《苏利亚历》中的视差算法

Parallax Theory in The Surya Siddhanta

古代印度的天文学家很早就认识到视差现象,并开始设计相应的算法来消除视差对日食的影响。《苏利亚历》是古代印度天文学的一部经典,它的视差算法代表了古代印度视差算法的主流。在前人的研究基础上,通过对原始文献的系统解读,廓清了《苏利亚历》中视差算法的造术方法,证明《苏利亚历》中视差算法与理论算法完全等价,并成功地将《苏利亚历》中的视差算法化为一个以太阳的黄经和时角为自变量的二元函数。《苏利亚历》中视差算法的模型与理论算法虽然完全等价,但是按照《苏利亚历》中视差算法所得结果与理论结果之间有一定的误差。讨论了这种误差的大小,并分析造成这种误差的原因。

Astronomers in ancient India found parallax phenomena and designed a relevant algorithm to eliminate their effect on solar eclipse. The Surya Siddhanta is a classical work in the history of ancient Indian astronomy. Parallax algorithm in The Surya Siddhanta is the most representative algorithm among the ancient Indian works on mathematical astronomy. So it is very important to expurgate the parallax algorithm in The Surya Siddhanta. Based on previous studies, this paper expurgates the construction of parallax algorithm in The Surya Siddhanta, verifies that the parallax algorithm in The Surya Siddhanta is the same as the theoretic algorithm, and simplifies successively the parallax algorithm in The Surya Siddhanta to a function which includes two independent variables. Although the model of the parallax algorithm in The Surya Siddhanta is equivalent to the theoretic algorithm,there is an error between the results in The Surya Siddhanta and the theoretic results. The paper also discusses the error and analyzes the reason for it .