Astronomical Calculations in Ancient India by Bhāskara II: A Mathematical and Historical Analysis

In the 12th century, the Indian polymath Bhāskara II integrated mathematical rigor with astronomical observation to create models of unprecedented precision. This paper provides a hybrid mathematical and historical analysis of his celestial calculations, emphasizing their applicability to modern problems in computational astronomy and archaeoastronomy. By examining his sine-table interpolation methods, his revolutionary chakravala cyclic algorithm, and his foundational work on zero and infinity, we demonstrate that Bhāskara II was not merely a preserver of ancient knowledge but a creator of functional, computationally implementable systems. His models for planetary mean motion and spherical geometry are assessed against modern reconstructions, revealing an accuracy that is often within 1% of contemporary values. We argue that Bhāskara II’s work represents a high-water mark in pre-modern applied mathematics, with frameworks that remain directly translatable into modern programming code for astronomical simulation.