortex and the dividing ring. For the distances between the planets and stars see Ibid., III, pp. 7, 20, 41.
Ibid., III, pp. 126–127.
Ibid., III, p. 129.
It is also interesting that in Descartes’ theory comets are vehicles to transfer matter from one vortex to another, although he used this concept to explain problems associated with the visibility of comets at their entrance to the new vortex.
Ibid., III, p. 132.
Descartes did not discuss this kind of reflection in his Dioptrics, because it was not observed in terrestrial bodies. See Ibid., III, p. 134.
Descartes, Principles, III, pp. 135–138.
Aspects of Descartes’ theory of vortices were modified or developed by Cartesians even after the publication of Newton’s Principia. In the late seventeenth and early eighteenth centuries, Christian Huygens (1629–1695), Philippe Villemot (1651–1713), Nicolas Malebranche (1638–1715) and Joseph Saurin (1659–1737) were among those who developed theories of planetary motion or explained the earth’s gravity based on Cartesian concepts. See: Aiton, The Vortex Theory, chapters IV to IX (pp. 65–209), Eric J. Aiton, “The vortex theory in competition with Newtonian celestial dynamics”, in The General History of Astronomy: Planetary Astronomy from the Renaissance to the Rise of Astrophysics, vol. 2B: The Eighteenth and Nineteenth Centuries, Edited by R. Taton and C. Wilson (Cambridge: Cambridge University Press, 1995), pp. 3–21.
Kepler, influenced by William Gilbert (1544–1603), proposed a magnetic philosophy to explain the planetary motions. In his theory, a magnet like force or virtue inhabited in the sun and planets cause the orbital motions of planets. See: Johannes Kepler, New Astronomy, trans. William H. Donahue (Cambridge: Cambridge University Press, 1992), pp. 376–406; Stephen Pumfrey, “Magnetical Philosophy and Astronomy, 1600–1650” in The General History of Astronomy: Planetary Astronomy from the Renaissance to the Rise of Astrophysics, vol. 2A: Tycho Brahe to Newton. Edited by R. Taton and C. Wilson (Cambridge: Cambridge University Press, 1989), pp. 45–53; J. A. Bennet, “Cosmology and the magnetical Philosophy, 1640–1680”, Journal of History of Astronomy 12 (1981), 165–177.
For example, in Tycho’s system, all stars were located at a distance of 14, 000 Er (earth radii), while the thickness of the sphere of the fixed stars in Kepler’s universe was only 2 German miles or 9 English miles at a distance of 60, 000, 000 Er. See Van Helden, Measuring the Universe, pp. 50, 87–88.
Descartes, The World, p. 40.
As we shall see in the next chapter, in Newtonian celestial mechanics, periodicity, and close approach of comets to the earth (both absent in Cartesian theory of comets) were acknowledged, which led to development of a new brand of cometary prognostication and earth theory.
According to Kepler scholar John L. Russell, after the publication of the Rudolphine Tables in 1627, there was a steady increase of interest in Kepler’s laws and by the 1660s many astronomers adopted ellipses as the true planetary orbits. See Wilbur Applebaum, “Keplerian Astronomy after Kepler: Research and Problems”, History of Science, 34 (1996), 456. It has to be mentioned that although the Cartesian vortices were assumed to be elliptical, planets were not moving in them according to Kepler’s laws. The sun was located at the center of its vortex and not in one of the foci of the ellipses described by the planets.
For the works of Giovanni Borelli (1608–1679), Georg Samuel Dörffel (1643–1688), Christian Huygens (1629–1695), Christopher Wren (1632–1723) and John Wallis (616–1703), who mostly worked on cometary trajectories, see Ruffner, The Background, pp. 184–204, and Yeomans, Comets, pp. 70–99.
Ruffner, The Background, pp. 134–139.
Ibid., pp. 140–146.
Ibid., pp. 146–152.
Anonymous, “An Account of Hevelius His Prodromus Cometicus, Together with Some Animadversions Made upon it by a French Philosopher”, Philosophical Transactions, 1 (1665–1666), 106; Anonymous, “An Account of Some Books: Joh. Hevelii Cometographia. Printed at Dantzick A. 1668, in large Folio”, Philosophical Transactions, 3 (1668), 805–809.
Ibid.
Ruffner, The Background, pp. 163–166.
Yeomans, Comets, p. 93.
When Hevelius built an observatory at his home and constructed a telescope of a very large focal length, his observatory for a while received many visits from leading European astronomers. See Steven Shapin, A Social History of Truth (Chicago: The University of Chicago Press, 1994), p. 272.
Victor J. Katz, A History of Mathematics, An Introduction, 2nd ed. (New York: Addison-Wesley, 1998), p. 420.
Scot John Napier (1550–1617), realizing that the major calculations in astronomy were trigonometric (and especially that they involved sine equations), attempted to built a conversion table in which multiplication of sines could be performed by addition. He published his first logarithmic tables in 1614 and his full account of logarithm was published posthumously in 1619. Kepler was one of the astronomers who employed logarithms in his calculations immediately after Napier’s publication. See: Ibid., pp. 418–419; Carl B. Boyer, A History of Mathematics, 2nd ed. (New York: Wiley, 1989), pp. 311–318.
Chaisson, Astronomy Today, pp. 362–366.
Observation of canals on Mars is an excellent example of this vision illusion. In 1877 after the observation of a network of linear marking on Mars by Giovanni Schiaparelli, telescopes pointed to the red planet to see the details of those marks. Percival Lowell (1855–1916), the most famous of those Mars observers, used one of the best telescopes of his time and created numerous drawings of Martian connected canals. Observations made by larger telescopes and photographs taken by Viking 1 and 2 (1976) revealed that those connected canals were separate surface features illusively connected through telescopic observation and sketching. See Ibid., p. 259.
Chapman, “The Accuracy of Angular Measuring”, pp. 134–135. For a review of the history of micrometers see Rondall C. Brooks, “The Development of Micrometers in the Seventeenth, Eighteenth and Nineteenth Centuries”, Journal of History of Astronomy 12 (1991), 127–173.
As an example, Newton, based on accurate data prepared by Flamsteed, was able to solve the ancient problem of the motion of the moon’s orbital apse. The lunar apse (or major axis in its orbit) moves about 3 degrees per month, a problem that had not been explained since antiquity. In 1689, the Royal Society established a mural arc equipped with a micrometer, and Flamsteed, using a new observational technique, produced precise data of lunar position and motion, which were used by Newton. See: Ibid., p. 133; Curtis Wilson, “Newton on the Moon’s Variation and Apsidal Motion: The Need for a Newer ‘New Analysis’, ” in Jed Z. Buchwald and I. Bernard Cohen (eds.), Isaac Newton’s Natural Philosophy (Cambridge: The MIT Press, 2001), pp. 139–140.
Eric G. Forbes (eds.), The Gresham Lectures of John Flamsteed (London: Mansell Publications, 1975), pp. 21–27.
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(2008). From Brahe to Newton. 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_3
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