Abstract
Because early telescopic astronomers did not understand the spurious nature of star images formed by their telescopes, their observations of the stars yielded data that apparently confirmed the geocentric Tychonic world system. Both Galileo Galilei (1564–1642) and Simon Marius (1570–1624) obtained such data. Galileo backed Nicholas Copernicus (1473–1543) despite his data. Marius supported Tycho Brahe (1546–1601) on the basis of his data.
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Notes
The angular diameter θ of the Airy disk goes as λ/d, where λ is the wavelength and d is the diameter of the telescope aperture.
Recall that dimmer stars have larger magnitudes: Stars of magnitude 1 are bright, those of magnitude 6 are barely visible to the naked eye.
Note that the inverse-square law is not used here—only simple geometry.
I note that Johannes Kepler (1571–1630), in his Epitome of Copernican Astronomy, argued that the appearance of the night sky shows that the stars are not scattered throughout space; see Max Casper, ed., Johannes Kepler Gesammelte Werke. Band VII. Epitome Astronomiæ Copernicanæ [1618]. Liber Primvs. Pars Secvnda (München: C.H. Beck’sche Verlagsbuchhandlung, 1953), pp. 42–46; see also the 1635 edition, Book I, Part II, pp. 32–37, available online through Google books. His argument, however, assumed that stars in an infinite universe must be uniformly arranged throughout space with geometric regularity, and that if stars varied in distance by a factor of two or three or more, then the more distant stars would not be visible; see Rhonda Martens, Kepler’s Philosophy and the New Astronomy (Princeton and Oxford: Princeton University Press, 2000), p. 146. Kepler’s arguments did not persuade those who had accepted Digges’s ideas; see Johnson and Larkey, “Thomas Digges” (Ref. 3), p. 116.
Mizar was neither the only double (or multiple) star that Galileo observed, nor the only one for which he left precise notes; see Seibert, “Early Search” (Ref. 16). Galileo made a precise observation of the Trapezium; see Graney, “On the Accuracy” (Ref. 10). His observing notes on the Trapezium are available in Favaro, Opere. Vol. III (Ref. 7), p. 880. The reader will recognize these values as the ones used in calculating the differential parallax of the hypothetical double star in our thought experiment.
The evidence suggests that Galileo could indeed make the precise measurements he claimed to have made: He certainly seems to have been able to measure positions and diameters of stars at the arcsecond level; see Graney, “On the Accuracy” (Ref. 10), pp. 443–446.
One is tempted to impose sense on these questions by deciding that Galileo must have concluded that, in the case of Mizar, its two stars actually were physically close. This requires that Galileo allow for some variation in their physical sizes, but would explain why Mizar does not display the expected differential parallax. Then one decides that in his Dialogue he was speaking of what would occur “if” a true line-of-sight double star were found. However, in his observation of the Trapezium he records a factor of four or five in the variation in the size of stars separated by no more than Mizar’s separation; see Favaro, Opere. Vol. III (Ref. 7), p. 880. To explain the lack of differential parallax in the Trapezium requires those stars to be physically close—and varying in physical size by a factor of four or five. Galileo, as we saw, believed that the difference in apparent size between the brightest and faintest stars visible to the naked eye was only a factor of six. If stars can vary in physical size by a factor of four or five, then all of Galileo’s ideas about stellar sizes and distances are completely undermined, and he may as well have advocated that the stars lie on the surface of a sphere.
I infer this, because Marius notes that these disks are most prominent in the brighter stars.
References
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Acknowledgment
I thank Roger H. Stuewer for his careful and thoughtful editorial work on my paper.
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Christopher M. Graney teaches physics and astronomy at Jefferson Community & Technical College in Louisville, Kentucky, and runs the college’s observatory at Otter Creek Park in Louisville.
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Graney, C.M. Seeds of a Tychonic Revolution: Telescopic Observations of the Stars by Galileo Galilei and Simon Marius. Phys. Perspect. 12, 4–24 (2010). https://doi.org/10.1007/s00016-009-0002-0
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DOI: https://doi.org/10.1007/s00016-009-0002-0
Keywords
- Aristotle
- Ptolemy
- Nicholas Copernicus
- Tycho Brahe
- Galileo Galilei
- Simon Marius
- Aristotelian–Ptolemaic world system
- Copernican world system
- Tychonic world system
- Airy disk
- stellar observations
- telescope
- history of astronomy