Ideas of Physical Forces and Differential Calculus in Ancient India

TL;DR

This paper explores the early development of ideas related to physical forces and differential calculus in ancient India, highlighting their historical significance and parallels with later European scientific concepts.

Contribution

It uncovers and analyzes the ancient Indian origins of concepts like natural forces and differential calculus, predating European developments by centuries.

Findings

Naisargika Bala proportional to planetary size and inverse to distance

Development of differential calculus concepts in India by 6th century AD

Ancient Indian contributions to planetary dynamics and physics

Abstract

We have studied the context and development of the ideas of physical forces and differential calculus in ancient India by studying relevant literature related to both astrology and astronomy since pre-Greek periods. The concept of Naisargika Bala (natural force) discussed in Hora texts from India is defined to be proportional to planetary size and inversely related to planetary distance. This idea developed several centuries prior to Isaac Newton resembles fundamental physical forces in nature especially gravity. We show that the studies on retrograde motion and Chesta Bala of planets like Mars in the context of astrology lead to development of differential calculus and planetary dynamics in ancient India. The idea of instantaneous velocity was first developed during the 1st millennium BC and Indians could solve first order differential equations as early as 6th cent AD. Indian contributions to astrophysics and calculus during European dark ages can be considered as a land mark in the pre-renaissance history of physical sciences. Key words: physical forces, differential calculus, history of science, planetary dynamics, ancient India