A Research On Parallax Theory In Ancient Greece, India And China

Parallax plays an important role in the solar eclipse theory because it will affect the calculation and prediction of a solar eclipse, such as the time of the middle eclipse, the magnitude of the solar eclipse and the interval of a solar eclipse. In order to calculate and predict a solar eclipse accurately, the ancient astronomers need to design a relevant algorithm to eliminate the effect of lunar parallax. As the core algorithm in solar eclipse calculation, parallax algorithm was highly emphasized by all ancient civilizations. Because of the importance of the parallax in calculating and predicting a solar eclipse, it is necessary and useful to study the construction, history and precision of parallax algorithm in the solar eclipse theory of Greece, India and China.The main researches and achievements of this thesis are as follows:(1) Based on the study of the original works, this paper explains the construction of the parallax algorithm in Almagest, especially how Ptolemy used lunar parallax to calculate a solar eclipse.(2) Based on the original works and previous studies, this paper discusses the evolution of parallax algorithm from the 5th to the 12th century in India;clarifies the construction of parallax algorithm in Suyra Siddhanta and verifies that the parallax algorithm in Suyra Siddhanta is the same as the modern theoretic algorithm. It also discusses the precision of parallax algorithm in Suyra Siddhanta and analyzes the causes of the error.(3) Based on previous researches and the modern astronomy theory, this paper explains clearly the meanings of Shicha(时差) algorithm of mathematical astronomy in China and reconstructs a theoretical model of Shicha algorithm which is the base of the precision of a solar eclipse. This paper discusses the history of Shicha algorithm from Zhang Zixin(张子信) to Guo Shoujing(郭守敬) and divides the history of Shicha algorithm into several stages according to its characters. It also analyzes the precession of Shicha in Xuanming Calendar , Jiyuan Calendar and Shoushi Calendar and points out the shortcomings of Shicha algorithm in the completeness of the variables and the choice of the sign of Shicha in ancient China. Based on this, the paper summarizes systematically and evaluates objectively the Shicha algorithm in ancient China.(4) Based on previous researches, this paper discusses in detail the history of Shicha(食差) algorithm from Zhang Zixin(张子信) to Guo Shoujing(郭守敬), especially the history of Shicha algorithm before Xuanming Calendar and divides the history of Shicha algorithm into several stages according to its characters. This paper illustrates the real meanings of Shicha algorithm by Chongtian Calendar and Guantian Calendar and reveals the connection between Shicha(时差) and Shicha(食差 ). It also analyzes the precision of Shicha in Xuanming Calendar, Jiyuan Calendar and Shoushi Calendar and points out the shortcomings of Shicha algorithm in ancient China. This conclusion about the precision of Shicha not only proves that the sign of) and Kecha (M%k) are right but also points out that the Shicha algorithm designed by the ancient Chinese astronomers is an excellent one.(5) Based on previous researches, this paper analyzes the parallax precision and algorithm of the table in Huihui Calendar. The analysis shows that the construction of the table of parallax algorithm in Huihui Calendar is consistent with the theoretical model established in the thesis which is useful to evaluate the parallax algorithm in Huihui Calendar.