Stars as the Armies of God: Lansbergen's Incorporation of Tycho Brahe's Star-size Argument into the Copernican Theory

How did a Copernican deal with the 'star size' objection to the Copernican theory articulated by Tycho Brahe (1546-1601)? According to Giovanni Battista Riccioli (1598-1671), a Copernican did so by appealing to divine power: an infinite and omnipotent God can make stars as large as He desires; such stars are nothing compared to God. A fascinating illustration of this approach to the Copernican theory's 'star size' problem can be found in the work of the Dutch Copernican Philips Lansbergen (1561-1632).Tycho's 'star size' objection was straightforward. Fixed stars appear to the naked eye to have measurable sizes. Tycho measured first magnitude stars to be about two arc minutes in apparent diameter, and lesser stars to be progressively smaller - values that generally agreed with earlier measurements.1 By geometry, the more distant an object of a given apparent size is, the physically larger it must be. Therefore, the great Copernican distance to the fixed stars, required in that theory to explain the lack of observable annual stellar parallax, translated into large physical sizes. Tycho's measurements and calculations indicated even a third magnitude Copernican star to be as physically large as the orbit of the Earth - dwarfing even the Sun. By contrast, in Tycho's geo-heliocentric theory, the stars lay just beyond Saturn (Figure 1), and had reasonable physical sizes (consistent with the other celestial bodies - Figure 2).Here was a weighty anti-Copernican argument. As Albert van Helden has put it: 'Tycho's logic was impeccable; his measurements above reproach. A Copernican simply had to accept the results of this argument."2 The telescope is often said to have dissolved this argument, because the telescope "made necessary a re-estimation of the true diameter of the fixed stars, which were now known to be far smaller than they appear to the naked eye".3 However, early telescopes produced images of stars that had the appearance of distinct disks, whose spurious nature was not understood at the time.4 The telescope did reveal stars to have smaller diameters than those Tycho measured non-telescopically, but it also increased the Copernican theory's sensitivity to parallax. The net result was that Tycho's objection remained. Simon Marius, Riccioli, and even the Copernican Martinus Hortensius all noted the problem that telescopically measured star diameters posed for the Copernican theory; even Galileo's telescopic star observations challenged the Copernican theory, although Galileo did not address this.5How could a Copernican respond to Tycho's objection? According to Riccioli, by appeal to the power of God.6 Indeed, the English Copernican Thomas Digges wrote in 1576 of the starry heaven with its stars "far excelling our sun" as being "the palace of felicity" and the "habitacle of the elect". The German Copernican Christoph Rothmann defended giant stars to Tycho in 1590 by invoking imagery of a palace of God and claiming that size was irrelevant to an infinite creator.7 Responding to Rothmann, Tycho had rejected such reasoning:On what is such an assertion based? Where in nature do we see the Will of God acting in an irregular or disorderly manner? In nature where all things are wellordered in all ways of time, measure, and weight? In nature where there is nothing empty, nothing irrational, nothing disproportionate or inharmonious. Consider 700,000 or more Earth semidiameters being between Saturn and the fixed stars in the Copernican hypothesis. Consider those same fixed stars each being as large as the whole Orbit of Earth (and some larger still) and thus dwarfing the Sun, the luminary and centre of motion for all the planets. These are the same fixed stars which are noted as the least of the heavenly lights in the account of the Creation of the World. This is empty, irrational, disproportionate and inharmonious. Is such a disproportionate universe reasonable?8Tycho went on to say that by Divine providence such an ageometrical, asymmetrical, disorderly, and most unworthy method of philosophizing will go away. …