The Anomalous Sun

Four clockwork-driven planetary automata built to show the true motion of the planets according to Ptolemaic theory, not just their mean motion, survive from the sixteenth century: one each in Paris, Vienna, Kassel, and Dresden. Close, on-site examination of their mechanisms by a team of historians of science and clockmakers has gone beyond existing accounts and revealed that, though they share a common aim, the machines differ fundamentally in their realization of even the “simplest” of the planetary motions, namely that of the Sun. Indeed, three different ways have been detected for producing the solar anomaly, the Sun’s non-uniform motion along the ecliptic in the course of a year. The oldest of the surviving machines (Paris) uses the uniform motion of an eccentric gear, another (Vienna) adapts what would be a geometrically equivalent epicycle, and the two other machines (Kassel and Dresden) make use of a centered gear with non-uniformly spaced teeth. This paper discusses these findings in detail. It argues that such differing approaches not only reflect varying degrees of collaboration among the actors involved in the construction of these four technical masterpieces – princely commissioners, learned astronomers, and artful craftsmen (with these categories sometimes overlapping) – but also that they offer a further, mechanical contribution to the centuries-old reception and refinement of Ptolemaic planetary theory.

A Second Order Secular J–S Planetary Theory Part I : Lemma

A concise lemma is given for the construction of a semi – analytic Hamiltonian second order secular J–S planetary theory using the Jacobi – Radau system of origins and in terms of the non-singular variables of H. Poincaré. We truncate our expansions at the desired power in the eccentricities and the sines of the inclinations.

Ptolemaic Orbs in Twelfth-Century England: A Study and Edition of the Anonymous Liber de motibus planetarum

This article offers the first study and critical edition of the Liber de motibus planetarum (Lmp), a neglected Latin text on planetary theory that appears anonymously and without any clear indication of date or place of origin in nine manuscripts of the thirteenth to fifteenth centuries. An analysis of its sources and parallels to other Latin treatises and translations from Arabic indicates that the Lmp originated in England in the third quarter of the twelfth century. A plausible terminus post quem is provided by the appearance of similar passages in the anonymous treatise Ptolomeus et multi sapientum (1145), which can be linked to Abraham Ibn Ezra and his astronomical tables for the meridian of Pisa. The Lmp would appear to be historically significant for its relatively detailed textual and diagrammatic presentations of Ptolemy’s planetary models as composed of multipart physical orbs. While it is generally accepted that physicalized or ‘orbed’ versions of these models entered Latin astronomy through the influence of Ibn al-Haytham’s Maqāla fī hayʾat al-ʿālam (On the Configuration of the World), the early history of this idea in a Latin context has not been studied to any deeper extent. In this regard, the Lmp offers clear evidence that Ptolemaic orbs and diagrams representing them already were a part of Latin astronomy three centuries before Peuerbach’s Theoricae novae planetarum (1454).

Research on the Motion of Mars in the Sovereign Pole System (a.d. 600)

The Sovereign Pole System (a.d. 600) is the first Chinese system to take account of the equation of centre for the sun and planets in the planetary theory. In this paper, we mainly discuss the motion of Mars in the Sovereign Pole System. First, we discuss the algorithm for calculating the time of Mars’ first appearance, especially we discuss the influence of the equation of centre for the sun and Mars at the time of Mars’ first appearance. Then, we discuss the segmented motion of Mars in one single synodic period and its accuracy. Finally, we discuss the method for computing the position of Mars at any given time and the error in longitude of Mars. The result shows that the innovations in planetary theory found in the Sovereign Pole System were a fruitful development in ancient Chinese planetary theory and it obviously improved the accuracy of calculation of the position of Mars. However, the planetary theory in the Sovereign Pole System is still relatively rough because it was impossible for Sui astronomers to obtain the correct model of the motion of planet.