Medieval Eclipse Prediction: A Parallel Bias in Indian and Chinese Astronomy
By Jayant Shah
Gaõita Bharata, Vol. 37:1-2 (2015)
Abstract: Since lunar and solar parallax play a crucial role in predicting solar eclipses, the focus of this paper is on the computation of parallax. A brief history of parallax computation in India and China is traced. Predictions of solar eclipses based on Nilakaõcha’s Tantrasaôgraha are statistically analyzed. They turn out to be remarkably accurate, but there is a pronounced bias towards predicting false positives rather than false negatives. The false positives occur more to the south of the ecliptic at northerly terrestrial latitudes and more to the north of the ecliptic at southerly latitudes.
A very similar bias is found in Chinese astronomy providing another hint at possible links between Indian and Chinese astronomy. The Chinese have traditionally used different values for the eclipse limit north and south of the ecliptic, perhaps to compensate for the southward bias.
Introduction: David Mumford has formulated a statistical framework for testing the accuracy of ancient eclipse predictions. I have adapted his framework and computer code to test the accuracy of eclipse predictions based on Nilakaõcha’s eclipse theory. Mumford’s formulation tests the accuracy of solar eclipse prediction for randomly chosen mean conjunctions. It involves determination of the time when the true conjunction will be observed at a given location and the distance between the centers of the sun and the moon at that time.