| Chapter 1: | The New Astronomy |
were at unacceptably large distances (figures 1.3a, 1.3b). Specifically, if heliocentricism were the case and Tycho adopted Copernicus'value of 1,142 Earth radii for the Earth's orbital radius, then the stars would have to lie more than 700 times farther than the average distance of the orbit of Saturn, which was then believed to be 10,550 Earth radii. Because the volume of a sphere increases as the cube of its radius, the volume of space surrounding the Solar System would have to exceed that occupied by Tycho's model by a factor of 700 cubed—over 300 million times (Thoren 279). In accordance with prevailing ideology, Tycho thought that such a huge amount of “wasted” space was absurd, and concluded therefore that the Universe was geocentric. The irony in this calculation is that, unwittingly, Tycho had made a great advancement because his accurate position measurements placed a lower limit on the size of the Copernican immensum.
Another argument that persuaded him against heliocentricism was the apparent angular sizes of stars. These vary with atmospheric conditions and appear smaller under conditions of diminished glare (as one might obtain during twilight), but no one took account of these facts. Tycho made the standard erroneous assumption that the appearance of a star was a measure of its real size, meaning that stars lying at the great distances dictated by the absence of detectable parallax had to be enormous. Rather than challenge his assumptions, Tycho concluded that this result was absurd too. Ergo, the Earth lies inert at the center of creation.
During his travels in 1575, Tycho acquired a book that pictured the Ptolemaic model, but with Mercury and Venus in orbit about the Sun. By 1583–1584, he had started to think in terms of this hybrid geo-heliocentric model whose origins date to Martianus Capella (fl.410–439), Heraclides Pontus, and the ancient Egyptians (Dreyer 167; Thoren 239–241). Accordingly, in 1583 he devised a model which appeared five years later in modified form in his De Mundi aetherei recentioribus Phaenomenis Liber Secundus (“Second Book concerning recent appearances in the Celestial World,” or Liber Secundus for short). The model combined what he believed were the best features of geocentricism and heliocentricism. He opted for a stationary Earth for reasons stated and because