Ein astronomisch-astrologisches Gedicht des persischen Dichters Ḥusain Ḥakīm Ṯanāʾī Mašhadī auf der Berliner Indischen Weltkarte

One does not encounter short astronomical-astrological poems in Persian very frequently. One such poem, by the Persian-Indian poet Ṯanāʾī (d. 1587/8) is inscribed on the Indian world map in the Museum of Islamic Art in Berlin. This map probably originated in the sphere of the court of the ruler of Rajastan, Sawai Jai Singh II. (1700‒1743). The poem does not bear a relationship to the other inscriptions and paintings found on the map, and is known only from this map. It presupposes a significant degree of knowledge of astronomy and astrology on the reader’s part, especially since Ṯanāʾī had developed a style in India by means of which he was able to “pack longwinded ideas and multiple meanings into a succinct expression”. The poem reflects a world view that is based on the cosmology of Aristotle and the planetary theories of Ptolemy. In particular, it addresses the heavenly spheres, with the earth at their center, the system of astronomical coordinates, the course and the characteristics of the planets, including Sun and Moon, and a short characterization of the four elements and the twelve signs of the zodiac. This article provides a philological reading, translation, and line-by-line commentary of the poem.

Solar barycentric dynamics from a new solar-planetary ephemeris

Aims. The barycentric dynamics of the Sun has increasingly been attracting the attention of researchers from several fields, due to the idea that interactions between the Sun’s orbital motion and solar internal functioning could be possible. Existing high-precision ephemerides that have been used for that purpose do not include the effects of trans-Neptunian bodies, which cause a significant offset in the definition of the solar system’s barycentre. In addition, the majority of the dynamical parameters of the solar barycentric orbit are not routinely calculated according to these ephemerides or are not publicly available. Methods. We developed a special version of the IAA RAS lunar–solar–planetary ephemerides, EPM2017H, to cover the whole Holocene and 1 kyr into the future. We studied the basic and derived (e.g., orbital torque) barycentric dynamical quantities of the Sun for that time span. A harmonic analysis (which involves an application of VSOP2013 and TOP2013 planetary theories) was performed on these parameters to obtain a physics-based interpretation of the main periodicities present in the solar barycentric movement. Results. We present a high-precision solar barycentric orbit and derived dynamical parameters (using the solar system’s invariable plane as the reference plane), widely accessible for the whole Holocene and 1 kyr in the future. Several particularities and barycentric phenomena are presented and explained on dynamical bases. A comparison with the Jet Propulsion Laboratory DE431 ephemeris, whose main differences arise from the modelling of trans-Neptunian bodies, shows significant discrepancies in several parameters (i.e., not only limited to angular elements) related to the solar barycentric dynamics. In addition, we identify the main periodicities of the Sun’s barycentric movement and the main giant planets perturbations related to them.

VÉNUS SELON IBN AL-ŠĀṬIR

We attempt to grasp the mathematics behind the planetary theories of the Syrian astronomer Ibn al-Šāṭir (1304–1375) in his treatise Nihāyat al-Sūl. Following the astronomers of the Marāgha school, by composing circular movements with constant angular velocity, Ibn al-Šāṭir attains two goals. He eliminates the need of excentrics and equant points in astronomy; but he also describes longitudes and latitudes with a unique method, with no more orbs than what is strictly necessary for the longitudes. A better understanding of rotation as a spatial transformation enables this ultimate economy of thought. In our commentary, we take Venus as an example offering an interesting problem about the latitudes. This is an opportunity to give a critical edition of the chapter of the Nihāyat al-Sūl dedicated to the latitudes of Mercury and Venus.

Reconstruction Synthesis of the Lost Subsystem for the Planetary Motions of Antikythera Mechanism

The mechanism for the planetary motions contained in the lost subsystem of Antikythera mechanism is a strict challenge of the reconstruction design. This work presents a systematic procedure of the reconstruction design to synthesize all feasible designs which agree with the science and technology standards of the subject’s time period. Based on the kinematic analysis of ancient planetary theories, the anomaly planetary motions could be formulated. By the mechanism analysis, two types of feasible topological structures with the minimum numbers of members are obtained, and the relationships of teeth for the inferior and superior planets are derived. Through the study of the historical literature, the astronomical theories and the existing designs, the required design constraints are concluded. For the two reconstruction designs, one, the design by Edmunds and Morgan, and three feasible design concepts are, respectively, synthesized in accordance with the concepts of generalization and specialization. Focusing on each feasible design concepts, this work derives the relationships of teeth. Furthermore, one feasible combination of these feasible designs for different planets is adopted for detail design. And, it could be the original structure for the planetary motions of the lost subsystem of Antikythera mechanism.