Trepidation spheres: Variant representations of the eighth sphere and the debate about the movement of the apogees and the fixed stars in Alfonsine astronomy

Abstract

In what way does the construction of three-dimensional spherical models in the early modern period reflect the search for an appropriate representation of subtle, slow changes perceived in the firmament of the fixed stars? The present paper analyses some of the preserved models and assesses the potential they held to stimulate contemporary thinking on this question, termed the “motion of the eighth sphere.” The spheres discussed here reveal different ways of conceiving and visualizing stellar precession, which was more commonly expressed in tabular form, such as the Alfonsine tables, or by means of theoretical texts, such as Peurbach's Theoricae novae planetarum. One of the spheres unexpectedly turns out to be the only known material representation of Johannes Werner's alternative theory of trepidation. Although our knowledge of the context in which these spheres were produced is limited, their material characteristics point to their distinct origins. A focus on the rare and understudied species of “trepidation spheres” leads to questions not addressed in studies drawing only on written sources. It brings additional actors into the spotlight, in particular instrument-makers. Moreover, the variety of constructions found in the group of surviving spheres indicates that the available traditional sources allowed for variant interpretations. Besides texts and diagrams, the trepidation spheres are historical tools of thought that can literally be touched. While further investigation is needed, this paper looks at the spheres' potential role for practitioners in exploring the geometric implications of trepidation in Alfonsine astronomy from the second half of the 15th century onwards.