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«The Accuracy of Galileo’s Observations and the Early Search for Stellar Parallax Christopher M. Graney Jefferson Community College 1000 Community ...»

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The Accuracy of Galileo’s Observations

and the Early Search for Stellar Parallax

Christopher M. Graney

Jefferson Community College

1000 Community College Drive

Louisville, Kentucky 40272

(502) 213-7292




The question of annual stellar parallax is usually viewed as having been a “win-win

situation” for seventeenth-century astronomers who subscribed to the Copernican view of

universe in which the Earth orbits the Sun and the Sun is one of many suns (the fixed stars) scattered throughout space. Detecting parallax would be solid evidence for the Earth’s motion, but failure to detect parallax could be explained by the stars lying at great distances. Recent work pertaining to Galileo’s observations of double stars illustrates Galileo’s skill as an observer. It also indicates that, given the knowledge of optics of the time, Galileo could expect his measurements to be accurate enough that they would have revealed stellar parallax had it existed. Thus parallax was not a “win-win situation” after all. It could be solid evidence against the Earth’s motion, evidence which fortunately did not dissuade Galileo from the Copernican view.

R1.1 I. INTRODUCTION For the greater part of the five centuries that have elapsed since Copernicus proposed a heliocentric model of the universe in his De Revolutionibus Orbium Coellestium, astronomers who subscribed to Copernicus’s view had to deal with the issue of annual stellar parallax. Until stellar parallax was actually observed roughly two centuries ago, heliocentrists had to argue that, while they believed the universe was populated with stars whose distances from Earth’s Sun varied and therefore stellar parallax should exist, lack of observable parallax did not disprove the heliocentric model. After all, if the stars are sufficiently distant the stellar parallax would exist but simply be too small to measure.

Copernicus himself stated that the lack of any parallax meant that the stars lay at vast distances beyond the planets.1 Stellar parallax was a “win-win situation” for heliocentrists – failure to detect it proved nothing, while a successful detection would be powerful evidence for heliocentrism.2 Copernicus, On the Revolutions of Heavenly Spheres [De rev.], translated by Charles Glen Wallis (Prometheus Books, Amherst, New York, 1995). After describing his heliocentric model, Copernicus states “…now the careful observer can note why progression and retrogradation appear greater in Jupiter than in Saturn and smaller than in Mars…. And why these reciprocal eventsappear more often in Saturn than in Jupiter, and even less often than in Mars…. In addition, why when Saturn, Jupiter, and Mars are in opposition they are nearer to the Earth than at the time of their occultation and their reappearance….

All these things proceed from the same cause, which resides in the movement of the Earth.” In other words, retrograde motion and varying brightness in the planets is essentially a manifestation of Earth’s motion – it is a planetary parallax akin to annual stellar parallax. Copernicus then continues “But that there are no such appearances among the fixed stars argues that they are at an immense height away, which makes the circle of annual movement or its image disappear from before our eyes since every visible thing has a certain distance beyond which it is no longer seen, as in optics. For the brilliance of their lights shows that there is a very great distance between Saturn the highest of the planets and the sphere of the fixed stars. By this mark in particular they are distinguished from the planets, as it is proper to have the greatest difference between the moved and the unmoved. How exceedingly fine is the godlike work of the Best and Greatest Artist! [pp. 26-27]” Harald Siebert, “The Early Search for Stellar Parallax: Galileo, Castelli, and Ramponi”, Journal for the History of Astronomy, Vol. 36 (2005), 251-271. Siebert writes “Thus Copernicans were actually placed in a win-win situation to resolve the dispute over the true world system. They had in hand the ‘experimentum crucis’ of the debate, and Galileo himself, as he tells us in his Dialogo, was fully aware of this unequal balance…. [pp. 251-2] ” R1.1 Recent work has brought to light evidence that as early as the 1610’s Galileo Galilei and Benedetto Castelli were actively searching for stellar parallax using the newly developed telescope.3,4 However, the assumption in this recent work remains that parallax could not disprove heliocentrism – only prove it. This assumption may not be

correct. In this paper I will argue the following:

–  –  –

At the end of the paper I will discuss questions for future study relating to Galileo’s fortuitous decision to support heliocentrism despite what his observations told him.


There are many reasons for believing that Galileo could make and record observations with arc-second accuracy. For example, Galileo’s observations of Jupiter have been shown to be of high quality – he recorded the separations between Jupiter and its moons to within 0.1 Jovian radii; in his sketches he places Jupiter’s moons to an accuracy of less than the width of the dots he uses to mark the moons’ positions; he recorded positions of Leos Ondra, “A New View of Mizar”, Sky and Telescope, July 2004, 72-75. p. 73.

Siebert, JHA (ref. 2), p. 257.

R1.1 objects as faint as Neptune.5 An interesting illustration of the accuracy of Galileo’s work can be seen by comparing some of his sketches of the Jovian system to a simulated telescopic view generated by planetarium software [Figure 1]. This accuracy is also on display in a sketch Galileo made on 4 February 1617 of a grouping of stars in Orion (including three stars in the Trapezium).6 A comparison of that sketch to modern data on those stars again reveals Galileo’s skill and the quality of his instruments – Galileo was able to produce an accurate sketch of stars that were separated by less than 15 arcseconds [Figure 2].

By 1612 Galileo had stated that he was able to make measurements accurate to within arc-seconds,7 and his statements about and measurements of stars are consistent with that claim. In his Dialogue Concerning the Two Chief World Systems (1632) Galileo states that a first-magnitude star has a diameter of 5 arc-seconds while a sixthmagnitude star has a diameter of one-sixth that size (50/60 arc-second or 0.83 arcsecond).8 He goes on to calculate the distance to a sixth-magnitude star (2160 times the distance to the Sun, or 2160 A.U.) based on the assumption that a star is equal to the Sun E. Myles Standish and Anna M. Nobili, “Galileo’s Observations of Neptune”, Baltic Astronomy, Vol. 6 (1997), 97-104, pp. 99-100.

Galileo Galilei, Le Opere di Galileo -- Edizione Nazionale Sotto gli Auspicii di Sua Maestà il re d'Italia, edited by Antonio Favaro (20 vols, Florence, 1890-1909; referenced as Opere from here forward), Vol. 3 part 2, p. 880.

Galileo, Opere, Vol. 4, p. 61. (Galileo’s Discourse on Bodies Floating in Water.) Galileo mentions having improved the accuracy of his measurements from errors of not more than a minute to errors of seconds.

Galileo, Dialogue Concerning the Two Chief World Systems – Ptolemaic & Copernican (2nd edition), translated by Stillman Drake (University of California Press, Los Angeles, California, 1967), p. 359.

Galileo also states that the 5 arc-second diameter of first-magnitude stars can be ascertained without a telescope (p. 362).

R1.1 in actual size and that its apparent size is determined by distance and geometry.9 This

implies that stellar magnitudes and sizes are linearly related:

–  –  –

Today we know that the apparent size of a star as viewed through a small but optically fine telescope10 is largely a function of wave optics and does not reflect the physical size of the star. However, a linear relationship between magnitude, size, and distance would have been a defensible proposition for an observer such as Galileo who knew nothing of wave optics [Figure 3]. Galileo believed that a good telescope did not produce illusions – that it accurately showed the true sizes of stars.11 Galileo’s recorded observations of stellar sizes agree with the values given above, although not perfectly. For example, undated notes of Galileo’s show that he observed Sirius and measured its diameter to be 5 and 18/60 arc-seconds.12 This is consistent with the sizes implied in the Dialogue. Galileo also observed the star Mizar and found it to consist of two component stars, the brighter of which (A) he measured to have a radius of 3 arc-seconds, and the fainter of which (B) he measured to have a radius of 2 arcGalileo, Dialogue (ref. 8) p. 359-360.

Vincenzo Greco and Guiseppe Molesini, “Optical Test of Galileo’s Lenses”, Nature, Vol. 358 (1992),

101. Tests on lenses and telescopes attributed to Galileo show them to be of high optical quality.

Henry R. Frankel, “The Importance of Galileo’s Nontelescopic Observations concerning the Size of the Fixed Stars”, Isis, Vol. 69 (1978), 77-82. Frankel discusses Galileo’s arguments that the telescope reliably revealed the true size of heavenly bodies, such as stars. Frankel includes (p. 81) an argument of Galileo’s which discusses observing Sirius from dark through dawn to sunrise with both the eye and the telescope: While Sirius seen with the eye diminishes in size and disappears as the sky brightens, as seen with the telescope the star’s appearance does not change. This shows that what is seen through the telescope is the pure object. The argument can be found in Opere, Vol. 6, p. 81.

Galileo, Opere, Vol. 3 part 2, p. 878.

R1.1 seconds.13,14 This undated observation was probably made on 15 January 1617.15 Mizar A is about magnitude 2 and B is about magnitude 4, so the diameters of 6 and 4 arcseconds that Galileo determined in 1617 differ from the sizes implied in the Dialogue fifteen years later, but by less than two arc-seconds. Galileo measured the center-tocenter separation between the two stars to be 15 arc-seconds. Galileo’s separation measurement is within half an arc-second of modern measurements,16 and his radius measurements agree closely in proportions to what would be expected for optically good telescopes of the sizes he used [Figure 4].

In short, Galileo’s notes and writings indicate that he was able to make and record observations to a high level of accuracy. That Galileo achieved such results with some of the first telescopes known to be used to study the heavens, especially when some of his contemporaries were unable to see even relatively easy celestial sights with their telescopes17, is a testament to his talent and work ethic.18 III. STELLAR PARALLAX – NOT A “WIN-WIN” SITUATION Unless the previously mentioned results were all flukes, and his claim of arc-seconds accuracy an exaggeration, Galileo must have been able to produce similar-quality Ondra, S&T (ref. 3), p. 74. Ondra’s article includes a copy of Galileo’s original notes on Mizar.

Galileo, Opere, Vol. 3 part 2, p. 877. Galileo’s Mizar notes in the Opere.

Siebert, JHA (ref. 2), p. 259.

Siebert assumes that the closeness of Galileo’s value to the modern value is an accident (Siebert, JHA (ref. 2), p. 259).

Albert Van Helden, “The Telescope in the Seventeenth Century”, Isis, Vol. 65 (1974) 38-58. pp. 43-44,

52. Van Helden notes one observer in 1612, Jacob Christmann, describing Jupiter as three or four fiery balls with hairs coming out like a comet. This was at the same time that Galileo was noting that he had improved his observations to an accuracy of a few arc-seconds.

For another testament to Galileo’s talent, and a further demonstration of his accuracy and of what he was able to achieve with his telescopes, the reader is advised to study Tom Pope and Jim Mosher’s web site, “CCD Images from a Galilean Telescope”, (www.pacifier.com/~tpope). Pope and Mosher constructed a Galilean telescope and obtained afocal CCD images through it. By comparing their CCD images with Galileo’s notes and sketches, they too find Galileo to be remarkably accurate in his observations. Pope and Mosher’s work served as the inspiration for a large part of this paper.

R1.1 observations at other times. The quality of Galileo’s observations now comes to bear on the question of parallax and whether it was a “win-win situation” for heliocentrists.

Galileo used his observation of Mizar to calculate that Mizar A, being 1/300 the apparent radius of the Sun, must be 300 times more distant than the Sun (300 A.U.).19 In doing this Galileo assumed that stars are suns. By the same logic, Mizar B would be 450 A.U. distant.

Today we know these distances to be inaccurate in the extreme. We know that the differing stellar radii Galileo was measuring represented nothing more than a combination of a wave optics diffraction pattern/Airy Disk and the limits of the human eye [Figures 3 and 4]. However, as mentioned earlier in this paper, he could not know this. He thought he was seeing the physical bodies of stars. For all other objects Galileo observed, size was inversely proportional to distance. He used size arguments to argue, for example, that Mars and Venus orbited the Sun.20 An understanding of wave optics and Airy Disks was far in the future when Galileo was using his telescope. There was no Galileo, Opere, Vol. 3 part 2, p. 877.

Galileo, Dialogue (ref. 8), “SIMP. How do you deduce that it is not the earth, but the sun, which is the center of the revolutions of the planets? SALV. This is deduced from the most obvious and therefore most powerfully convincing observations. The most palpable of these, which excludes the earth from the center and places the sun there, is that we find all the planets closer to the earth at one time and further from it at another. The differences are so great that Venus, for example, is six times as distant from us at its farthest as at its closest, and Mars soars nearly eight times as high in the one state as in the other….

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