On the Telescopic Disks of Stars: A Review and Analysis of Stellar Observations from the Early Seventeenth through the Middle Nineteenth Centuries

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Notes

¹M.A. Finocchiaro, The Galileo Affair (Berkley, CA: University of California Press), pp. 167–168, 173–174, 180.

²E. Halley, ‘Some Remarks on a Late Essay of Mr. Cassini, Wherein He Proposes to Find, by Observation, the Parallax and Magnitude of Sirius’, Philosophical Transactions, 31 (1720) 1–4, p. 3.

³W. Herschel, ‘Experiments for Ascertaining How Far Telescopes Will Enable Us to Determine Very Small Angles, and to Distinguish the Real from the Spurious Diameters of Celestial and Terrestrial Objects: With an Application of the Result of These Experiments to a Series of Observations on the Nature and Magnitude of Mr. Harding's Lately Discovered Star’, Philosophical Transactions of the Royal Society of London, 95 (1805) 31–64, pp. 40–44.

⁴G.B. Airy, ‘On the Diffraction of an Object-Glass with Circular Aperture’, Transactions of the Cambridge Philosophical Society, 5 (1835) 283–291.

⁵Recall that the magnitude system was a way of ranking stars by brightness. Thus a star that is among the brightest in the sky is a star of first magnitude (a first-rate star). A star that is still fairly bright but not among the brightest is of second magnitude (a second-rate star). A star barely visible to the naked eye under dark skies is of sixth magnitude. The higher the magnitude, the fainter the star.

⁶S. Drake, Discoveries and Opinions of Galileo (New York: Anchor Books, 1957), p. 47.

⁸S. Marius, Mundus Iovialis/Die Welt des Jupiter, translated by J. Schlör (Gunzenhausen: Schenk-Verlag, 1988), pp. 46–48. Translation from Latin to English by C. Graney.

⁷J.L.E. Dreyer, ‘The Tercentenary of the Telescope’, Nature, 82 (1909) 190–191, p. 191.

⁹Galileo actually mentions seeing telescopic disks of stars in his 1612/1613 letters on sunspots, where he says stars are spherical or round in shape (see Drake op. cit., pp. 100, 137), but he does not mention brighter stars having larger disks than fainter stars.

¹⁴Finocchiaro op. cit., p. 167.

¹⁶Galileo Galilei, Dialogue Concerning the Two Chief World Systems – Ptolemaic & Copernican with foreword by Albert Einstein, translated by Stillman Drake, 2nd edition (Berkeley, CA: University of California Press, 1967), p. 359.

¹⁰U. Fedele, ‘Le prime osservazioni di stelle doppie’, Coelum, 17 (1949) 65–69; L. Ondra, ‘A New View of Mizar’, Sky and Telescope, (July 2004), 72–75; H. Siebert, ‘The Early Search for Stellar Parallax: Galileo, Castelli, and Ramponi’, Journal for the History of Astronomy, 36 (2005) 251–271.

¹¹A. Favaro (editor), Le Opere di Galileo: Edizione Nazionale Sotto gli Auspicii di Sua Maestà il re d'Italia (Florence, 1890), III, p. 877.

¹²C.M. Graney, ‘But Still, It Moves: Tides, Stellar Parallax, and Galileo's Commitment to the Copernican Theory’, Physics in Perspective, 10 (2008) 258–268, p. 262.

¹³Favaro op. cit., III, p. 880.

¹⁵Finocchiaro op. cit., pp. 167–168, 174, 180.

¹⁷ Galileo Galilei, Dialogue Concerning the Two Chief World Systems – Ptolemaic & Copernican with foreword by Albert Einstein, translated by Stillman Drake, 2nd edition (Berkeley, CA: University of California Press, 1967), p. 359, p. 388.

¹⁸Marius op. cit., p. 48; C.M. Graney, ‘Seeds of a Tychonic Revolution: Telescopic Observations of the Stars by Galileo Galilei and Simon Marius’, Physics in Perspective, 12 (2010) 4–24.

¹⁹Galilei op. cit., pp. 358–360; Finocchiaro op. cit., pp. 166–180.

²⁰M. Hortensius, Dissertatio de Mercurio in Sole Viso (Lieden, 1633), pp. 61–62.

²¹G. B. Riccioli, Almagestum Novum, I (Bologna, 1651), p. 716.

²²G. B. Riccioli, Astronomia Reformata (Bologna, 1665), p. 360.

²³J. Hevelius, Mercurius in Sole Visus Gedani (Gdansk, 1662), p. 94.

²⁴J. Cassini, Mem. Adac. des Sciences, (1717), p. 258, cited in Robert Grant, History of Physical Astronomy (London, 1852), p. 545.

²⁵C. Huygens, Systema Saturnium (Hague, 1659), p. 7; F. Roberts, ‘Concerning the Distance of the Fixed Stars’, Philosophical Transactions, 18 (1694) 101–103. Huygens’ argument was not necessarily convincing to early astronomers who observed the telescopic disks of stars. For example, Flamsteed argued that the disks were real, and that the soot on Huygens’ glass merely allowed thin rays of light to pass through, rendering the appearance of smaller size, see F. Bailey, An Account of the Rev. John Flamsteed (London, 1835), pp. 206–207.

²⁶Halley op. cit., p. 3.

²⁸W. Herschel, ‘Catalogue of Double Stars. By Mr. Herschel, F.R.S. Communicated by Dr. Watson’, Philosophical Transactions of the Royal Society of London, 72 (1782) 112–162, p. 112, p. 130.

²⁷W. Herschel, ‘Catalogue of Double Stars. By Mr. Herschel, F.R.S. Communicated by Dr. Watson’, Philosophical Transactions of the Royal Society of London, 72 (1782) 112–162, p. 112.

³¹Herschel (1782) op. cit., pp. 129–130.

³³Herschel (1805) op. cit., p. 44.

²⁹The two stars are of spectral classes K and A in the OBAFGKM classification system, where class O stars are hotter stars with a blue color and class M are cooler stars with a red color.

³⁰Herschel (1782) op. cit., pp. 142–143.

³²Herschel (1805) op. cit., pp. 40–42.

³⁴J.F.W. Herschel, ‘Light’ in Treatises on Physical Astronomy, Light and Sound contributed to the Encyclopædia Metropolitana (London, 1828), p. 491.

³⁵J.F.W. Herschel, ‘Light’ in Treatises on Physical Astronomy, Light and Sound contributed to the Encyclopædia Metropolitana (London, 1828), p. 491.

³⁶J.F.W. Herschel, ‘Light’ in Treatises on Physical Astronomy, Light and Sound contributed to the Encyclopædia Metropolitana (London, 1828), p. 491.

³⁷J.F.W. Herschel, ‘Light’ in Treatises on Physical Astronomy, Light and Sound contributed to the Encyclopædia Metropolitana (London, 1828), p. 491.

³⁸J.F.W. Herschel, ‘Light’ in Treatises on Physical Astronomy, Light and Sound contributed to the Encyclopædia Metropolitana (London, 1828), p. 491.

³⁹J.F.W. Herschel, ‘Light’ in Treatises on Physical Astronomy, Light and Sound contributed to the Encyclopædia Metropolitana (London, 1828), p. 492.

⁴⁰Airy op. cit., p. 290.

⁴¹Airy op. cit., p. 287.

⁴²Airy op. cit., pp. 287–288.

⁴³Airy op. cit., p. 288.

⁴⁴C.M. Graney, ‘On the Accuracy of Galileo's Observations’, Baltic Astronomy, 16 (2007) 443–449.

⁴⁵C.M. Graney, ‘17th Century Photometric Data in the Form of Telescopic Measurements of the Apparent Diameters of Stars by Johannes Hevelius’, Baltic Astronomy, 18 (2009) 253–263.

⁴⁷G. Hunt, ‘The Diameter of the Spurious Disk of a Star’, The Observatory, 3 (1879) 151–153, p. 152.

⁴⁸G. Hunt, ‘The Diameter of the Spurious Disk of a Star’, The Observatory, 3 (1879) 151–153, pp. 152–153.

⁴⁶G. Knott, ‘On the Telescopic Disks of Stars’, Monthly Notices of the Royal Astronomical Society, 27 (1867) 87–88, p. 88.

⁴⁹‘Meeting of the Royal Astronomical Society’, The Observatory, 9 (1886) 241–254.

⁵¹T. Dickinson, Nightwatch: A Practical Guide to Viewing the Universe, with foreword by Timothy Ferris, 3rd edition (Willowdale, Ont. and Buffalo, NY: Firefly Books, 1988), pp. 83–84.

⁵²P. Moore, The Amateur Astronomer (London: Springer-Verlag, 2006), p. 127.

⁵³Orion ShortTube 80-A 80mm Rich-Field Refracting Telescope Instruction Manual #9947, IN 305 Rev. A 02/07; Santa Cruz: Orion Telescopes and Binoculars. Orion is a major seller of amateur telescopes.

⁵⁴Herschel (1828) op. cit., p. 491.

⁵⁰D. Lardner and E. Dunkin, Handbook of Astronomy (London: Lockwood & Co., 1875), p. 379. Apparently the Handbook is erroneously interpreting Herschel's ideas about the effect of magnification on stars (see Figure 2) as meaning that their disks actually reduce in size as it appears to the eye.

⁵⁵Drake op. cit., p. 47 note 16.

⁵⁶J. Preston, G. Munévar, D. Lamb, The Worst Enemy of Science?: Essays in Memory of Paul Feyerabend (New York: Oxford University Press, 2000).

⁵⁷‘Papal visit scuppered by scholars’, BBC News (Tuesday, 15 January 2008, 18:42 GMT, <http://news.bbc.co.uk/2/hi/7188860.stm>), accessed 02/04/2010.

⁵⁸Feyerabend is selected here simply as a recognizable example. A discussion of the presence of the conventional wisdom in the writings of historians and philosophers of science would occupy a full paper. However, a brief list of sources will help to illustrate the point:

⁵⁸Feyerabend includes the subject of magnification of stars, couched in terms of the conventional wisdom, in his Against Method [3rd edition (New York: Verso, 1993), pp. 92–93], including a lengthy footnote that refers to Herschel talking about stars not responding to dramatic increases in magnification, see Figure 2. In critiquing Feyerabend, Alan Chalmers [‘Galileo's Telescopic Observations of Venus and Mars’, British Journal for the Philosophy of Science 36 (1985) 175–184, p. 176] brings up the issue of Galileo's telescopes not magnifying stars. Feyerabend aside, we find other writers working based on the conventional wisdom. Harold Brown [‘Galileo on the Telescope and the Eye’, Journal of the History of Ideas, 46 (1985) 487–501, p. 490] discusses the issue of stars not being magnified. Henry Frankel's paper on Galileo's non-telescopic star observations [‘The Importance of Galileo's Nontelescopic Observations concerning the Size of the Fixed Stars’, Isis, 69 (1978) 77–82, pp. 77–80, 78 note 6] includes quotes from Galileo making reference to disks of stars, but also includes quotes from other writers, including Dreyer [A History of Astronomy from Thales to Kepler (Cambridge: Cambridge University Press, 1906), p. 414] and Kuhn [The Copernican Revolution (Cambridge, MA: Harvard University Press, [1957] 1985), p. 221)], who state the conventional wisdom. All these writers understandably follow the conventional wisdom. Their analyses likely would have been influenced by the information that stars show disks in small telescopes, which are magnifiable with defined sizes of a few seconds, and which were seen by Marius and Galileo.

⁵⁹Marius op. cit., p. 48; Graney (2010) op. cit.

⁶⁰M.M. Shara, A.F.J. Mofatt, R.F. Webbink, ‘Unraveling the oldest and faintest recovered nova – CK Vulpeculae (1670)’, Astrophysical Journal, Part 1, 294 (1985) 271–285.

⁶¹Graney (2009) op. cit.

⁶²Historians write that the telescope provided no help in measuring the magnitudes of stars:

Part of the problem lay in the lack of a sufficiently delicate technique for monitoring the apparent brightness of a star. Stars were simply grouped according to the crude classification inherited from Antiquity, whereby the brightest stars were first magnitude and the faintest, sixth. The mid-nineteenth century would see the invention of new instruments to give an objective measure of the brightness of stars, and a new definition of magnitude. But before then, in the closing years of the eighteenth century, astronomers were at last provided with a simple method of determining whether a star had in fact altered in brightness [this being William Herschel's ‘Catalogues of the Comparative Brightnesses of Stars’; M. Hoskin, in The Cambridge Illustrated History of Astronomym edited by M. Hoskin (Cambridge: Cambridge University Press,, 1997), pp. 201–202]

J.B. Hearnshaw [The Measurement of Starlight: Two Centuries of Astronomical Photometry (Cambridge: Cambridge University Press, 1996), pp. 12–13] and R. Miles [‘A light history of photometry: from Hipparchus to the Hubble Space Telescope’, Journal of the British Astronomical Association, 117 (2007) 172–186, p. 173] attribute to the telescope no opportunity for improvement in photometry. Yet as Airy illustrated, disk diameter reflects the brightness of stars. It can, and at least in the case of Hevelius, did serve as a means of distinguishing magnitude to some precision [Graney (2009) op. cit.]. In similar manner to what is mentioned in the earlier footnote on Feyerabend, etc., correct information about how stars show disks in small telescopes would likely affect these various writers’ analyses.

⁶³The Rayleigh criterion is a standard means of assessing the theoretical ability of a telescope to resolve fine detail. It says a telescope's ability to resolve detail is defined by Airy's first dark ring. Using Airy's s = 2.76/a formula for the radius of the first dark ring, where a (the aperture radius) is 0.75 inches since the aperture is 1.5 inches, yields 3.7 seconds.

⁶⁴Finocchiaro op. cit., p. 174.

⁶⁵S. Drake and C.T. Kowal, ‘Galileo's sighting of Neptune’, Scientific American, 243 (1980) 74–80.

⁶⁶E.M. Standish and A.M. Nobili, ‘Galileo's Observations of Neptune’, Baltic Astronomy, 6 (1997) 97–104.

⁶⁷Graney (2007) op. cit.

⁶⁸G.P. Bond, ‘An Account of the Nebula in Andromeda’, Memoirs of the American Academy of Arts and Sciences (New Series), 3 (1848) 75–86, pp. 75–76.

⁶⁹F. Watson, Stargazer: The Life and Times of the Telescope (Da Capo Press, 2005), p. 86.

⁷⁰A.O. Prickard, ‘The Mundus Jovialis of Simon Marius’, The Observatory, 39 (1916) 367–381, 403–412, 443–452, 498–503; pp. 404, 408–409.

⁷¹M.M. Waldrop, ‘Supernova 1987 A: Facts and Fancies’, Science (New Series) 239 (1988) 460–462, p. 462.

⁷²V. Greco, G. Molesini and F. Quercioli, ‘Optical tests of Galileo's lenses’, Nature, 358 (1992) 101.

⁷³V.N. Mahajan, Optical Imaging and Aberrations (Bellingham Washington: The International Society for Optical Engineering, 2001), pp. 129–130, 135.